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Properties

Label 3330.2.cn
Level $3330$
Weight $2$
Character orbit 3330.cn
Rep. character $\chi_{3330}(2267,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $304$
Sturm bound $1368$

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Defining parameters

Level: \( N \) \(=\) \( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3330.cn (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 555 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1368\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3330, [\chi])\).

Total New Old
Modular forms 2800 304 2496
Cusp forms 2672 304 2368
Eisenstein series 128 0 128

Trace form

\( 304 q + O(q^{10}) \) \( 304 q - 8 q^{13} + 152 q^{16} - 32 q^{22} - 16 q^{25} - 128 q^{31} - 36 q^{37} - 4 q^{40} - 32 q^{46} + 8 q^{52} + 32 q^{55} - 4 q^{58} + 96 q^{61} - 32 q^{67} + 16 q^{70} - 16 q^{73} + 64 q^{76} - 8 q^{82} + 56 q^{85} + 64 q^{88} + 48 q^{91} + 136 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3330, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3330, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3330, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(555, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1110, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1665, [\chi])\)\(^{\oplus 2}\)