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Properties

Label 3630.2.x
Level $3630$
Weight $2$
Character orbit 3630.x
Rep. character $\chi_{3630}(323,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1728$
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.x (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 165 \)
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 1728 4992
Cusp forms 5952 1728 4224
Eisenstein series 768 0 768

Trace form

\( 1728 q - 8 q^{3} - 8 q^{7} + O(q^{10}) \) \( 1728 q - 8 q^{3} - 8 q^{7} + 8 q^{10} - 32 q^{12} + 16 q^{13} - 8 q^{15} + 432 q^{16} + 16 q^{21} - 72 q^{25} - 8 q^{27} + 12 q^{28} + 16 q^{31} - 16 q^{36} + 64 q^{37} + 32 q^{42} + 128 q^{43} - 32 q^{45} + 24 q^{46} + 8 q^{48} - 88 q^{51} + 24 q^{52} + 48 q^{57} + 84 q^{58} + 8 q^{60} + 48 q^{61} + 40 q^{63} + 368 q^{67} + 28 q^{70} - 76 q^{73} - 88 q^{75} + 16 q^{78} + 136 q^{81} + 32 q^{82} + 16 q^{85} - 64 q^{87} - 48 q^{90} + 240 q^{91} - 28 q^{93} - 88 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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