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Properties

Label 3150.3.ea
Level $3150$
Weight $3$
Character orbit 3150.ea
Rep. character $\chi_{3150}(67,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $7680$
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.ea (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1575 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(2160\)

Dimensions

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

Total New Old
Modular forms 23168 7680 15488
Cusp forms 22912 7680 15232
Eisenstein series 256 0 256

Trace form

\( 7680 q + O(q^{10}) \) \( 7680 q - 12 q^{15} - 3840 q^{16} + 36 q^{17} - 64 q^{18} - 96 q^{23} - 144 q^{27} + 48 q^{30} + 20 q^{33} - 72 q^{35} + 400 q^{39} + 64 q^{42} + 380 q^{45} + 96 q^{50} - 360 q^{53} + 808 q^{57} + 96 q^{58} - 32 q^{60} - 1152 q^{62} - 1656 q^{63} - 48 q^{65} - 576 q^{68} - 700 q^{69} + 64 q^{72} - 592 q^{75} - 576 q^{77} + 256 q^{78} + 2016 q^{83} + 1200 q^{84} - 856 q^{87} - 1500 q^{89} + 320 q^{90} + 96 q^{92} + 276 q^{93} + 576 q^{95} - 288 q^{98} + O(q^{100}) \)

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

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