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Properties

Label 656.6.bu
Level $656$
Weight $6$
Character orbit 656.bu
Rep. character $\chi_{656}(5,\cdot)$
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.bu (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

\( 3344 q - 10 q^{2} - 16 q^{3} - 6 q^{4} - 10 q^{5} - 378 q^{6} + 1268 q^{8} + 268272 q^{9} + O(q^{10}) \) \( 3344 q - 10 q^{2} - 16 q^{3} - 6 q^{4} - 10 q^{5} - 378 q^{6} + 1268 q^{8} + 268272 q^{9} - 6 q^{10} - 10 q^{11} - 1958 q^{12} - 6 q^{13} - 1318 q^{14} - 16 q^{15} - 6 q^{16} - 16 q^{17} - 2628 q^{18} - 10 q^{19} - 10 q^{20} - 1468 q^{21} - 2308 q^{22} - 1844 q^{24} + 532 q^{26} + 3560 q^{27} - 9234 q^{28} - 6 q^{29} - 13354 q^{30} + 23052 q^{31} - 20 q^{33} - 66050 q^{34} - 11950 q^{35} + 59632 q^{36} - 6 q^{37} - 44956 q^{38} + 45756 q^{39} - 16 q^{40} + 28424 q^{42} - 1322 q^{43} + 19254 q^{44} - 21186 q^{45} - 10 q^{46} - 16 q^{47} + 5894 q^{48} - 20 q^{49} + 123560 q^{50} - 2436 q^{51} - 192416 q^{52} - 10 q^{53} - 169258 q^{54} - 12500 q^{55} - 159430 q^{56} - 4860 q^{57} - 19752 q^{58} + 30498 q^{59} - 31454 q^{60} - 10 q^{61} - 72828 q^{62} - 268928 q^{63} - 128004 q^{64} - 110768 q^{65} - 117204 q^{66} - 10 q^{67} - 107056 q^{68} - 2440 q^{69} - 242194 q^{70} + 250642 q^{72} + 20144 q^{73} - 332930 q^{74} - 2440 q^{75} + 451150 q^{76} - 67238 q^{77} + 95108 q^{78} - 16 q^{79} - 648910 q^{80} + 21100144 q^{81} + 109364 q^{82} - 16 q^{83} + 501864 q^{84} - 6 q^{86} - 366228 q^{87} - 396908 q^{88} + 70232 q^{89} + 3198 q^{90} + 67228 q^{91} - 374578 q^{92} + 360888 q^{93} + 61476 q^{94} + 38408 q^{95} + 435752 q^{96} - 16 q^{97} - 322722 q^{98} - 592930 q^{99} + O(q^{100}) \)

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.