Properties

Label 3630.2.bv
Level $3630$
Weight $2$
Character orbit 3630.bv
Rep. character $\chi_{3630}(7,\cdot)$
Character field $\Q(\zeta_{220})$
Dimension $10560$
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.bv (of order \(220\) and degree \(80\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 605 \)
Character field: \(\Q(\zeta_{220})\)
Sturm bound: \(1584\)

Dimensions

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

Total New Old
Modular forms 64000 10560 53440
Cusp forms 62720 10560 52160
Eisenstein series 1280 0 1280

Trace form

\( 10560q - 16q^{5} - 40q^{7} + O(q^{10}) \) \( 10560q - 16q^{5} - 40q^{7} + 44q^{10} + 8q^{11} + 88q^{13} - 12q^{15} - 264q^{16} - 40q^{17} + 84q^{22} + 16q^{23} - 40q^{25} + 16q^{26} - 20q^{28} + 16q^{31} - 12q^{33} - 264q^{36} - 232q^{37} - 40q^{41} + 12q^{42} + 40q^{46} + 88q^{47} + 80q^{50} + 80q^{51} + 40q^{52} + 72q^{53} + 28q^{55} - 16q^{56} + 80q^{57} + 12q^{58} + 24q^{60} + 80q^{61} + 80q^{62} + 40q^{63} + 32q^{66} + 336q^{67} + 40q^{68} + 12q^{70} - 20q^{73} + 32q^{75} - 88q^{76} - 24q^{80} + 2640q^{81} + 32q^{82} + 192q^{85} + 32q^{86} - 4q^{88} + 40q^{91} + 72q^{92} - 24q^{93} + 40q^{95} + 96q^{97} + O(q^{100}) \)

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

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