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Properties

Label 656.6.bp
Level $656$
Weight $6$
Character orbit 656.bp
Rep. character $\chi_{656}(45,\cdot)$
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.bp (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

\( 3344 q - 6 q^{2} - 6 q^{4} - 6 q^{5} - 10 q^{6} + 486 q^{8} + O(q^{10}) \) \( 3344 q - 6 q^{2} - 6 q^{4} - 6 q^{5} - 10 q^{6} + 486 q^{8} + 1596 q^{10} - 10 q^{11} - 10 q^{12} - 10 q^{13} - 20 q^{15} - 6 q^{16} - 20 q^{17} + 186 q^{18} - 10 q^{19} - 6 q^{20} - 1464 q^{21} - 10 q^{22} - 10 q^{24} - 10 q^{26} - 5460 q^{28} - 10 q^{29} - 10 q^{30} + 23052 q^{31} - 18596 q^{32} - 12 q^{33} - 10 q^{34} - 11950 q^{35} + 71726 q^{36} - 6 q^{37} + 59224 q^{40} + 33088 q^{42} + 1306 q^{43} + 20202 q^{45} + 74896 q^{46} - 20 q^{47} - 10 q^{48} - 1949624 q^{49} - 68676 q^{50} + 1452 q^{51} - 10 q^{52} - 10 q^{53} + 77750 q^{54} - 10 q^{56} - 32500 q^{58} + 30498 q^{59} + 353890 q^{60} - 6 q^{61} + 239366 q^{62} + 336120 q^{63} + 262212 q^{64} + 138420 q^{65} - 424978 q^{66} - 10 q^{67} - 2440 q^{69} - 703660 q^{70} + 368024 q^{72} + 193510 q^{74} - 2440 q^{75} + 105140 q^{76} + 67222 q^{77} - 166466 q^{78} - 253130 q^{80} - 21100208 q^{81} + 317790 q^{82} - 16 q^{83} - 74730 q^{84} + 92774 q^{86} - 499600 q^{88} - 228912 q^{90} + 267324 q^{91} + 316376 q^{92} + 2420 q^{93} + 253770 q^{94} - 20 q^{95} - 20 q^{97} - 209902 q^{98} + 592910 q^{99} + O(q^{100}) \)

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.