Properties

Label 3630.2.bg
Level $3630$
Weight $2$
Character orbit 3630.bg
Rep. character $\chi_{3630}(43,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $2640$
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.bg (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 605 \)
Character field: \(\Q(\zeta_{44})\)
Sturm bound: \(1584\)

Dimensions

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

Total New Old
Modular forms 16000 2640 13360
Cusp forms 15680 2640 13040
Eisenstein series 320 0 320

Trace form

\( 2640q + 16q^{5} + O(q^{10}) \) \( 2640q + 16q^{5} - 44q^{10} - 8q^{11} - 88q^{13} - 8q^{15} + 264q^{16} - 84q^{22} - 16q^{23} - 16q^{26} - 16q^{31} + 12q^{33} + 264q^{36} + 232q^{37} + 8q^{42} + 32q^{47} + 48q^{53} + 52q^{55} + 16q^{56} + 8q^{58} + 16q^{60} + 8q^{66} - 336q^{67} - 112q^{70} - 32q^{75} + 88q^{76} - 16q^{80} - 2640q^{81} - 32q^{82} - 352q^{85} - 32q^{86} + 4q^{88} - 72q^{92} - 16q^{93} + 24q^{97} + O(q^{100}) \)

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

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