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Properties

Label 656.6.v
Level $656$
Weight $6$
Character orbit 656.v
Rep. character $\chi_{656}(331,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $1672$
Sturm bound $504$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 1688 1688 0
Cusp forms 1672 1672 0
Eisenstein series 16 16 0

Trace form

\( 1672 q - 4 q^{2} - 4 q^{3} - 360 q^{6} - 8 q^{7} - 4 q^{8} + O(q^{10}) \) \( 1672 q - 4 q^{2} - 4 q^{3} - 360 q^{6} - 8 q^{7} - 4 q^{8} - 8 q^{10} - 4 q^{11} - 3160 q^{12} - 4 q^{13} - 4 q^{14} + 1944 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 4 q^{19} + 2424 q^{20} - 9932 q^{22} + 968 q^{24} - 1025000 q^{25} + 23132 q^{26} + 8432 q^{27} + 10584 q^{28} - 4 q^{29} + 9760 q^{30} + 24656 q^{32} - 8 q^{33} + 40960 q^{34} + 17272 q^{35} - 38528 q^{36} - 8 q^{37} + 50308 q^{38} - 8 q^{39} + 25000 q^{40} - 8 q^{42} + 42616 q^{44} + 25000 q^{45} + 28484 q^{46} + 130512 q^{47} + 172384 q^{48} - 8 q^{49} + 12368 q^{50} - 8 q^{51} + 128504 q^{52} - 4 q^{53} + 154404 q^{54} - 8 q^{55} - 195116 q^{56} + 52736 q^{58} - 61016 q^{59} + 42628 q^{60} + 239112 q^{62} + 1944 q^{63} - 8 q^{65} - 89260 q^{67} - 53276 q^{68} + 968 q^{69} + 90596 q^{70} - 8 q^{71} - 398520 q^{72} - 194940 q^{74} - 181724 q^{75} + 351564 q^{76} + 194824 q^{78} + 12204 q^{80} - 159388 q^{82} - 8 q^{83} - 395980 q^{84} + 12496 q^{85} + 256 q^{86} - 8 q^{87} + 30124 q^{88} - 140464 q^{89} + 681360 q^{90} + 400216 q^{91} + 502152 q^{92} - 363328 q^{93} + 634844 q^{94} + 25000 q^{95} - 199336 q^{96} - 8 q^{97} + 645168 q^{98} - 237172 q^{99} + O(q^{100}) \)

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.