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Properties

Label 3630.2.bd
Level $3630$
Weight $2$
Character orbit 3630.bd
Rep. character $\chi_{3630}(131,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $1760$
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.bd (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 363 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(1584\)

Dimensions

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

Total New Old
Modular forms 8000 1760 6240
Cusp forms 7840 1760 6080
Eisenstein series 160 0 160

Trace form

\( 1760 q - 4 q^{3} - 176 q^{4} - 4 q^{9} + O(q^{10}) \) \( 1760 q - 4 q^{3} - 176 q^{4} - 4 q^{9} + 18 q^{12} + 36 q^{15} - 176 q^{16} - 12 q^{22} + 176 q^{25} + 44 q^{27} - 80 q^{31} - 16 q^{33} - 16 q^{34} - 4 q^{36} + 16 q^{37} + 16 q^{42} - 4 q^{48} + 248 q^{49} - 22 q^{51} + 12 q^{55} - 22 q^{57} - 72 q^{58} - 8 q^{60} - 176 q^{64} - 2 q^{66} + 24 q^{67} - 16 q^{69} - 88 q^{73} + 4 q^{75} + 132 q^{76} + 32 q^{78} + 88 q^{79} + 12 q^{81} - 48 q^{82} - 264 q^{85} + 120 q^{88} + 88 q^{90} - 200 q^{91} + 132 q^{93} + 40 q^{97} + 16 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3630, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(363, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(726, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1815, [\chi])\)\(^{\oplus 2}\)