Properties

Label 3630.2.bn
Level $3630$
Weight $2$
Character orbit 3630.bn
Rep. character $\chi_{3630}(41,\cdot)$
Character field $\Q(\zeta_{110})$
Dimension $7040$
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.bn (of order \(110\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 363 \)
Character field: \(\Q(\zeta_{110})\)
Sturm bound: \(1584\)

Dimensions

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

Total New Old
Modular forms 32000 7040 24960
Cusp forms 31360 7040 24320
Eisenstein series 640 0 640

Trace form

\( 7040q + 4q^{3} + 176q^{4} - 10q^{6} - 16q^{9} + O(q^{10}) \) \( 7040q + 4q^{3} + 176q^{4} - 10q^{6} - 16q^{9} - 18q^{12} - 56q^{15} + 176q^{16} - 10q^{18} - 60q^{19} + 12q^{22} + 10q^{24} - 176q^{25} + 16q^{27} + 120q^{31} + 6q^{33} + 16q^{34} + 14q^{36} + 24q^{37} + 40q^{39} + 24q^{42} - 20q^{46} + 4q^{48} - 248q^{49} + 12q^{51} + 8q^{55} + 12q^{57} + 72q^{58} + 8q^{60} + 20q^{63} + 176q^{64} + 2q^{66} - 24q^{67} - 44q^{69} - 40q^{72} + 128q^{73} + 6q^{75} - 132q^{76} - 32q^{78} - 68q^{79} + 48q^{81} + 108q^{82} - 20q^{84} + 264q^{85} - 120q^{88} - 88q^{90} + 320q^{91} - 92q^{93} + 80q^{94} + 60q^{97} + 64q^{99} + O(q^{100}) \)

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

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