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Properties

Label 3150.3.t
Level $3150$
Weight $3$
Character orbit 3150.t
Rep. character $\chi_{3150}(599,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $576$
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.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(2160\)

Dimensions

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

Total New Old
Modular forms 2928 576 2352
Cusp forms 2832 576 2256
Eisenstein series 96 0 96

Trace form

\( 576 q - 576 q^{4} - 16 q^{6} + 8 q^{9} + O(q^{10}) \) \( 576 q - 576 q^{4} - 16 q^{6} + 8 q^{9} + 72 q^{14} - 1152 q^{16} + 44 q^{21} + 16 q^{24} + 72 q^{29} - 80 q^{36} - 28 q^{39} - 144 q^{41} - 144 q^{44} + 24 q^{46} + 96 q^{49} - 152 q^{51} + 112 q^{54} + 96 q^{61} + 4608 q^{64} + 160 q^{66} + 124 q^{69} + 96 q^{79} + 112 q^{81} - 128 q^{84} - 828 q^{89} + 336 q^{94} + 32 q^{96} - 48 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{3}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)