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Properties

Label 656.6.bb
Level $656$
Weight $6$
Character orbit 656.bb
Rep. character $\chi_{656}(3,\cdot)$
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.bb (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

\( 1672 q - 4 q^{2} - 4 q^{3} - 8 q^{5} - 104 q^{6} - 8 q^{7} - 4 q^{8} + O(q^{10}) \) \( 1672 q - 4 q^{2} - 4 q^{3} - 8 q^{5} - 104 q^{6} - 8 q^{7} - 4 q^{8} - 8 q^{10} - 4 q^{11} - 3160 q^{12} - 4 q^{13} - 4 q^{14} - 1944 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 4 q^{19} - 2432 q^{20} - 8 q^{21} - 10188 q^{22} - 976 q^{24} + 1025000 q^{25} - 23140 q^{26} - 8440 q^{27} - 2400 q^{28} - 4 q^{29} - 15240 q^{30} - 24664 q^{32} - 8 q^{33} - 28208 q^{34} - 7728 q^{35} - 38528 q^{36} - 8 q^{37} + 19324 q^{38} - 8 q^{39} - 25000 q^{40} - 8 q^{42} - 8 q^{43} - 42624 q^{44} - 25000 q^{45} - 28236 q^{46} - 130512 q^{47} + 15688 q^{48} - 8 q^{49} - 12632 q^{50} - 8 q^{51} - 55024 q^{52} - 4 q^{53} + 154148 q^{54} - 8 q^{55} - 284036 q^{56} + 52480 q^{58} - 61016 q^{59} - 333948 q^{60} - 8 q^{61} + 239112 q^{62} - 1944 q^{63} - 8 q^{65} - 89260 q^{67} + 113100 q^{68} + 968 q^{69} + 337860 q^{70} - 8 q^{71} + 398520 q^{72} + 285684 q^{74} - 206724 q^{75} - 435692 q^{76} - 8 q^{77} + 194824 q^{78} - 12796 q^{80} + 159380 q^{82} - 8 q^{83} - 1056492 q^{84} - 12504 q^{85} - 256 q^{86} - 8 q^{87} + 122444 q^{88} + 140464 q^{89} - 208976 q^{90} + 502152 q^{92} + 361376 q^{93} - 387076 q^{94} - 25000 q^{95} - 197392 q^{96} - 8 q^{97} + 645168 q^{98} + 237164 q^{99} + O(q^{100}) \)

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.