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.

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.

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.

For each of the five Euclidean fields we also 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. We also have dimension 2 newforms over $\mathbb{Q}(\sqrt{-1})$ for levels of norm up to $5000$. For each of these newforms the database contains several Hecke eigenvalues.

Browse Bianchi modular forms

Browse newform spaces by base field:

Find a specific form or space by label

e.g. 2.0.4.1-65.2-a (single form) or 2.0.4.1-65.2 (space of forms at a level)

Examples of base change forms

• base-change of a newform with rational coefficients: 2.0.4.1-100.2-a (with an associated elliptic curve which is a base-change)
• base-change of a newform with coefficients in $\mathbb{Q}(\sqrt{2})$: 2.0.4.1-16384.1-d (with an associated elliptic curve which is not a base-change)
• base-change of a newform with coefficients in $\mathbb{Q}(\sqrt{6})$: 2.0.3.1-6561.1-b (with no associated elliptic curve)
• base-change of a newform with coefficients in $\mathbb{Q}(\sqrt{5})$, with CM by $\mathbb{Q}(\sqrt{-35})$: 2.0.7.1-10000.1-b (with no associated elliptic curve)

A random Bianchi modular form from the database

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 base field either a field label, e.g. 2.0.4.1 for $\mathbb{Q}(\sqrt{-1})$, or a nickname, e.g. Qsqrt-1 level norm e.g. 1 or 1-100 dimension e.g. 1 or 2 sign any +1 -1 base change forms exclude include CM include exclude only Maximum number