Properties

Label 3234.2.j
Level 3234
Weight 2
Character orbit j
Rep. character \(\chi_{3234}(295,\cdot)\)
Character field \(\Q(\zeta_{5})\)
Dimension 328
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.j (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 2816 328 2488
Cusp forms 2560 328 2232
Eisenstein series 256 0 256

Trace form

\( 328q - 82q^{4} - 8q^{5} - 2q^{6} - 82q^{9} + O(q^{10}) \) \( 328q - 82q^{4} - 8q^{5} - 2q^{6} - 82q^{9} + 12q^{10} - 24q^{11} - 8q^{13} + 14q^{15} - 82q^{16} + 32q^{17} - 4q^{19} - 8q^{20} - 10q^{22} - 16q^{23} - 2q^{24} - 94q^{25} - 4q^{26} + 12q^{29} - 4q^{30} + 14q^{31} + 6q^{33} + 24q^{34} - 82q^{36} - 48q^{37} - 4q^{38} + 8q^{39} + 2q^{40} - 4q^{41} - 48q^{43} + 16q^{44} - 8q^{45} - 20q^{46} + 28q^{47} - 24q^{50} + 36q^{51} - 8q^{52} - 44q^{53} + 8q^{54} - 32q^{55} - 28q^{57} + 14q^{58} - 44q^{59} - 16q^{60} + 28q^{61} - 36q^{62} - 82q^{64} + 56q^{65} - 12q^{66} + 64q^{67} + 32q^{68} - 32q^{69} + 44q^{71} + 46q^{73} + 16q^{74} + 8q^{75} + 16q^{76} + 12q^{79} + 12q^{80} - 82q^{81} + 36q^{82} + 36q^{83} + 88q^{85} + 56q^{86} + 12q^{87} + 10q^{88} - 16q^{89} - 8q^{90} + 4q^{92} + 4q^{93} + 32q^{94} - 52q^{95} - 2q^{96} - 4q^{97} - 4q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3234, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(539, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1078, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1617, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database