Properties

Label 3630.2.l
Level $3630$
Weight $2$
Character orbit 3630.l
Rep. character $\chi_{3630}(967,\cdot)$
Character field $\Q(\zeta_{4})$
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.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(i)\)
Sturm bound: \(1584\)

Dimensions

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

Total New Old
Modular forms 1680 216 1464
Cusp forms 1488 216 1272
Eisenstein series 192 0 192

Trace form

\( 216q + 16q^{5} + O(q^{10}) \) \( 216q + 16q^{5} - 8q^{15} - 216q^{16} - 16q^{23} - 16q^{26} - 16q^{31} - 216q^{36} - 32q^{37} + 8q^{42} + 32q^{47} + 48q^{53} + 16q^{56} + 8q^{58} + 16q^{60} - 16q^{67} + 8q^{70} - 16q^{80} - 216q^{81} - 32q^{86} + 16q^{92} - 16q^{93} + 24q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3630, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(330, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(605, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1815, [\chi])\)\(^{\oplus 2}\)