Properties

Label 3234.2.bg
Level 3234
Weight 2
Character orbit bg
Rep. character \(\chi_{3234}(361,\cdot)\)
Character field \(\Q(\zeta_{15})\)
Dimension 640
Sturm bound 1344

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3234.bg (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3234, [\chi])\).

Total New Old
Modular forms 5632 640 4992
Cusp forms 5120 640 4480
Eisenstein series 512 0 512

Trace form

\( 640q + 80q^{4} - 8q^{5} - 8q^{6} + 80q^{9} + O(q^{10}) \) \( 640q + 80q^{4} - 8q^{5} - 8q^{6} + 80q^{9} - 36q^{10} - 8q^{11} - 16q^{13} - 12q^{15} + 80q^{16} - 12q^{17} + 16q^{20} - 4q^{22} - 8q^{23} + 4q^{24} + 44q^{25} - 8q^{26} - 24q^{29} + 16q^{30} + 6q^{31} - 2q^{33} - 32q^{34} - 160q^{36} - 12q^{37} - 8q^{38} + 14q^{40} + 24q^{41} + 16q^{43} + 12q^{44} - 8q^{45} + 8q^{46} - 88q^{47} + 24q^{51} + 8q^{52} - 16q^{53} - 16q^{54} - 12q^{55} - 32q^{57} + 2q^{58} + 32q^{59} - 4q^{60} - 20q^{61} + 96q^{62} - 160q^{64} + 128q^{65} + 128q^{67} - 12q^{68} + 40q^{69} + 240q^{71} + 32q^{73} + 16q^{74} - 8q^{75} + 80q^{76} + 16q^{79} + 12q^{80} + 80q^{81} + 24q^{82} + 208q^{83} + 200q^{85} + 36q^{86} - 4q^{87} + 22q^{88} + 80q^{89} - 8q^{90} + 16q^{92} - 40q^{93} + 56q^{94} + 44q^{95} + 4q^{96} + 24q^{97} + 16q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3234, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3234, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3234, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(539, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1078, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1617, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database