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Properties

Label 3630.2.m
Level $3630$
Weight $2$
Character orbit 3630.m
Rep. character $\chi_{3630}(511,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $288$
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.m (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(1584\)

Dimensions

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

Total New Old
Modular forms 3360 288 3072
Cusp forms 2976 288 2688
Eisenstein series 384 0 384

Trace form

\( 288 q - 72 q^{4} - 72 q^{9} + O(q^{10}) \) \( 288 q - 72 q^{4} - 72 q^{9} - 16 q^{10} - 16 q^{13} + 4 q^{14} - 72 q^{16} - 8 q^{17} + 8 q^{19} - 48 q^{23} - 72 q^{25} + 24 q^{26} - 24 q^{29} + 4 q^{30} + 16 q^{31} - 56 q^{34} + 8 q^{35} - 72 q^{36} - 8 q^{37} + 32 q^{38} + 8 q^{39} + 4 q^{40} + 4 q^{41} + 16 q^{42} - 16 q^{43} - 4 q^{46} + 24 q^{47} - 4 q^{49} - 8 q^{51} + 24 q^{52} + 64 q^{53} + 24 q^{56} + 8 q^{57} + 48 q^{58} + 56 q^{59} - 16 q^{61} - 24 q^{62} - 72 q^{64} + 8 q^{65} - 112 q^{67} - 8 q^{68} + 32 q^{69} + 64 q^{71} - 64 q^{73} - 40 q^{74} + 8 q^{76} - 52 q^{79} - 72 q^{81} - 16 q^{82} - 8 q^{83} + 8 q^{85} + 32 q^{86} + 16 q^{87} - 88 q^{89} + 4 q^{90} - 52 q^{91} + 32 q^{92} - 96 q^{93} - 12 q^{94} - 56 q^{97} + 32 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{2}^{\mathrm{old}}(3630, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(242, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(330, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(363, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(605, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(726, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1815, [\chi])\)\(^{\oplus 2}\)