Properties

Label 912.3.s
Level $912$
Weight $3$
Character orbit 912.s
Rep. character $\chi_{912}(77,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $576$
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.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
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 648 576 72
Cusp forms 632 576 56
Eisenstein series 16 0 16

Trace form

\( 576 q - 12 q^{6} + O(q^{10}) \) \( 576 q - 12 q^{6} + 60 q^{12} - 32 q^{16} + 100 q^{18} - 88 q^{22} + 124 q^{24} + 96 q^{27} - 120 q^{28} + 40 q^{30} - 160 q^{34} - 332 q^{36} - 184 q^{40} - 220 q^{42} + 128 q^{43} + 52 q^{48} - 4032 q^{49} - 160 q^{51} + 472 q^{52} - 56 q^{54} + 1128 q^{58} + 720 q^{60} + 504 q^{64} + 508 q^{66} - 256 q^{67} + 420 q^{72} - 492 q^{78} - 1312 q^{82} - 996 q^{84} - 432 q^{88} - 1336 q^{90} - 192 q^{91} + 96 q^{93} + 744 q^{94} - 272 q^{96} + 128 q^{99} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(912, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)