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Properties

Label 3234.2.g
Level $3234$
Weight $2$
Character orbit 3234.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

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

Display 100 coefficients 10 coefficients

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

\( S_{2}^{\mathrm{old}}(3234, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1617, [\chi])\)\(^{\oplus 2}\)