Properties

Label 3234.2.ci
Level 3234
Weight 2
Character orbit ci
Rep. character \(\chi_{3234}(95,\cdot)\)
Character field \(\Q(\zeta_{210})\)
Dimension 10752
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.ci (of order \(210\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1617 \)
Character field: \(\Q(\zeta_{210})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 32640 10752 21888
Cusp forms 31872 10752 21120
Eisenstein series 768 0 768

Trace form

\( 10752q - 224q^{4} + O(q^{10}) \) \( 10752q - 224q^{4} - 224q^{16} - 10q^{22} + 228q^{25} - 90q^{27} + 10q^{28} + 6q^{31} - 24q^{33} + 32q^{34} + 4q^{37} + 130q^{40} + 108q^{42} - 28q^{45} + 148q^{49} - 238q^{55} + 80q^{57} + 388q^{58} - 80q^{61} + 100q^{63} + 448q^{64} + 48q^{66} - 32q^{67} + 80q^{69} + 84q^{70} + 20q^{72} - 20q^{73} + 28q^{75} - 32q^{78} + 204q^{81} + 16q^{82} + 40q^{84} + 160q^{85} - 2q^{88} + 160q^{90} + 200q^{91} + 10q^{93} - 640q^{94} + 32q^{97} - 760q^{99} + O(q^{100}) \)

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

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

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database