Properties

Label 3630.2.j
Level $3630$
Weight $2$
Character orbit 3630.j
Rep. character $\chi_{3630}(1937,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $436$
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.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
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 436 1244
Cusp forms 1488 436 1052
Eisenstein series 192 0 192

Trace form

\( 436q + 4q^{3} - 4q^{6} + 4q^{7} + O(q^{10}) \) \( 436q + 4q^{3} - 4q^{6} + 4q^{7} - 4q^{10} - 4q^{12} - 16q^{13} + 16q^{15} - 436q^{16} + 8q^{18} - 8q^{21} + 16q^{25} + 4q^{27} + 4q^{28} - 12q^{30} - 24q^{31} + 12q^{36} - 40q^{37} + 8q^{40} - 28q^{42} - 24q^{43} + 24q^{45} + 32q^{46} - 4q^{48} + 40q^{51} + 16q^{52} + 16q^{57} + 36q^{58} - 12q^{60} + 8q^{61} - 44q^{63} + 16q^{67} - 4q^{70} - 8q^{72} + 36q^{73} - 44q^{75} + 16q^{76} - 16q^{78} - 68q^{81} - 48q^{82} - 8q^{85} + 84q^{87} - 24q^{90} + 96q^{93} + 4q^{96} + 100q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3630, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(330, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1815, [\chi])\)\(^{\oplus 2}\)