Properties

Label 3150.3.cp
Level $3150$
Weight $3$
Character orbit 3150.cp
Rep. character $\chi_{3150}(193,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1152$
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.cp (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(2160\)

Dimensions

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

Total New Old
Modular forms 5856 1152 4704
Cusp forms 5664 1152 4512
Eisenstein series 192 0 192

Trace form

\( 1152 q + 32 q^{6} + O(q^{10}) \) \( 1152 q + 32 q^{6} - 96 q^{11} + 2304 q^{16} + 36 q^{17} - 64 q^{18} - 96 q^{21} - 96 q^{23} - 144 q^{27} + 20 q^{33} - 96 q^{36} + 96 q^{41} + 64 q^{42} + 48 q^{46} + 288 q^{51} - 360 q^{53} + 192 q^{56} + 168 q^{57} + 96 q^{58} - 192 q^{61} + 288 q^{62} + 544 q^{63} + 144 q^{68} + 384 q^{71} + 64 q^{72} + 384 q^{77} + 256 q^{78} + 256 q^{81} - 504 q^{83} - 576 q^{86} - 856 q^{87} + 96 q^{92} + 276 q^{93} + 64 q^{96} - 288 q^{98} + O(q^{100}) \)

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

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