Properties

Label 912.3.t
Level $912$
Weight $3$
Character orbit 912.t
Rep. character $\chi_{912}(37,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $320$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 912.t (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 304 \)
Character field: \(\Q(i)\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(912, [\chi])\).

Total New Old
Modular forms 648 320 328
Cusp forms 632 320 312
Eisenstein series 16 0 16

Trace form

\( 320q + O(q^{10}) \) \( 320q + 56q^{16} - 32q^{19} - 72q^{24} - 200q^{26} + 120q^{28} - 192q^{35} + 24q^{36} + 112q^{38} + 280q^{44} - 2240q^{49} + 72q^{54} - 168q^{58} + 64q^{61} - 24q^{62} - 312q^{64} + 144q^{66} + 1016q^{68} - 520q^{74} - 384q^{76} - 328q^{80} - 2880q^{81} - 40q^{82} - 320q^{83} - 320q^{85} + 264q^{92} - 768q^{95} - 360q^{96} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(912, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(912, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(912, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 2}\)