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The database contains information about Bianchi modular forms over several imaginary quadratic fields including all nine fields of class number $1$, for a range of levels.

### 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 the nine imaginary quadratic fields of class number one and the first two fields of class number $3$, we have a complete set of Bianchi newforms of dimension 1 (that is, with rational coefficients) for levels of norm up to a bound that depends on the field:

 Discriminant Bound -3 -4 -7 -8 -11 -19 -43 -67 -163 -23 -31 150000 100000 50000 50000 50000 15000 15000 10000 5000 2000 5000

Over $\mathbb{Q}(\sqrt{-1})$ only, for levels of norm up to 5000, we also have all newforms of dimension 2.

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 included. $\SL_2$-dimension data for the three remaining imaginary quadratic fields of class number one (discriminants -3, -4, -7) is in preparation.

Over each of the imaginary quadratic fields with class number one and the first two fields of class number $3$, we have the dimensions of the full cuspidal space and the new subspace at each $\GL_2$-level, for weight 2 forms of level norm up to a bound depending on the field (listed above). Over these fields, and also over $\mathbb{Q}(\sqrt{-5})$, we have the cuspidal and new dimensions for a range of $\SL_2$-levels, and for a range of weights.

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• Review status: reviewed
• Last edited by John Cremona on 2021-10-15 09:53:33
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