Properties

Label 3234.2.v
Level 3234
Weight 2
Character orbit v
Rep. character \(\chi_{3234}(391,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 320
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.v (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 2816 320 2496
Cusp forms 2560 320 2240
Eisenstein series 256 0 256

Trace form

\( 320q + 80q^{4} + 80q^{9} + O(q^{10}) \) \( 320q + 80q^{4} + 80q^{9} - 16q^{11} - 12q^{15} - 80q^{16} + 12q^{22} - 16q^{23} + 96q^{25} - 40q^{29} - 80q^{36} + 24q^{37} - 24q^{44} - 80q^{51} - 20q^{58} - 8q^{60} + 80q^{64} + 64q^{67} + 144q^{71} + 80q^{74} + 120q^{79} - 80q^{81} + 80q^{85} + 72q^{86} + 28q^{88} + 16q^{92} + 8q^{93} + 40q^{95} + 16q^{99} + O(q^{100}) \)

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