Properties

Label 3234.2.bp
Level 3234
Weight 2
Character orbit bp
Rep. character \(\chi_{3234}(169,\cdot)\)
Character field \(\Q(\zeta_{35})\)
Dimension 2688
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.bp (of order \(35\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 539 \)
Character field: \(\Q(\zeta_{35})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 16320 2688 13632
Cusp forms 15936 2688 13248
Eisenstein series 384 0 384

Trace form

\( 2688q + 112q^{4} - 16q^{5} - 4q^{6} + 8q^{7} + 112q^{9} + O(q^{10}) \) \( 2688q + 112q^{4} - 16q^{5} - 4q^{6} + 8q^{7} + 112q^{9} + 24q^{10} + 12q^{11} - 8q^{13} + 4q^{14} - 30q^{15} + 112q^{16} - 36q^{17} + 32q^{19} + 40q^{20} + 2q^{22} - 16q^{23} - 4q^{24} + 88q^{25} + 40q^{26} - 2q^{28} + 24q^{29} + 12q^{31} - 4q^{33} + 32q^{34} + 28q^{35} + 112q^{36} - 56q^{37} + 40q^{38} - 38q^{40} - 24q^{41} + 30q^{42} - 16q^{43} + 52q^{44} + 40q^{45} - 16q^{46} - 156q^{47} + 96q^{49} - 120q^{51} - 8q^{52} + 24q^{53} + 16q^{54} + 102q^{55} + 40q^{56} - 10q^{58} + 24q^{59} + 20q^{60} + 32q^{61} - 108q^{62} + 8q^{63} + 112q^{64} + 128q^{65} + 128q^{67} + 48q^{68} - 40q^{69} - 12q^{70} - 48q^{71} - 200q^{73} + 88q^{74} - 16q^{75} + 16q^{76} + 92q^{77} + 32q^{79} + 24q^{80} + 112q^{81} + 24q^{82} + 176q^{83} + 8q^{85} - 180q^{86} + 20q^{87} - 84q^{88} + 248q^{89} - 16q^{90} + 32q^{91} - 16q^{92} - 32q^{93} - 68q^{94} + 184q^{95} - 4q^{96} - 528q^{97} - 48q^{98} - 16q^{99} + O(q^{100}) \)

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

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

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database