Properties

Label 3234.2.n
Level 3234
Weight 2
Character orbit n
Rep. character \(\chi_{3234}(263,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 320
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.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 231 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 1408 320 1088
Cusp forms 1280 320 960
Eisenstein series 128 0 128

Trace form

\( 320q - 160q^{4} - 16q^{9} + O(q^{10}) \) \( 320q - 160q^{4} - 16q^{9} + 32q^{15} - 160q^{16} + 12q^{22} + 140q^{25} + 24q^{27} + 4q^{31} - 26q^{33} + 8q^{34} + 32q^{36} + 12q^{37} + 56q^{45} - 84q^{55} + 32q^{58} - 16q^{60} + 320q^{64} - 8q^{66} - 8q^{67} + 64q^{69} + 52q^{75} + 64q^{78} + 24q^{81} - 16q^{82} - 6q^{88} + 68q^{93} - 32q^{97} + 136q^{99} + O(q^{100}) \)

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