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Properties

Label 3150.2.cq
Level $3150$
Weight $2$
Character orbit 3150.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

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

Display 100 coefficients 10 coefficients

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

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