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Properties

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

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

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

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