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Properties

Label 3381.2.e
Level $3381$
Weight $2$
Character orbit 3381.e
Rep. character $\chi_{3381}(344,\cdot)$
Character field $\Q$
Dimension $318$
Sturm bound $896$

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Defining parameters

Level: \( N \) \(=\) \( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3381.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
Character field: \(\Q\)
Sturm bound: \(896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3381, [\chi])\).

Total New Old
Modular forms 464 338 126
Cusp forms 432 318 114
Eisenstein series 32 20 12

Trace form

\( 318 q + 4 q^{3} - 308 q^{4} - 9 q^{6} - 4 q^{9} + O(q^{10}) \) \( 318 q + 4 q^{3} - 308 q^{4} - 9 q^{6} - 4 q^{9} - 7 q^{12} + 8 q^{13} + 272 q^{16} + 9 q^{18} + 18 q^{24} + 274 q^{25} + 4 q^{27} + 8 q^{31} + 31 q^{36} + 32 q^{39} + 8 q^{46} + 29 q^{48} - 22 q^{52} + 28 q^{54} + 54 q^{58} - 282 q^{64} - 8 q^{69} - 70 q^{72} - 40 q^{73} + 80 q^{75} - 127 q^{78} - 4 q^{81} - 46 q^{82} - 16 q^{85} - 20 q^{87} + 38 q^{93} + 90 q^{94} - 63 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3381, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3381, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3381, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 2}\)