↑

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 $1584$

Related objects

Downloads

Learn more

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

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

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

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