Properties

Label 784.4.x
Level $784$
Weight $4$
Character orbit 784.x
Rep. character $\chi_{784}(165,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $944$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 784.x (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(784, [\chi])\).

Total New Old
Modular forms 1376 976 400
Cusp forms 1312 944 368
Eisenstein series 64 32 32

Trace form

\( 944q + 2q^{2} + 2q^{3} + 22q^{4} + 2q^{5} + 8q^{6} - 100q^{8} + O(q^{10}) \) \( 944q + 2q^{2} + 2q^{3} + 22q^{4} + 2q^{5} + 8q^{6} - 100q^{8} + 8q^{10} + 42q^{11} + 2q^{12} + 8q^{13} - 32q^{15} + 302q^{16} + 4q^{17} + 48q^{18} + 2q^{19} - 72q^{20} - 48q^{22} - 498q^{24} + 2q^{26} + 116q^{27} + 784q^{29} + 1178q^{30} + 748q^{31} - 488q^{32} + 4q^{33} - 312q^{34} - 640q^{36} - 14q^{37} - 218q^{38} + 494q^{40} + 1600q^{43} - 1884q^{44} + 556q^{45} - 412q^{46} - 1876q^{47} + 984q^{48} - 12q^{50} + 918q^{51} + 1604q^{52} - 750q^{53} + 1274q^{54} + 3916q^{58} - 686q^{59} + 5998q^{60} + 2q^{61} + 1748q^{62} + 124q^{64} + 4q^{65} - 2498q^{66} + 1118q^{67} - 1264q^{68} + 116q^{69} - 1938q^{72} - 6032q^{74} + 360q^{75} - 3052q^{76} + 2052q^{78} + 4q^{79} - 108q^{80} + 33052q^{81} + 1726q^{82} - 2432q^{83} - 516q^{85} + 8358q^{86} + 3868q^{88} + 9332q^{90} - 7348q^{92} + 218q^{93} + 150q^{94} - 3860q^{95} - 4032q^{96} + 16q^{97} - 808q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(784, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(784, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(784, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)