Properties

Label 3234.2.k
Level 3234
Weight 2
Character orbit k
Rep. character \(\chi_{3234}(815,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 264
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.k (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 1408 264 1144
Cusp forms 1280 264 1016
Eisenstein series 128 0 128

Trace form

\( 264q + 132q^{4} - 4q^{9} + O(q^{10}) \) \( 264q + 132q^{4} - 4q^{9} - 8q^{15} - 132q^{16} - 16q^{18} + 24q^{19} + 12q^{24} - 124q^{25} + 8q^{30} - 24q^{31} - 8q^{36} - 44q^{37} + 28q^{39} + 128q^{43} - 48q^{45} - 8q^{46} - 20q^{51} + 24q^{52} + 36q^{54} + 8q^{57} - 20q^{58} - 4q^{60} - 264q^{64} + 48q^{67} + 16q^{72} - 48q^{73} + 36q^{75} + 56q^{79} + 36q^{81} - 24q^{82} - 16q^{85} + 36q^{87} + 52q^{93} + 48q^{94} + 12q^{96} + O(q^{100}) \)

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

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

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database