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Properties

Label 3234.2.be
Level $3234$
Weight $2$
Character orbit 3234.be
Rep. character $\chi_{3234}(659,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $1344$
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.be (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1617 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 4080 1344 2736
Cusp forms 3984 1344 2640
Eisenstein series 96 0 96

Trace form

\( 1344 q - 224 q^{4} + O(q^{10}) \) \( 1344 q - 224 q^{4} - 224 q^{16} - 10 q^{22} + 216 q^{25} + 60 q^{27} + 8 q^{31} - 16 q^{33} - 8 q^{34} - 8 q^{37} + 88 q^{42} + 20 q^{45} - 72 q^{49} - 10 q^{55} - 160 q^{58} - 224 q^{64} + 8 q^{66} - 16 q^{67} - 60 q^{70} + 104 q^{75} - 32 q^{78} + 104 q^{81} - 8 q^{82} + 4 q^{88} + 200 q^{91} + 40 q^{93} + 32 q^{97} + 200 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3234, [\chi]) \cong \)