Properties

Label 3234.2.ce
Level 3234
Weight 2
Character orbit ce
Rep. character \(\chi_{3234}(25,\cdot)\)
Character field \(\Q(\zeta_{105})\)
Dimension 5376
Sturm bound 1344

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Defining parameters

Level: \( N \) \(=\) \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3234.ce (of order \(105\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 539 \)
Character field: \(\Q(\zeta_{105})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 32640 5376 27264
Cusp forms 31872 5376 26496
Eisenstein series 768 0 768

Trace form

\( 5376q - 112q^{4} - 8q^{5} - 8q^{6} - 8q^{7} - 112q^{9} + O(q^{10}) \) \( 5376q - 112q^{4} - 8q^{5} - 8q^{6} - 8q^{7} - 112q^{9} - 36q^{10} - 36q^{11} - 16q^{13} - 4q^{14} + 30q^{15} - 112q^{16} + 72q^{17} - 56q^{19} - 40q^{20} - 2q^{22} - 8q^{23} + 4q^{24} - 124q^{25} - 64q^{26} - 22q^{28} - 24q^{29} + 6q^{31} - 2q^{33} - 32q^{34} - 64q^{35} + 224q^{36} - 28q^{37} + 104q^{38} - 70q^{40} + 24q^{41} + 42q^{42} + 16q^{43} + 68q^{44} + 104q^{45} - 8q^{46} + 276q^{47} + 216q^{49} - 312q^{51} + 8q^{52} + 96q^{53} - 16q^{54} - 54q^{55} + 104q^{56} + 100q^{58} - 24q^{59} + 52q^{60} - 20q^{61} - 72q^{62} - 20q^{63} + 224q^{64} + 64q^{65} + 64q^{67} - 12q^{68} + 40q^{69} + 108q^{70} + 48q^{71} + 284q^{73} - 40q^{74} - 8q^{75} + 80q^{76} - 20q^{77} + 16q^{79} + 12q^{80} - 112q^{81} + 24q^{82} + 40q^{83} - 8q^{85} + 288q^{86} - 32q^{87} + 126q^{88} + 136q^{89} - 8q^{90} - 20q^{91} + 16q^{92} - 16q^{93} + 140q^{94} + 428q^{95} + 4q^{96} + 528q^{97} + 48q^{98} + 16q^{99} + O(q^{100}) \)

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