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Properties

Label 3330.2.cl
Level $3330$
Weight $2$
Character orbit 3330.cl
Rep. character $\chi_{3330}(1207,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $380$
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.cl (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
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 380 2420
Cusp forms 2672 380 2292
Eisenstein series 128 0 128

Trace form

\( 380 q + 2 q^{2} - 190 q^{4} - 2 q^{5} - 4 q^{8} + O(q^{10}) \) \( 380 q + 2 q^{2} - 190 q^{4} - 2 q^{5} - 4 q^{8} - 2 q^{10} + 8 q^{14} - 190 q^{16} + 20 q^{19} - 8 q^{20} - 8 q^{23} - 2 q^{25} + 8 q^{26} - 18 q^{29} - 48 q^{31} + 2 q^{32} - 64 q^{35} + 42 q^{37} - 2 q^{40} + 78 q^{41} - 16 q^{43} - 12 q^{44} - 8 q^{47} - 24 q^{49} - 52 q^{50} - 18 q^{53} - 44 q^{55} - 4 q^{56} - 6 q^{58} - 12 q^{59} - 36 q^{61} + 4 q^{62} + 380 q^{64} + 12 q^{65} - 28 q^{67} - 8 q^{70} - 8 q^{71} + 4 q^{73} - 12 q^{74} + 8 q^{76} - 12 q^{77} + 10 q^{80} + 32 q^{83} - 8 q^{86} - 22 q^{89} + 28 q^{91} + 4 q^{92} - 4 q^{94} + 4 q^{95} - 24 q^{98} + O(q^{100}) \)

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

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