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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

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

Display 100 coefficients 10 coefficients

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

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