Imaginary quadratic field data (2013 updates)

Numbers of newforms (rational, cuspidal, weight 2)

These counts are expected to equal the number of isogeny classes of elliptic curves defined over the field $K$ in question with conductor equal to the level of the newform, with two provisos:
  1. Elliptic curves with CM by an order in $K$ will not be counted. These are characterised as those curves having specific $j$-invariants, as listed. (These $j$-invariants my be listed using the Sage command cm_j_invariants_and_orders(QQ))
  2. Newforms which are base-changes of newforms over Q with extra twist may not have associated elliptic curves defined over $K$: see Abelian Varieties with Extra Twist, Cusp Forms, and Elliptic Curves Over Imaginary Quadratic Fields
    Journal of the London Mathematical Society 45 (1992) 402-416

For each field (currently just the five Euclidean fields) we give

  1. basic data about the field, specifically the primes of norm ${}<1000$ in standard order (norm, label, characteristic, degree, ramification degree);
  2. a list giving the number of rational weight 2 newforms at each level in some range;
  3. a list of these newforms $F$ (label, level, sign of functional equation of $L(F,s)$, ratio $L(F,1)/\Omega\in\mathbb{Q}$ showing whether or not $L(F,1)=0$, Atkin-Lehner eigenvalues, first 25 Fourier coefficients $a_{\mathfrak{p}}$ indexed by all prime ideals in standard order).

Plain text index of ancient data