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Properties

Label 784.4.bh
Level $784$
Weight $4$
Character orbit 784.bh
Rep. character $\chi_{784}(29,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $4008$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 784.bh (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 784 \)
Character field: \(\Q(\zeta_{28})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 4056 4056 0
Cusp forms 4008 4008 0
Eisenstein series 48 48 0

Trace form

\( 4008 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 10 q^{6} + 74 q^{8} + O(q^{10}) \) \( 4008 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 10 q^{6} + 74 q^{8} + 2 q^{10} - 10 q^{11} - 10 q^{12} - 10 q^{13} - 132 q^{14} - 20 q^{15} - 10 q^{16} - 20 q^{17} - 196 q^{18} - 24 q^{19} + 70 q^{20} - 66 q^{21} + 494 q^{22} + 490 q^{24} - 10 q^{26} - 118 q^{27} - 546 q^{28} - 10 q^{29} + 8 q^{30} + 4416 q^{31} - 990 q^{32} - 20 q^{33} - 698 q^{34} - 490 q^{35} - 266 q^{36} - 10 q^{37} + 210 q^{38} + 830 q^{40} + 666 q^{42} - 10 q^{43} + 1530 q^{44} - 402 q^{45} - 742 q^{46} + 1860 q^{47} - 1120 q^{48} - 24 q^{49} + 1372 q^{50} + 1498 q^{51} + 3194 q^{52} - 10 q^{53} + 1874 q^{54} - 2928 q^{56} + 3378 q^{58} - 1386 q^{59} - 4654 q^{60} - 10 q^{61} - 458 q^{62} - 1396 q^{63} - 1102 q^{64} - 20 q^{65} + 2786 q^{66} - 1872 q^{67} - 1788 q^{68} - 118 q^{69} + 330 q^{70} - 2058 q^{72} - 2166 q^{74} + 382 q^{75} - 7660 q^{76} - 698 q^{77} - 2366 q^{78} - 48 q^{79} - 13708 q^{80} + 51496 q^{81} - 8742 q^{82} + 2430 q^{83} + 11116 q^{84} + 490 q^{85} - 2068 q^{86} + 760 q^{88} - 6742 q^{90} + 9254 q^{91} + 3444 q^{92} - 280 q^{93} - 698 q^{94} - 7748 q^{95} + 12840 q^{96} - 48 q^{97} - 10688 q^{98} - 2832 q^{99} + O(q^{100}) \)

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.