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Properties

Label 656.6.t
Level $656$
Weight $6$
Character orbit 656.t
Rep. character $\chi_{656}(237,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $836$
Sturm bound $504$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 844 844 0
Cusp forms 836 836 0
Eisenstein series 8 8 0

Trace form

\( 836 q - 4 q^{3} - 4 q^{4} + 48 q^{6} + 852 q^{8} + 67068 q^{9} + O(q^{10}) \) \( 836 q - 4 q^{3} - 4 q^{4} + 48 q^{6} + 852 q^{8} + 67068 q^{9} - 4 q^{10} - 482 q^{12} - 4 q^{13} + 1308 q^{14} - 4 q^{15} - 4 q^{16} - 4 q^{17} - 132 q^{18} - 972 q^{21} + 2298 q^{22} - 596 q^{24} - 542 q^{26} - 8440 q^{27} + 14674 q^{28} - 4 q^{29} + 10914 q^{30} - 23072 q^{31} - 20420 q^{34} + 46588 q^{36} - 4 q^{37} + 5896 q^{38} - 50616 q^{39} - 4 q^{40} - 28444 q^{42} + 1312 q^{43} - 19264 q^{44} - 12504 q^{45} - 4 q^{47} - 8334 q^{48} - 123560 q^{50} - 4 q^{51} - 61494 q^{52} + 88738 q^{54} + 12500 q^{55} + 159420 q^{56} + 19742 q^{58} - 30508 q^{59} + 29014 q^{60} + 85488 q^{62} - 67232 q^{63} + 243044 q^{64} - 27692 q^{65} + 198564 q^{66} + 42496 q^{68} + 210934 q^{70} - 63172 q^{72} - 20144 q^{73} + 332920 q^{74} + 208890 q^{76} + 67228 q^{77} - 97548 q^{78} - 4 q^{79} + 32800 q^{80} + 5275036 q^{81} - 109374 q^{82} - 4 q^{83} + 79976 q^{84} - 4 q^{86} + 361368 q^{87} + 463718 q^{88} - 70232 q^{89} - 596128 q^{90} - 67228 q^{91} - 242892 q^{92} - 363328 q^{93} + 590054 q^{94} - 38428 q^{95} + 57708 q^{96} - 4 q^{97} + 322712 q^{98} + O(q^{100}) \)

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.