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Properties

Label 3330.2.fx
Level $3330$
Weight $2$
Character orbit 3330.fx
Rep. character $\chi_{3330}(277,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $2736$
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.fx (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1665 \)
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 8304 2736 5568
Cusp forms 8112 2736 5376
Eisenstein series 192 0 192

Trace form

\( 2736 q - 24 q^{3} + O(q^{10}) \) \( 2736 q - 24 q^{3} + 24 q^{12} - 12 q^{27} + 12 q^{33} + 36 q^{35} - 48 q^{39} + 96 q^{41} + 84 q^{42} - 48 q^{45} + 12 q^{53} + 48 q^{57} + 36 q^{62} + 1368 q^{64} - 72 q^{67} - 168 q^{69} - 48 q^{74} - 96 q^{75} + 48 q^{77} + 12 q^{80} + 144 q^{81} - 216 q^{87} + 24 q^{92} - 12 q^{93} + 192 q^{95} + O(q^{100}) \)

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

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