Properties

Label 3150.3.dg
Level $3150$
Weight $3$
Character orbit 3150.dg
Rep. character $\chi_{3150}(389,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $3840$
Sturm bound $2160$

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Defining parameters

Level: \( N \) \(=\) \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 3150.dg (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1575 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(2160\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(3150, [\chi])\).

Total New Old
Modular forms 11584 3840 7744
Cusp forms 11456 3840 7616
Eisenstein series 128 0 128

Trace form

\( 3840 q - 1920 q^{4} + O(q^{10}) \) \( 3840 q - 1920 q^{4} + 58 q^{15} - 3840 q^{16} + 60 q^{21} + 420 q^{27} + 8 q^{30} + 100 q^{33} - 90 q^{35} + 340 q^{39} + 276 q^{45} - 240 q^{51} - 24 q^{55} - 44 q^{60} + 550 q^{63} - 7680 q^{64} - 320 q^{66} - 210 q^{69} + 192 q^{70} - 1590 q^{75} + 720 q^{77} - 240 q^{79} - 40 q^{81} - 180 q^{84} - 1350 q^{89} + 256 q^{90} - 720 q^{92} - 160 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(3150, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{3}^{\mathrm{old}}(3150, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)