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Properties

Label 3283.2.bg
Level $3283$
Weight $2$
Character orbit 3283.bg
Rep. character $\chi_{3283}(361,\cdot)$
Character field $\Q(\zeta_{33})$
Dimension $4460$
Sturm bound $634$

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Defining parameters

Level: \( N \) \(=\) \( 3283 = 7^{2} \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3283.bg (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 6500 4620 1880
Cusp forms 6180 4460 1720
Eisenstein series 320 160 160

Trace form

\( 4460 q + q^{2} + 12 q^{3} - 439 q^{4} + 13 q^{5} + 46 q^{6} - 73 q^{8} + 227 q^{9} + O(q^{10}) \) \( 4460 q + q^{2} + 12 q^{3} - 439 q^{4} + 13 q^{5} + 46 q^{6} - 73 q^{8} + 227 q^{9} + 35 q^{10} + 17 q^{11} + 10 q^{12} + 52 q^{13} - 60 q^{15} - 479 q^{16} + 14 q^{17} + 43 q^{18} + 15 q^{19} + 48 q^{20} - 166 q^{22} + 17 q^{23} - 117 q^{24} + 218 q^{25} + 8 q^{26} + 24 q^{27} - 44 q^{29} + 2 q^{30} - 37 q^{31} + 5 q^{32} + 6 q^{33} + 54 q^{34} + 23 q^{36} + 22 q^{37} + 238 q^{38} + 54 q^{39} - 35 q^{40} + 92 q^{41} - 74 q^{43} + 117 q^{44} + 49 q^{45} - 17 q^{46} - 46 q^{47} + 29 q^{48} - 21 q^{50} + 9 q^{51} - 105 q^{52} + 25 q^{53} + q^{54} + 42 q^{55} - 183 q^{57} - 61 q^{58} - 33 q^{59} - 341 q^{60} - 105 q^{61} + 64 q^{62} - 153 q^{64} - 87 q^{65} - 160 q^{66} + 19 q^{67} - 90 q^{68} + 98 q^{69} + 90 q^{71} + 268 q^{72} - 235 q^{73} - 169 q^{74} + 122 q^{75} + 122 q^{76} + 92 q^{78} - 24 q^{79} - 52 q^{80} + 130 q^{81} - 35 q^{82} + 20 q^{83} - 77 q^{85} - 175 q^{86} + 236 q^{87} + 191 q^{88} - 13 q^{89} + 307 q^{90} - 222 q^{92} - 52 q^{93} - 17 q^{94} + 42 q^{95} - 400 q^{96} - 85 q^{97} - 68 q^{99} + O(q^{100}) \)

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

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