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Properties

Label 3283.2.g
Level $3283$
Weight $2$
Character orbit 3283.g
Rep. character $\chi_{3283}(2843,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $454$
Sturm bound $634$

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Defining parameters

Level: \( N \) \(=\) \( 3283 = 7^{2} \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3283.g (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 67 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(634\)

Dimensions

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

Total New Old
Modular forms 652 474 178
Cusp forms 620 454 166
Eisenstein series 32 20 12

Trace form

\( 454 q + 4 q^{3} - 222 q^{4} + 10 q^{5} + 4 q^{6} - 24 q^{8} + 434 q^{9} + O(q^{10}) \) \( 454 q + 4 q^{3} - 222 q^{4} + 10 q^{5} + 4 q^{6} - 24 q^{8} + 434 q^{9} - 3 q^{10} + 8 q^{11} + 3 q^{12} + 6 q^{13} + 6 q^{15} - 220 q^{16} - 14 q^{18} + 4 q^{19} - 11 q^{20} - 72 q^{22} + 8 q^{23} + 2 q^{24} + 424 q^{25} - q^{26} - 2 q^{27} + 4 q^{29} + 9 q^{30} - 4 q^{31} + 29 q^{32} - 6 q^{33} - 42 q^{34} - 200 q^{36} - 11 q^{37} - 7 q^{38} + 27 q^{39} + 30 q^{40} + 16 q^{41} - 96 q^{43} + 59 q^{44} + 58 q^{45} + 43 q^{46} - q^{47} - 16 q^{48} + 52 q^{50} + 14 q^{51} - 16 q^{52} - 14 q^{54} - 22 q^{57} + 40 q^{58} + 54 q^{59} - 58 q^{60} - 14 q^{61} + 48 q^{62} + 392 q^{64} + 16 q^{65} + 102 q^{66} - 14 q^{67} + 10 q^{68} + 17 q^{69} + 7 q^{71} - 62 q^{72} + 6 q^{73} + 32 q^{74} - 38 q^{75} + 40 q^{76} + 18 q^{78} - 10 q^{79} - 31 q^{80} + 318 q^{81} + 46 q^{82} + 10 q^{83} + 18 q^{85} - 49 q^{86} + 3 q^{87} + 77 q^{88} + 12 q^{89} - 75 q^{90} - 26 q^{92} + 23 q^{93} + 64 q^{94} + 9 q^{95} - 33 q^{96} - 32 q^{97} + 47 q^{99} + O(q^{100}) \)

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

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