Properties

Label 3630.2.u
Level $3630$
Weight $2$
Character orbit 3630.u
Rep. character $\chi_{3630}(331,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $880$
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.u (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 121 \)
Character field: \(\Q(\zeta_{11})\)
Sturm bound: \(1584\)

Dimensions

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

Total New Old
Modular forms 8000 880 7120
Cusp forms 7840 880 6960
Eisenstein series 160 0 160

Trace form

\( 880q - 88q^{4} + 880q^{9} + O(q^{10}) \) \( 880q - 88q^{4} + 880q^{9} - 4q^{10} - 12q^{11} + 64q^{13} + 64q^{14} - 88q^{16} - 32q^{17} - 8q^{19} - 8q^{22} - 16q^{23} - 88q^{25} - 8q^{26} - 16q^{29} - 4q^{30} + 48q^{31} - 8q^{33} - 8q^{34} - 8q^{35} - 88q^{36} - 16q^{37} - 16q^{38} - 8q^{39} + 40q^{40} - 24q^{41} - 24q^{43} - 12q^{44} - 16q^{46} - 16q^{47} - 40q^{49} - 32q^{51} - 24q^{52} + 56q^{53} - 12q^{55} - 24q^{56} - 8q^{57} + 72q^{58} - 24q^{59} - 64q^{61} - 16q^{62} - 88q^{64} - 8q^{65} - 12q^{66} + 72q^{67} - 32q^{68} - 16q^{69} - 48q^{71} - 8q^{73} - 40q^{74} + 36q^{76} - 80q^{77} + 88q^{79} + 880q^{81} + 40q^{82} - 112q^{83} - 8q^{85} - 16q^{86} - 16q^{87} - 8q^{88} + 72q^{89} - 4q^{90} + 184q^{91} - 16q^{92} - 16q^{93} + 128q^{94} + 200q^{97} - 32q^{98} - 12q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3630, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(242, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(363, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(605, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(726, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1815, [\chi])\)\(^{\oplus 2}\)