Properties

Label 3630.2.s
Level $3630$
Weight $2$
Character orbit 3630.s
Rep. character $\chi_{3630}(1219,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $432$
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.s (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1584\)

Dimensions

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

Total New Old
Modular forms 3360 432 2928
Cusp forms 2976 432 2544
Eisenstein series 384 0 384

Trace form

\( 432q + 108q^{4} - 8q^{5} + 4q^{6} + 108q^{9} + O(q^{10}) \) \( 432q + 108q^{4} - 8q^{5} + 4q^{6} + 108q^{9} - 4q^{10} - 12q^{14} + 14q^{15} - 108q^{16} - 16q^{19} + 8q^{20} - 32q^{21} - 4q^{24} - 4q^{25} - 8q^{26} - 8q^{30} - 20q^{31} + 8q^{34} - 44q^{35} - 108q^{36} + 8q^{39} - 6q^{40} + 60q^{41} + 8q^{45} + 36q^{46} + 128q^{49} + 24q^{50} + 32q^{51} + 16q^{54} - 8q^{56} + 80q^{59} + 16q^{60} + 56q^{61} + 108q^{64} + 64q^{65} + 40q^{69} + 22q^{70} - 64q^{71} + 8q^{74} - 32q^{75} - 24q^{76} - 4q^{79} + 12q^{80} - 108q^{81} - 8q^{84} - 88q^{86} + 24q^{89} + 4q^{90} - 52q^{91} - 20q^{94} + 60q^{95} + 4q^{96} + O(q^{100}) \)

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

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