Properties

Label 3630.2.f
Level $3630$
Weight $2$
Character orbit 3630.f
Rep. character $\chi_{3630}(3629,\cdot)$
Character field $\Q$
Dimension $216$
Sturm bound $1584$

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Defining parameters

Level: \( N \) \(=\) \( 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3630.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 165 \)
Character field: \(\Q\)
Sturm bound: \(1584\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3630, [\chi])\).

Total New Old
Modular forms 840 216 624
Cusp forms 744 216 528
Eisenstein series 96 0 96

Trace form

\( 216q - 216q^{4} - 16q^{9} + O(q^{10}) \) \( 216q - 216q^{4} - 16q^{9} + 8q^{15} + 216q^{16} - 4q^{25} - 48q^{31} + 8q^{34} + 16q^{36} + 48q^{45} + 256q^{49} - 8q^{60} - 216q^{64} - 32q^{69} + 24q^{70} + 32q^{75} - 96q^{81} - 96q^{91} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3630, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3630, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3630, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(330, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1815, [\chi])\)\(^{\oplus 2}\)