Properties

Label 3234.2.be
Level 3234
Weight 2
Character orbit 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

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

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

\( S_{2}^{\mathrm{old}}(3234, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1617, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database