Properties

Label 3234.2.bl
Level 3234
Weight 2
Character orbit bl
Rep. character \(\chi_{3234}(557,\cdot)\)
Character field \(\Q(\zeta_{30})\)
Dimension 1280
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.bl (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 231 \)
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 1280 4352
Cusp forms 5120 1280 3840
Eisenstein series 512 0 512

Trace form

\( 1280q + 160q^{4} - 24q^{9} + O(q^{10}) \) \( 1280q + 160q^{4} - 24q^{9} + 48q^{15} + 160q^{16} - 12q^{22} - 180q^{25} + 36q^{27} + 6q^{31} - 24q^{33} + 32q^{34} - 32q^{36} - 12q^{37} - 40q^{39} - 10q^{40} - 56q^{45} - 40q^{51} + 84q^{55} + 80q^{57} + 38q^{58} + 16q^{60} - 80q^{61} - 320q^{64} + 48q^{66} - 32q^{67} + 136q^{69} + 20q^{72} - 20q^{73} + 28q^{75} + 96q^{78} + 76q^{81} + 16q^{82} + 240q^{85} + 6q^{88} + 160q^{90} - 38q^{93} - 80q^{94} + 32q^{97} + 24q^{99} + O(q^{100}) \)

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

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

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database