Properties

Label 3234.2.p
Level 3234
Weight 2
Character orbit p
Rep. character \(\chi_{3234}(901,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 160
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.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
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 160 1248
Cusp forms 1280 160 1120
Eisenstein series 128 0 128

Trace form

\( 160q + 80q^{4} - 24q^{5} + 80q^{9} + O(q^{10}) \) \( 160q + 80q^{4} - 24q^{5} + 80q^{9} + 8q^{11} + 8q^{15} - 80q^{16} - 12q^{22} + 8q^{23} + 68q^{25} - 24q^{26} - 12q^{31} - 6q^{33} + 160q^{36} - 36q^{37} + 24q^{38} - 8q^{44} - 24q^{45} + 48q^{47} + 4q^{60} - 160q^{64} + 64q^{67} + 176q^{71} + 24q^{75} + 24q^{80} - 80q^{81} + 24q^{82} + 24q^{86} - 6q^{88} + 72q^{89} + 16q^{92} + 16q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3234, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(539, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1078, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1617, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database