Properties

Label 3234.2.bj
Level 3234
Weight 2
Character orbit bj
Rep. character \(\chi_{3234}(19,\cdot)\)
Character field \(\Q(\zeta_{30})\)
Dimension 640
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.bj (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{30})\)
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

\( 640q - 80q^{4} + 24q^{5} - 80q^{9} + O(q^{10}) \) \( 640q - 80q^{4} + 24q^{5} - 80q^{9} - 8q^{11} + 12q^{15} + 80q^{16} - 60q^{17} + 12q^{22} - 8q^{23} - 108q^{25} + 24q^{26} + 40q^{29} - 18q^{31} + 6q^{33} - 160q^{36} + 36q^{37} - 24q^{38} - 30q^{40} - 12q^{44} + 24q^{45} - 48q^{47} - 40q^{51} - 10q^{58} - 4q^{60} + 60q^{61} + 160q^{64} - 64q^{67} + 60q^{68} + 144q^{71} + 180q^{73} + 40q^{74} - 24q^{75} + 60q^{79} + 36q^{80} + 80q^{81} + 96q^{82} + 280q^{85} + 36q^{86} + 26q^{88} + 48q^{89} - 16q^{92} + 40q^{93} + 20q^{95} - 16q^{99} + O(q^{100}) \)

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