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Properties

Label 656.6.bl
Level $656$
Weight $6$
Character orbit 656.bl
Rep. character $\chi_{656}(197,\cdot)$
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.bl (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

\( 3344 q - 10 q^{2} - 6 q^{4} - 10 q^{5} + 134 q^{6} - 1288 q^{8} - 268272 q^{9} + O(q^{10}) \) \( 3344 q - 10 q^{2} - 6 q^{4} - 10 q^{5} + 134 q^{6} - 1288 q^{8} - 268272 q^{9} - 6 q^{10} - 6 q^{11} + 1930 q^{12} - 10 q^{13} + 1430 q^{14} - 16 q^{15} - 6 q^{16} - 16 q^{17} + 2232 q^{18} - 6 q^{19} - 10 q^{20} + 1448 q^{21} - 2180 q^{22} + 1828 q^{24} - 548 q^{26} - 2742 q^{28} - 10 q^{29} - 21966 q^{30} + 23052 q^{31} - 20 q^{33} + 72286 q^{34} + 19658 q^{35} - 80132 q^{36} - 6 q^{37} + 10120 q^{38} - 45756 q^{39} - 16 q^{40} + 28424 q^{42} + 1302 q^{43} - 19270 q^{44} - 16326 q^{45} - 10 q^{46} - 16 q^{47} + 88130 q^{48} - 20 q^{49} - 123560 q^{50} + 2424 q^{51} + 234072 q^{52} - 6 q^{53} - 109454 q^{54} + 12500 q^{55} - 12930 q^{56} + 4860 q^{57} - 19880 q^{58} + 30498 q^{59} + 161694 q^{60} - 10 q^{61} + 72808 q^{62} - 268928 q^{63} + 165876 q^{64} - 110768 q^{65} + 712256 q^{66} + 89250 q^{67} + 4280 q^{68} + 1452 q^{69} - 106510 q^{70} + 255502 q^{72} - 20144 q^{73} + 332910 q^{74} - 204296 q^{75} - 404686 q^{76} + 67218 q^{77} + 99968 q^{78} - 16 q^{79} - 583310 q^{80} + 21100144 q^{81} - 61292 q^{82} - 16 q^{83} + 666676 q^{84} - 12516 q^{85} - 6 q^{86} + 366228 q^{87} + 73812 q^{88} - 70232 q^{89} - 1184198 q^{90} - 67228 q^{91} - 374578 q^{92} + 2420 q^{93} + 866492 q^{94} + 38408 q^{95} + 55632 q^{96} - 16 q^{97} - 322722 q^{98} - 352842 q^{99} + O(q^{100}) \)

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.