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Properties

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

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

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

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