Properties

Label 3630.2.r
Level $3630$
Weight $2$
Character orbit 3630.r
Rep. character $\chi_{3630}(161,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $576$
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.r (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
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 576 2784
Cusp forms 2976 576 2400
Eisenstein series 384 0 384

Trace form

\( 576q + 4q^{3} - 144q^{4} - 10q^{6} - 16q^{9} + O(q^{10}) \) \( 576q + 4q^{3} - 144q^{4} - 10q^{6} - 16q^{9} + 4q^{12} - 12q^{15} - 144q^{16} - 10q^{18} - 60q^{19} + 10q^{24} + 144q^{25} + 16q^{27} + 32q^{31} + 80q^{34} + 14q^{36} + 8q^{37} + 40q^{39} + 24q^{42} - 20q^{46} + 4q^{48} + 144q^{49} - 10q^{51} - 10q^{57} + 8q^{60} + 20q^{63} - 144q^{64} - 24q^{67} - 44q^{69} - 40q^{72} + 40q^{73} + 6q^{75} - 160q^{78} + 20q^{79} + 80q^{81} + 36q^{82} - 20q^{84} + 168q^{91} + 72q^{93} + 80q^{94} - 68q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3630, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(330, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(363, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(726, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1815, [\chi])\)\(^{\oplus 2}\)