Properties

Label 3150.2.cz
Level 3150
Weight 2
Character orbit cz
Rep. character \(\chi_{3150}(79,\cdot)\)
Character field \(\Q(\zeta_{30})\)
Dimension 1920
Sturm bound 1440

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Defining parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.cz (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 1575 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3150, [\chi])\).

Total New Old
Modular forms 5824 1920 3904
Cusp forms 5696 1920 3776
Eisenstein series 128 0 128

Trace form

\( 1920q - 240q^{4} + O(q^{10}) \) \( 1920q - 240q^{4} - 38q^{15} + 240q^{16} - 12q^{21} + 96q^{26} + 60q^{27} + 2q^{30} - 50q^{33} + 34q^{35} - 32q^{39} - 32q^{41} - 90q^{45} + 12q^{50} + 12q^{51} - 12q^{55} + 24q^{59} + 10q^{60} + 60q^{62} + 100q^{63} + 480q^{64} - 18q^{65} + 16q^{66} + 42q^{69} + 24q^{70} - 36q^{71} - 6q^{75} - 160q^{77} - 12q^{79} - 52q^{81} + 140q^{83} + 36q^{84} + 18q^{89} - 8q^{90} - 20q^{92} - 30q^{95} + 32q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3150, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3150, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database