Properties

Label 3150.2.df
Level 3150
Weight 2
Character orbit df
Rep. character \(\chi_{3150}(131,\cdot)\)
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.df (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

\( 1920q + 480q^{4} + O(q^{10}) \) \( 1920q + 480q^{4} - 26q^{15} - 480q^{16} + 36q^{17} + 8q^{18} + 12q^{21} - 24q^{23} - 36q^{27} + 2q^{30} - 30q^{35} - 4q^{39} - 28q^{42} - 96q^{45} + 12q^{50} + 24q^{51} + 80q^{57} - 12q^{58} - 14q^{60} + 108q^{62} - 50q^{63} + 480q^{64} + 144q^{68} - 126q^{69} - 24q^{70} - 8q^{72} + 180q^{75} - 144q^{77} - 16q^{78} - 24q^{79} + 44q^{81} + 18q^{84} + 36q^{87} - 90q^{89} + 72q^{90} - 36q^{92} + 112q^{93} + 32q^{99} + O(q^{100}) \)

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