Properties

Label 3234.2.by
Level 3234
Weight 2
Character orbit by
Rep. character \(\chi_{3234}(29,\cdot)\)
Character field \(\Q(\zeta_{70})\)
Dimension 5376
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.by (of order \(70\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1617 \)
Character field: \(\Q(\zeta_{70})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 16320 5376 10944
Cusp forms 15936 5376 10560
Eisenstein series 384 0 384

Trace form

\( 5376q + 224q^{4} + O(q^{10}) \) \( 5376q + 224q^{4} + 224q^{16} + 10q^{22} - 216q^{25} + 90q^{27} - 10q^{28} + 12q^{31} - 84q^{33} - 32q^{34} + 8q^{37} + 50q^{40} - 108q^{42} - 20q^{45} + 152q^{49} + 10q^{55} - 80q^{57} - 190q^{58} + 80q^{61} - 10q^{63} + 224q^{64} + 72q^{66} - 64q^{67} + 100q^{69} + 40q^{72} + 20q^{73} + 56q^{75} + 32q^{78} + 156q^{81} + 8q^{82} + 20q^{84} - 160q^{85} - 4q^{88} + 80q^{90} - 200q^{91} + 20q^{93} + 400q^{94} - 32q^{97} + 760q^{99} + O(q^{100}) \)

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