Properties

Label 3330.2.fw
Level $3330$
Weight $2$
Character orbit 3330.fw
Rep. character $\chi_{3330}(217,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $1140$
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.fw (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
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 1140 7260
Cusp forms 8016 1140 6876
Eisenstein series 384 0 384

Trace form

\( 1140 q + O(q^{10}) \) \( 1140 q - 24 q^{14} - 6 q^{17} + 6 q^{25} + 48 q^{31} - 60 q^{35} + 24 q^{37} - 12 q^{40} - 78 q^{41} - 12 q^{44} - 24 q^{49} + 48 q^{50} + 48 q^{53} - 30 q^{58} - 12 q^{61} + 12 q^{62} + 570 q^{64} + 36 q^{65} + 12 q^{67} + 24 q^{70} - 48 q^{71} + 6 q^{73} + 126 q^{74} + 12 q^{76} - 132 q^{77} + 48 q^{79} + 12 q^{80} - 96 q^{83} + 24 q^{86} - 24 q^{88} + 12 q^{89} - 72 q^{91} + 24 q^{92} - 108 q^{95} + 120 q^{97} - 24 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3330, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(370, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(555, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1110, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1665, [\chi])\)\(^{\oplus 2}\)