↑

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 $448$

Related objects

Downloads

Learn more

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

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

Display 100 coefficients 10 coefficients

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

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