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Properties

Label 3283.2.o
Level $3283$
Weight $2$
Character orbit 3283.o
Rep. character $\chi_{3283}(803,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $444$
Sturm bound $634$

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Defining parameters

Level: \( N \) \(=\) \( 3283 = 7^{2} \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3283.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 469 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(634\)

Dimensions

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

Total New Old
Modular forms 652 460 192
Cusp forms 620 444 176
Eisenstein series 32 16 16

Trace form

\( 444 q + 214 q^{4} - 214 q^{9} + O(q^{10}) \) \( 444 q + 214 q^{4} - 214 q^{9} + 24 q^{10} - 28 q^{15} - 218 q^{16} - 6 q^{17} - 72 q^{22} + 10 q^{23} - 108 q^{24} - 200 q^{25} + 18 q^{26} + 40 q^{29} + 6 q^{33} - 484 q^{36} + 40 q^{37} + 46 q^{39} + 24 q^{40} + 18 q^{47} - 18 q^{54} - 6 q^{59} + 116 q^{60} - 508 q^{64} + 32 q^{65} - 34 q^{67} + 48 q^{68} - 72 q^{71} + 12 q^{73} - 158 q^{81} + 66 q^{82} + 136 q^{86} - 92 q^{88} + 102 q^{89} + 68 q^{92} - 38 q^{93} - 120 q^{96} + O(q^{100}) \)

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

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