Properties

Label 3234.2.c
Level 3234
Weight 2
Character orbit c
Rep. character \(\chi_{3234}(197,\cdot)\)
Character field \(\Q\)
Dimension 164
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 704 164 540
Cusp forms 640 164 476
Eisenstein series 64 0 64

Trace form

\( 164q - 4q^{3} + 164q^{4} + 12q^{9} + O(q^{10}) \) \( 164q - 4q^{3} + 164q^{4} + 12q^{9} - 4q^{12} + 8q^{15} + 164q^{16} - 140q^{25} - 4q^{27} - 8q^{31} - 8q^{33} - 8q^{34} + 12q^{36} - 16q^{37} + 8q^{45} - 4q^{48} - 16q^{55} + 40q^{58} + 8q^{60} + 164q^{64} + 20q^{66} - 32q^{67} + 48q^{69} + 92q^{75} - 40q^{78} + 20q^{81} + 16q^{82} + 8q^{93} + 64q^{97} + 16q^{99} + O(q^{100}) \)

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

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

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database