Properties

Label 3234.2.bt
Level 3234
Weight 2
Character orbit bt
Rep. character \(\chi_{3234}(65,\cdot)\)
Character field \(\Q(\zeta_{42})\)
Dimension 2688
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.bt (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1617 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 8160 2688 5472
Cusp forms 7968 2688 5280
Eisenstein series 192 0 192

Trace form

\( 2688q + 224q^{4} + O(q^{10}) \) \( 2688q + 224q^{4} + 224q^{16} + 10q^{22} - 228q^{25} - 60q^{27} + 4q^{31} - 26q^{33} + 8q^{34} - 4q^{37} - 88q^{42} + 28q^{45} - 228q^{49} + 238q^{55} + 172q^{58} - 448q^{64} - 8q^{66} - 8q^{67} + 120q^{69} - 24q^{70} + 52q^{75} + 32q^{78} + 136q^{81} - 16q^{82} + 2q^{88} - 200q^{91} + 20q^{93} - 32q^{97} - 200q^{99} + O(q^{100}) \)

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