Properties

Label 3630.2.c
Level $3630$
Weight $2$
Character orbit 3630.c
Rep. character $\chi_{3630}(2179,\cdot)$
Character field $\Q$
Dimension $110$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Sturm bound: \(1584\)

Dimensions

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

Total New Old
Modular forms 840 110 730
Cusp forms 744 110 634
Eisenstein series 96 0 96

Trace form

\( 110q - 110q^{4} + 4q^{5} - 2q^{6} - 110q^{9} + O(q^{10}) \) \( 110q - 110q^{4} + 4q^{5} - 2q^{6} - 110q^{9} + 2q^{10} - 4q^{14} - 2q^{15} + 110q^{16} + 16q^{19} - 4q^{20} - 12q^{21} + 2q^{24} + 10q^{25} - 4q^{26} + 4q^{30} - 16q^{31} - 4q^{34} + 28q^{35} + 110q^{36} + 4q^{39} - 2q^{40} - 36q^{41} - 4q^{45} - 8q^{46} - 102q^{49} + 24q^{50} + 4q^{51} + 2q^{54} + 4q^{56} + 20q^{59} + 2q^{60} - 52q^{61} - 110q^{64} + 44q^{65} - 8q^{69} + 40q^{70} - 72q^{71} - 4q^{74} + 24q^{75} - 16q^{76} - 16q^{79} + 4q^{80} + 110q^{81} + 12q^{84} + 44q^{85} - 24q^{86} - 4q^{89} - 2q^{90} - 24q^{91} - 16q^{94} - 2q^{96} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3630, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(330, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(605, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1815, [\chi])\)\(^{\oplus 2}\)