Properties

Label 3234.2.g
Level 3234
Weight 2
Character orbit g
Rep. character \(\chi_{3234}(881,\cdot)\)
Character field \(\Q\)
Dimension 136
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.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
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 704 136 568
Cusp forms 640 136 504
Eisenstein series 64 0 64

Trace form

\( 136q - 136q^{4} - 8q^{9} + O(q^{10}) \) \( 136q - 136q^{4} - 8q^{9} - 40q^{15} + 136q^{16} + 16q^{18} + 152q^{25} - 32q^{30} + 8q^{36} + 24q^{37} + 8q^{39} + 32q^{43} - 64q^{46} + 56q^{51} + 40q^{57} + 8q^{58} + 40q^{60} - 136q^{64} + 32q^{67} - 16q^{72} - 24q^{81} + 16q^{85} - 40q^{93} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3234, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1617, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database