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Properties

Label 656.6.bq
Level $656$
Weight $6$
Character orbit 656.bq
Rep. character $\chi_{656}(37,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $3344$
Sturm bound $504$

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Defining parameters

Level: \( N \) \(=\) \( 656 = 2^{4} \cdot 41 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 656.bq (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 656 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(504\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(656, [\chi])\).

Total New Old
Modular forms 3376 3376 0
Cusp forms 3344 3344 0
Eisenstein series 32 32 0

Trace form

\( 3344 q - 6 q^{2} - 16 q^{3} - 6 q^{4} - 6 q^{5} - 234 q^{6} - 498 q^{8} + O(q^{10}) \) \( 3344 q - 6 q^{2} - 16 q^{3} - 6 q^{4} - 6 q^{5} - 234 q^{6} - 498 q^{8} - 1608 q^{10} - 6 q^{11} - 18 q^{12} - 6 q^{13} - 144 q^{14} - 12 q^{15} - 6 q^{16} - 12 q^{17} + 186 q^{18} - 6 q^{19} - 6 q^{20} + 1452 q^{21} - 15646 q^{22} - 6 q^{24} - 6 q^{26} - 3592 q^{27} + 9212 q^{28} - 6 q^{29} + 29826 q^{30} + 23052 q^{31} + 18564 q^{32} - 12 q^{33} + 6502 q^{34} - 5342 q^{35} + 9406 q^{36} - 6 q^{37} - 34836 q^{38} - 59256 q^{40} - 90000 q^{42} - 1318 q^{43} - 16 q^{44} + 17286 q^{45} - 75164 q^{46} - 12 q^{47} + 94034 q^{48} + 1949600 q^{49} + 68388 q^{50} - 1464 q^{51} - 115166 q^{52} - 6 q^{53} - 107630 q^{54} - 306806 q^{56} - 33124 q^{58} + 30498 q^{59} - 192850 q^{60} - 6 q^{61} + 239366 q^{62} + 201672 q^{63} - 300108 q^{64} + 83052 q^{65} - 170098 q^{66} + 89250 q^{67} - 95624 q^{68} + 1452 q^{69} + 354956 q^{70} + 368024 q^{72} - 5794 q^{74} - 179296 q^{75} + 184844 q^{76} - 67234 q^{77} + 361030 q^{78} - 32 q^{79} + 7262 q^{80} - 21100208 q^{81} - 365894 q^{82} - 16 q^{83} - 209186 q^{84} + 12484 q^{85} - 92786 q^{86} + 176504 q^{88} + 937488 q^{90} + 132868 q^{91} - 1065532 q^{92} - 363816 q^{93} - 933994 q^{94} - 76860 q^{95} + 1095464 q^{96} - 12 q^{97} - 435030 q^{98} + 352830 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(656, [\chi])\) into newform subspaces

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