Properties

Label 3630.2.v
Level $3630$
Weight $2$
Character orbit 3630.v
Rep. character $\chi_{3630}(403,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $864$
Sturm bound $1584$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3630.v (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(1584\)

Dimensions

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

Total New Old
Modular forms 6720 864 5856
Cusp forms 5952 864 5088
Eisenstein series 768 0 768

Trace form

\( 864q - 16q^{5} - 40q^{7} + O(q^{10}) \) \( 864q - 16q^{5} - 40q^{7} - 12q^{15} + 216q^{16} - 40q^{17} + 16q^{23} - 40q^{25} + 16q^{26} - 20q^{28} + 16q^{31} + 216q^{36} + 32q^{37} - 40q^{41} + 12q^{42} + 40q^{46} + 88q^{47} + 80q^{50} + 80q^{51} + 40q^{52} + 72q^{53} - 16q^{56} + 80q^{57} + 12q^{58} + 24q^{60} + 80q^{61} + 80q^{62} + 40q^{63} - 144q^{67} + 40q^{68} - 108q^{70} - 20q^{73} - 24q^{80} + 216q^{81} - 160q^{85} + 32q^{86} + 40q^{91} - 16q^{92} - 24q^{93} + 40q^{95} + 96q^{97} + O(q^{100}) \)

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

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