Properties

Label 3234.2.cf
Level 3234
Weight 2
Character orbit cf
Rep. character \(\chi_{3234}(5,\cdot)\)
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.cf (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

\( 10752q + 224q^{4} - 4q^{7} + O(q^{10}) \) \( 10752q + 224q^{4} - 4q^{7} - 12q^{10} - 224q^{16} + 8q^{18} + 16q^{21} - 10q^{22} - 228q^{25} - 126q^{27} - 6q^{28} - 18q^{31} + 132q^{33} + 4q^{37} - 20q^{39} - 66q^{40} - 108q^{42} - 64q^{43} + 76q^{45} + 148q^{49} + 12q^{51} + 322q^{55} + 88q^{57} - 284q^{58} + 12q^{63} - 448q^{64} + 120q^{66} + 32q^{67} + 56q^{69} + 100q^{70} + 12q^{72} + 96q^{73} + 204q^{75} - 32q^{78} - 44q^{79} - 108q^{81} - 24q^{82} + 36q^{84} - 96q^{85} + 452q^{87} + 2q^{88} + 184q^{91} + 26q^{93} - 192q^{94} + 736q^{99} + O(q^{100}) \)

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