Properties

Label 3234.2.t
Level 3234
Weight 2
Character orbit t
Rep. character \(\chi_{3234}(587,\cdot)\)
Character field \(\Q(\zeta_{10})\)
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.t (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 231 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 2816 640 2176
Cusp forms 2560 640 1920
Eisenstein series 256 0 256

Trace form

\( 640q + 160q^{4} - 24q^{9} + O(q^{10}) \) \( 640q + 160q^{4} - 24q^{9} - 24q^{15} - 160q^{16} + 16q^{18} + 4q^{22} - 144q^{25} - 16q^{36} + 24q^{37} - 80q^{39} + 64q^{43} + 16q^{46} + 32q^{51} - 88q^{57} - 92q^{58} - 16q^{60} + 160q^{64} + 64q^{67} + 24q^{72} + 96q^{78} - 184q^{79} + 112q^{81} - 40q^{85} - 4q^{88} + 100q^{93} + 216q^{99} + O(q^{100}) \)

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