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Properties

Label 3330.2.es
Level $3330$
Weight $2$
Character orbit 3330.es
Rep. character $\chi_{3330}(229,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $1368$
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.es (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1665 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(1368\)

Dimensions

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

Total New Old
Modular forms 4152 1368 2784
Cusp forms 4056 1368 2688
Eisenstein series 96 0 96

Trace form

\( 1368 q - 12 q^{9} + O(q^{10}) \) \( 1368 q - 12 q^{9} - 48 q^{11} + 18 q^{15} + 72 q^{26} - 72 q^{31} + 18 q^{35} - 48 q^{39} + 24 q^{41} + 96 q^{45} + 12 q^{59} + 684 q^{64} + 108 q^{69} + 60 q^{71} - 24 q^{74} + 78 q^{75} - 12 q^{80} + 84 q^{81} + 120 q^{89} - 18 q^{90} - 204 q^{95} + 60 q^{99} + O(q^{100}) \)

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

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