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Properties

Label 3283.2.be
Level $3283$
Weight $2$
Character orbit 3283.be
Rep. character $\chi_{3283}(244,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $2240$
Sturm bound $634$

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Defining parameters

Level: \( N \) \(=\) \( 3283 = 7^{2} \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3283.be (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 469 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(634\)

Dimensions

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

Total New Old
Modular forms 3240 2320 920
Cusp forms 3080 2240 840
Eisenstein series 160 80 80

Trace form

\( 2240 q + 22 q^{2} + 238 q^{4} - 110 q^{8} - 194 q^{9} + O(q^{10}) \) \( 2240 q + 22 q^{2} + 238 q^{4} - 110 q^{8} - 194 q^{9} + 22 q^{11} - 48 q^{15} - 210 q^{16} + 22 q^{18} - 154 q^{22} + 26 q^{23} - 198 q^{25} - 72 q^{29} + 22 q^{32} + 274 q^{36} + 68 q^{37} + 118 q^{39} - 88 q^{43} + 22 q^{44} - 88 q^{46} + 22 q^{50} + 22 q^{51} + 22 q^{53} - 110 q^{57} - 22 q^{58} + 214 q^{60} + 34 q^{64} - 82 q^{65} + 2 q^{67} - 108 q^{71} - 418 q^{72} - 66 q^{74} - 132 q^{78} - 110 q^{79} - 194 q^{81} - 44 q^{85} - 62 q^{86} - 274 q^{88} - 56 q^{92} + 154 q^{93} + 22 q^{95} - 44 q^{99} + O(q^{100}) \)

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

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