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Properties

Label 784.4.m
Level $784$
Weight $4$
Character orbit 784.m
Rep. character $\chi_{784}(197,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $482$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 784.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 688 502 186
Cusp forms 656 482 174
Eisenstein series 32 20 12

Trace form

\( 482 q + 2 q^{2} + 2 q^{3} - 8 q^{4} + 2 q^{5} - 28 q^{6} + 32 q^{8} + O(q^{10}) \) \( 482 q + 2 q^{2} + 2 q^{3} - 8 q^{4} + 2 q^{5} - 28 q^{6} + 32 q^{8} - 52 q^{10} - 18 q^{11} + 104 q^{12} + 2 q^{13} - 140 q^{15} - 16 q^{16} + 4 q^{17} - 78 q^{18} - 22 q^{19} - 112 q^{20} + 144 q^{22} - 344 q^{24} - 260 q^{26} + 80 q^{27} + 190 q^{29} + 112 q^{30} - 368 q^{31} - 8 q^{32} + 4 q^{33} + 760 q^{34} - 1300 q^{36} + 10 q^{37} - 1008 q^{38} + 516 q^{40} - 38 q^{43} - 1400 q^{44} - 194 q^{45} + 500 q^{46} + 944 q^{47} + 676 q^{48} + 2814 q^{50} - 312 q^{51} + 2972 q^{52} + 378 q^{53} + 512 q^{54} + 1180 q^{58} + 334 q^{59} - 2860 q^{60} + 914 q^{61} - 412 q^{62} - 1064 q^{64} - 484 q^{65} - 5328 q^{66} - 1942 q^{67} - 2640 q^{68} + 476 q^{69} - 36 q^{72} + 2352 q^{74} - 2558 q^{75} + 1836 q^{76} - 3280 q^{78} - 4408 q^{79} + 1228 q^{80} - 32558 q^{81} + 2748 q^{82} - 118 q^{83} + 480 q^{85} - 9460 q^{86} - 2796 q^{88} - 4832 q^{90} + 732 q^{92} - 2404 q^{93} + 3628 q^{94} - 820 q^{95} - 2344 q^{96} + 4 q^{97} + 342 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(784, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)