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

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

Decomposition of \(S_{2}^{\mathrm{new}}(3150, [\chi])\) into irreducible Hecke orbits

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

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