Learn more

The database contains information about Bianchi modular forms over several imaginary quadratic number fields, including all fields of absolute discrimant up to \(100\), and all fields of class number $1$, for a range of levels including all levels of norm up to \(1000\).

Newform data

Bianchi Newform data is available for levels of the form $\Gamma_0(\mathfrak{n})\le \GL_2(\mathcal{O}_K)$ and not for the larger spaces forms of level $\Gamma_0(\mathfrak{n})\cap \SL_2(\mathcal{O}_K)$.

For \(32\) imaginary quadratic fields, including all those of absolute discriminant less than \(100\) or class number \(1\), the database contains all Bianchi newforms of weight \(2\), trivial character, and dimension \(1\) for levels of norm up to a bound that depends on the field:

Absolute discriminant347, 8, 1119, 43671632331 15, 20, 24, 35, 39, 40, 47, 51, 52, 55, 56, 59, 68, 71, 79, 83, 84, 87, 88, 91, 95
Level norm bound1500001000005000015000100005000300050001000

For each of the newforms of dimension 1, the database contains all Atkin-Lehner eigenvalues and Hecke eigenvalues $a_{\mathfrak{p}}$ for at least the first 100 primes $\mathfrak{p}$ of smallest norm. For the newforms of dimension 2 it contains the first fifteen $a_{\mathfrak{p}}$, but no Atkin-Lehner eigenvalues.

Dimension data

Dimension data for full cuspidal and new spaces for a range of weights and $\SL_2$-levels over the imaginary quadratic fields of discriminant -8, -11, -19, -43, -67, -163 are available.

Over each of the imaginary quadratic fields and levels in the table above, we have the dimensions of the full cuspidal space and the new subspace at each $\GL_2$-level, for weight \(2\) forms with trivial character. Over some of these fields we also have the cuspidal and new dimensions for a range of $\SL_2$-levels, and for a range of weights.