Properties

Label 1620.2.bs
Level $1620$
Weight $2$
Character orbit 1620.bs
Rep. character $\chi_{1620}(77,\cdot)$
Character field $\Q(\zeta_{108})$
Dimension $1944$
Sturm bound $648$

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Defining parameters

Level: \( N \) \(=\) \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1620.bs (of order \(108\) and degree \(36\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 405 \)
Character field: \(\Q(\zeta_{108})\)
Sturm bound: \(648\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1620, [\chi])\).

Total New Old
Modular forms 11880 1944 9936
Cusp forms 11448 1944 9504
Eisenstein series 432 0 432

Trace form

\( 1944 q + O(q^{10}) \) \( 1944 q - 54 q^{35} + 36 q^{41} + 216 q^{51} - 54 q^{67} + 288 q^{77} + 288 q^{87} + 36 q^{93} - 54 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1620, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1620, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1620, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(810, [\chi])\)\(^{\oplus 2}\)