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Properties

Label 3330.2.x
Level $3330$
Weight $2$
Character orbit 3330.x
Rep. character $\chi_{3330}(1511,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $112$
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.x (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 111 \)
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 112 1288
Cusp forms 1336 112 1224
Eisenstein series 64 0 64

Trace form

\( 112 q + O(q^{10}) \) \( 112 q + 16 q^{13} - 112 q^{16} - 16 q^{19} + 64 q^{31} - 32 q^{34} - 16 q^{37} - 80 q^{43} + 144 q^{49} - 16 q^{52} - 48 q^{55} - 48 q^{61} + 16 q^{76} - 32 q^{79} + 64 q^{82} - 48 q^{91} + 32 q^{94} + 48 q^{97} + O(q^{100}) \)

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

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