↑

Properties

Label 3283.2.bh
Level $3283$
Weight $2$
Character orbit 3283.bh
Rep. character $\chi_{3283}(540,\cdot)$
Character field $\Q(\zeta_{33})$
Dimension $4540$
Sturm bound $634$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3283 = 7^{2} \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3283.bh (of order \(33\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 67 \)
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 4740 1780
Cusp forms 6200 4540 1660
Eisenstein series 320 200 120

Trace form

\( 4540 q + 22 q^{2} + 18 q^{3} + 244 q^{4} + 12 q^{5} + 18 q^{6} - 119 q^{8} - 412 q^{9} + O(q^{10}) \) \( 4540 q + 22 q^{2} + 18 q^{3} + 244 q^{4} + 12 q^{5} + 18 q^{6} - 119 q^{8} - 412 q^{9} - 8 q^{10} + 14 q^{11} + 52 q^{12} + 16 q^{13} - 94 q^{15} + 242 q^{16} + 55 q^{17} + 36 q^{18} + 40 q^{19} + 33 q^{20} - 93 q^{22} + 25 q^{23} - 46 q^{24} - 402 q^{25} + 23 q^{26} + 24 q^{27} - 48 q^{29} + 46 q^{30} + 70 q^{31} + 48 q^{32} + 39 q^{33} + 64 q^{34} + 35 q^{36} + 33 q^{37} - 48 q^{38} - 71 q^{39} + 47 q^{40} - 27 q^{41} - 14 q^{43} - 37 q^{44} + 74 q^{45} - 76 q^{46} - 10 q^{47} + 148 q^{48} - 52 q^{50} + 8 q^{51} - 72 q^{52} + 113 q^{54} - 22 q^{55} - 429 q^{57} + 48 q^{58} + 111 q^{59} + 14 q^{60} - 96 q^{61} - 70 q^{62} - 315 q^{64} + 94 q^{65} + 272 q^{66} - 8 q^{67} - 296 q^{68} - 39 q^{69} - 29 q^{71} + 194 q^{72} + 27 q^{73} + 56 q^{74} - 39 q^{75} - 216 q^{76} - 40 q^{78} - 342 q^{79} + 295 q^{80} - 406 q^{81} + 20 q^{82} + q^{83} - 128 q^{85} + 71 q^{86} - 80 q^{87} - 187 q^{88} + 43 q^{89} - 101 q^{90} - 128 q^{92} + 65 q^{93} + 2 q^{94} + 46 q^{95} - 154 q^{96} - q^{97} - 102 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3283, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(67, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(469, [\chi])\)\(^{\oplus 2}\)