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Properties

Label 912.4.bq
Level $912$
Weight $4$
Character orbit 912.bq
Rep. character $\chi_{912}(277,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $960$
Sturm bound $640$

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Defining parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 912.bq (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 304 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(640\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(912, [\chi])\).

Total New Old
Modular forms 1936 960 976
Cusp forms 1904 960 944
Eisenstein series 32 0 32

Trace form

\( 960 q - 168 q^{8} + O(q^{10}) \) \( 960 q - 168 q^{8} + 72 q^{10} - 240 q^{15} - 132 q^{16} - 24 q^{19} - 456 q^{24} + 40 q^{26} + 760 q^{28} - 2976 q^{31} + 900 q^{32} + 196 q^{34} + 912 q^{35} + 108 q^{36} + 2512 q^{38} + 820 q^{40} - 1064 q^{44} - 1336 q^{46} - 47040 q^{49} + 8552 q^{50} + 744 q^{51} - 432 q^{52} + 108 q^{54} - 3080 q^{56} - 2744 q^{58} + 2448 q^{60} + 1824 q^{61} + 1464 q^{62} - 840 q^{64} + 2736 q^{66} + 3696 q^{67} - 992 q^{68} - 2112 q^{69} - 2160 q^{70} + 3800 q^{74} - 280 q^{76} - 72 q^{78} - 11984 q^{79} - 8176 q^{80} + 38880 q^{81} - 5200 q^{82} - 5360 q^{83} - 240 q^{85} + 2368 q^{86} + 7040 q^{88} + 696 q^{92} + 18304 q^{94} + 7728 q^{95} - 600 q^{96} - 4324 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(912, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(912, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(912, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 2}\)