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Properties

Label 3283.2.bi
Level $3283$
Weight $2$
Character orbit 3283.bi
Rep. character $\chi_{3283}(226,\cdot)$
Character field $\Q(\zeta_{33})$
Dimension $4440$
Sturm bound $634$

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Defining parameters

Level: \( N \) \(=\) \( 3283 = 7^{2} \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3283.bi (of order \(33\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 469 \)
Character field: \(\Q(\zeta_{33})\)
Sturm bound: \(634\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3283, [\chi])\).

Total New Old
Modular forms 6520 4600 1920
Cusp forms 6200 4440 1760
Eisenstein series 320 160 160

Trace form

\( 4440 q + 13 q^{2} + 11 q^{3} + 229 q^{4} + 13 q^{5} + 52 q^{6} - 142 q^{8} + 217 q^{9} + O(q^{10}) \) \( 4440 q + 13 q^{2} + 11 q^{3} + 229 q^{4} + 13 q^{5} + 52 q^{6} - 142 q^{8} + 217 q^{9} + 44 q^{10} + 17 q^{11} + 21 q^{12} + 44 q^{13} - 60 q^{15} + 237 q^{16} + 5 q^{17} + 7 q^{18} + 7 q^{19} + 12 q^{20} + 140 q^{22} + 17 q^{23} + 45 q^{24} + 211 q^{25} + 5 q^{26} + 32 q^{27} - 152 q^{29} + 2 q^{30} + 15 q^{31} + 41 q^{32} + 21 q^{33} + 12 q^{34} - 296 q^{36} + 2 q^{37} - 110 q^{38} + 31 q^{39} + 31 q^{40} - 58 q^{41} + 44 q^{43} + 21 q^{44} + 7 q^{45} - 65 q^{46} - 73 q^{47} + 40 q^{48} - 186 q^{50} + 9 q^{51} + 99 q^{52} + 25 q^{53} - 11 q^{54} + 84 q^{55} - 366 q^{57} + 11 q^{58} - 39 q^{59} + 103 q^{60} + 79 q^{61} + 52 q^{62} - 262 q^{64} - 105 q^{65} - 166 q^{66} + 15 q^{67} + 240 q^{68} + 20 q^{69} - 449 q^{72} - 16 q^{73} + 95 q^{74} + 109 q^{75} + 84 q^{76} + 224 q^{78} + 237 q^{79} - 67 q^{80} + 57 q^{81} + 49 q^{82} + 32 q^{83} - 44 q^{85} - 217 q^{86} - 16 q^{87} + 107 q^{88} - 31 q^{89} - 452 q^{90} + 228 q^{92} - 135 q^{93} + 7 q^{94} - 51 q^{95} - 430 q^{96} + 228 q^{97} - 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3283, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3283, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3283, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(469, [\chi])\)\(^{\oplus 2}\)