Properties

Label 3150.2.cq
Level 3150
Weight 2
Character orbit cq
Rep. character \(\chi_{3150}(331,\cdot)\)
Character field \(\Q(\zeta_{15})\)
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.cq (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 1575 \)
Character field: \(\Q(\zeta_{15})\)
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

\( 1920q + 240q^{4} + O(q^{10}) \) \( 1920q + 240q^{4} + 26q^{15} + 240q^{16} + 12q^{17} - 16q^{18} + 12q^{21} + 16q^{23} - 96q^{26} - 48q^{27} - 14q^{30} + 30q^{33} + 14q^{35} - 32q^{39} + 32q^{41} + 28q^{42} - 50q^{45} + 4q^{50} - 12q^{51} - 40q^{53} + 12q^{55} + 96q^{57} + 24q^{58} + 24q^{59} - 2q^{60} + 36q^{62} + 16q^{63} - 480q^{64} + 10q^{65} - 16q^{66} + 96q^{68} + 42q^{69} - 24q^{70} + 36q^{71} + 8q^{72} - 226q^{75} - 112q^{77} - 16q^{78} - 12q^{79} + 52q^{81} + 84q^{83} + 36q^{84} + 88q^{87} + 18q^{89} + 88q^{90} + 12q^{92} - 116q^{93} - 34q^{95} + 48q^{98} + 32q^{99} + O(q^{100}) \)

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