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Properties

Label 3381.2.m
Level $3381$
Weight $2$
Character orbit 3381.m
Rep. character $\chi_{3381}(275,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $624$
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.m (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 483 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(896\)

Dimensions

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

Total New Old
Modular forms 928 656 272
Cusp forms 864 624 240
Eisenstein series 64 32 32

Trace form

\( 624 q + 2 q^{3} + 308 q^{4} + 24 q^{6} - 2 q^{9} + O(q^{10}) \) \( 624 q + 2 q^{3} + 308 q^{4} + 24 q^{6} - 2 q^{9} - 14 q^{12} + 16 q^{13} - 260 q^{16} - 6 q^{18} + 24 q^{24} - 292 q^{25} + 20 q^{27} + 4 q^{31} - 88 q^{36} + 4 q^{39} + 4 q^{46} - 140 q^{48} + 76 q^{52} + 2 q^{54} - 72 q^{55} + 36 q^{58} - 432 q^{64} + 20 q^{69} + 46 q^{72} - 20 q^{73} - 20 q^{75} + 28 q^{78} + 94 q^{81} - 80 q^{82} - 224 q^{85} - 46 q^{87} + 82 q^{93} - 36 q^{94} - 72 q^{96} + O(q^{100}) \)

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

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