Properties

Label 3234.2.cc
Level 3234
Weight 2
Character orbit cc
Rep. character \(\chi_{3234}(125,\cdot)\)
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.cc (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

\( 5376q - 224q^{4} + 4q^{7} + O(q^{10}) \) \( 5376q - 224q^{4} + 4q^{7} + 224q^{16} + 16q^{18} + 20q^{21} + 10q^{22} + 216q^{25} + 126q^{27} + 6q^{28} + 8q^{37} - 40q^{39} - 42q^{40} + 108q^{42} + 64q^{43} - 28q^{45} + 152q^{49} + 24q^{51} + 14q^{55} - 88q^{57} + 230q^{58} + 42q^{63} - 224q^{64} + 64q^{67} - 56q^{69} - 16q^{70} + 24q^{72} + 32q^{78} - 88q^{79} + 36q^{81} + 96q^{85} + 112q^{87} + 4q^{88} - 184q^{91} + 52q^{93} + 336q^{94} - 736q^{99} + O(q^{100}) \)

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