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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

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 $\Gamma_0(\mathfrak{n})\cap \SL_2(\mathcal{O}_K)$.

Over each of the five Euclidean fields we have the complete set of Bianchi newforms of dimension \(1\) (that is, with rational coefficients) for levels of norm up to a bound depending on the field, currently 100000, 50000, 150000, 50000, 50000 respectively.

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 primes $\mathfrak{p}$ of norm less than $50$. For the newforms of dimension 2 it contains the first 15 $a_{\mathfrak{p}}$, 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 $\mathbb{Q}(\sqrt{-d})$ for $d=2,11,19,43,67,163$ are included. $\SL_2$ dimension data for the remaining imaginary quadratic fields of class number $1$ ($d=1,3,7$) is in preparation.

Over the five Euclidean imaginary quadratic fields $\mathbb{Q}(\sqrt{-d})$ (for $d=1,2,3,7,11$), 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 all nine class number one fields (the Euclidean fields and also $\mathbb{Q}(\sqrt{-d})$ for $d=19, 43, 67, 163$), 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: beta
  • Last edited by John Cremona on 2019-05-21 04:55:32
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