Properties

Label 3630.2.bm
Level $3630$
Weight $2$
Character orbit 3630.bm
Rep. character $\chi_{3630}(49,\cdot)$
Character field $\Q(\zeta_{110})$
Dimension $5280$
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.bm (of order \(110\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 605 \)
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 5280 26720
Cusp forms 31360 5280 26080
Eisenstein series 640 0 640

Trace form

\( 5280q - 132q^{4} - 8q^{5} + 4q^{6} + 1320q^{9} + O(q^{10}) \) \( 5280q - 132q^{4} - 8q^{5} + 4q^{6} + 1320q^{9} + 18q^{10} - 84q^{11} - 12q^{14} + 14q^{15} + 132q^{16} - 16q^{19} + 8q^{20} - 32q^{21} - 4q^{24} - 4q^{25} - 8q^{26} - 8q^{30} - 20q^{31} + 8q^{34} - 44q^{35} + 132q^{36} + 8q^{39} - 6q^{40} + 60q^{41} + 36q^{44} + 8q^{45} + 36q^{46} - 200q^{49} + 24q^{50} + 32q^{51} + 16q^{54} + 56q^{55} - 8q^{56} + 80q^{59} + 16q^{60} + 56q^{61} - 132q^{64} - 68q^{65} + 16q^{66} + 40q^{69} + 82q^{70} - 240q^{71} + 8q^{74} - 16q^{75} + 20q^{76} - 92q^{79} + 12q^{80} - 1320q^{81} - 8q^{84} + 176q^{85} - 88q^{86} + 24q^{89} - 18q^{90} - 84q^{91} + 156q^{94} + 60q^{95} + 4q^{96} + 84q^{99} + O(q^{100}) \)

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

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