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Properties

Label 3330.2.ck
Level $3330$
Weight $2$
Character orbit 3330.ck
Rep. character $\chi_{3330}(251,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $224$
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.ck (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 111 \)
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 224 2576
Cusp forms 2672 224 2448
Eisenstein series 128 0 128

Trace form

\( 224 q + O(q^{10}) \) \( 224 q - 16 q^{13} + 112 q^{16} + 16 q^{19} - 48 q^{28} - 16 q^{31} - 16 q^{34} - 128 q^{37} - 16 q^{43} - 192 q^{49} + 16 q^{52} + 48 q^{55} - 48 q^{61} - 16 q^{76} + 128 q^{79} + 32 q^{82} + 96 q^{91} - 32 q^{94} - 144 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3330, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(222, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(333, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(555, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(666, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1110, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1665, [\chi])\)\(^{\oplus 2}\)