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Properties

Label 3330.2.r
Level $3330$
Weight $2$
Character orbit 3330.r
Rep. character $\chi_{3330}(253,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $190$
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.r (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
Character field: \(\Q(i)\)
Sturm bound: \(1368\)

Dimensions

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

Total New Old
Modular forms 1400 190 1210
Cusp forms 1336 190 1146
Eisenstein series 64 0 64

Trace form

\( 190 q - 2 q^{2} + 190 q^{4} + 2 q^{5} - 2 q^{8} + O(q^{10}) \) \( 190 q - 2 q^{2} + 190 q^{4} + 2 q^{5} - 2 q^{8} + 2 q^{10} + 4 q^{14} + 190 q^{16} - 20 q^{19} + 2 q^{20} + 8 q^{23} + 2 q^{25} - 8 q^{26} + 18 q^{29} - 2 q^{32} - 32 q^{35} - 18 q^{37} + 2 q^{40} + 16 q^{43} + 8 q^{47} + 22 q^{50} - 6 q^{53} + 44 q^{55} + 4 q^{56} - 18 q^{58} + 12 q^{59} - 42 q^{61} + 8 q^{62} + 190 q^{64} + 24 q^{65} + 16 q^{67} - 16 q^{70} - 16 q^{71} + 2 q^{73} - 6 q^{74} - 20 q^{76} + 24 q^{77} + 48 q^{79} + 2 q^{80} - 20 q^{83} - 16 q^{86} + 34 q^{89} + 8 q^{91} + 8 q^{92} + 4 q^{94} - 88 q^{95} + O(q^{100}) \)

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

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