Properties

Label 3234.2.bo
Level 3234
Weight 2
Character orbit bo
Rep. character \(\chi_{3234}(509,\cdot)\)
Character field \(\Q(\zeta_{30})\)
Dimension 1280
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.bo (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 231 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 5632 1280 4352
Cusp forms 5120 1280 3840
Eisenstein series 512 0 512

Trace form

\( 1280q - 160q^{4} + 24q^{9} + O(q^{10}) \) \( 1280q - 160q^{4} + 24q^{9} - 12q^{10} - 48q^{15} + 160q^{16} + 8q^{18} + 20q^{22} + 132q^{25} - 18q^{31} + 132q^{33} - 32q^{36} - 12q^{37} + 20q^{39} + 18q^{40} - 64q^{43} + 48q^{45} - 16q^{46} + 4q^{51} + 88q^{57} - 46q^{58} + 16q^{60} + 320q^{64} + 120q^{66} + 32q^{67} + 12q^{72} + 96q^{73} + 204q^{75} + 96q^{78} + 52q^{79} + 68q^{81} - 24q^{82} - 368q^{85} + 228q^{87} + 10q^{88} - 22q^{93} + 144q^{94} - 48q^{99} + O(q^{100}) \)

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

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

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database