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Properties

Label 3330.2.fp
Level $3330$
Weight $2$
Character orbit 3330.fp
Rep. character $\chi_{3330}(53,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $912$
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.fp (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 555 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(1368\)

Dimensions

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

Total New Old
Modular forms 8400 912 7488
Cusp forms 8016 912 7104
Eisenstein series 384 0 384

Trace form

\( 912 q + O(q^{10}) \) \( 912 q - 96 q^{25} + 96 q^{31} + 48 q^{37} - 24 q^{40} - 96 q^{55} + 12 q^{58} - 96 q^{61} + 96 q^{67} - 48 q^{70} + 24 q^{73} + 12 q^{85} + 48 q^{88} + 48 q^{91} + 96 q^{97} + O(q^{100}) \)

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

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