The database contains information about Bianchi modular forms over all imaginary quadratic number fields of absolute discrimant up to \(700\), for a range of levels which depends on the field.
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 \(212\) imaginary quadratic fields, which are all those of absolute discriminant less than \(700\) and include all of class number \(1\) and \(2\), 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 discriminant | 3 | 4 | 7, 8, 11 | 19, 43 | 67 | 163 | 23 | 31 | 15, 20, 24, 35--120 | 121--700 | Level norm bound | 150000 | 100000 | 50000 | 15000 | 10000 | 5000 | 3000 | 5000 | 1000 | 100 |
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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 few primes $\mathfrak{p}$ by 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.