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Properties

Label 3283.2.h
Level $3283$
Weight $2$
Character orbit 3283.h
Rep. character $\chi_{3283}(900,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $446$
Sturm bound $634$

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Defining parameters

Level: \( N \) \(=\) \( 3283 = 7^{2} \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3283.h (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 469 \)
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 650 462 188
Cusp forms 618 446 172
Eisenstein series 32 16 16

Trace form

\( 446 q + 10 q^{2} - q^{3} + 450 q^{4} - 2 q^{5} - 2 q^{6} + 18 q^{8} - 216 q^{9} + O(q^{10}) \) \( 446 q + 10 q^{2} - q^{3} + 450 q^{4} - 2 q^{5} - 2 q^{6} + 18 q^{8} - 216 q^{9} + 9 q^{10} - 6 q^{11} + q^{12} - 8 q^{13} - 28 q^{15} + 490 q^{16} - 3 q^{17} - 32 q^{18} - 4 q^{19} - 4 q^{20} - 32 q^{22} - 6 q^{23} - 4 q^{24} - 207 q^{25} + 3 q^{26} + 20 q^{27} + 20 q^{30} + 48 q^{31} + 6 q^{32} + 5 q^{33} - 10 q^{34} - 221 q^{36} + 48 q^{38} + 23 q^{39} + 46 q^{40} - 15 q^{41} - 58 q^{43} - 106 q^{44} - 38 q^{45} - 82 q^{46} - 9 q^{47} + 15 q^{48} - 34 q^{50} + 2 q^{51} - 16 q^{52} - 14 q^{53} + 10 q^{54} + 2 q^{55} - 26 q^{57} - 60 q^{58} + 176 q^{60} - 16 q^{61} - 20 q^{62} + 538 q^{64} + 10 q^{65} + 6 q^{66} - 8 q^{67} - 9 q^{68} - 54 q^{69} - 2 q^{71} - 37 q^{72} - 7 q^{73} + 4 q^{74} - 23 q^{75} - 56 q^{76} - 4 q^{78} - 53 q^{79} - 69 q^{80} - 207 q^{81} + 46 q^{82} + 24 q^{83} - 11 q^{85} - 34 q^{86} + 72 q^{87} - 48 q^{88} + 24 q^{89} - 65 q^{90} + 46 q^{92} - 25 q^{93} + 28 q^{94} - 31 q^{95} - 7 q^{96} + 19 q^{97} - 20 q^{99} + O(q^{100}) \)

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

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