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Properties

Label 3330.2.fe
Level $3330$
Weight $2$
Character orbit 3330.fe
Rep. character $\chi_{3330}(131,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $1824$
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.fe (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 333 \)
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 8304 1824 6480
Cusp forms 8112 1824 6288
Eisenstein series 192 0 192

Trace form

\( 1824 q + O(q^{10}) \) \( 1824 q - 144 q^{21} + 216 q^{23} - 24 q^{28} - 24 q^{37} - 96 q^{45} - 24 q^{49} - 72 q^{54} + 72 q^{57} - 216 q^{62} + 72 q^{63} + 24 q^{69} + 288 q^{71} - 192 q^{78} + 96 q^{81} + 216 q^{83} - 72 q^{87} + 168 q^{91} + 72 q^{93} + 144 q^{95} - 72 q^{99} + O(q^{100}) \)

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

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