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Properties

Label 3150.3.cv
Level $3150$
Weight $3$
Character orbit 3150.cv
Rep. character $\chi_{3150}(127,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1200$
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.cv (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(2160\)

Dimensions

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

Total New Old
Modular forms 11648 1200 10448
Cusp forms 11392 1200 10192
Eisenstein series 256 0 256

Trace form

\( 1200 q - 4 q^{2} - 8 q^{5} + 8 q^{8} + O(q^{10}) \) \( 1200 q - 4 q^{2} - 8 q^{5} + 8 q^{8} + 12 q^{10} + 12 q^{13} + 1200 q^{16} + 12 q^{17} - 400 q^{19} - 16 q^{20} - 64 q^{22} + 8 q^{23} - 52 q^{25} + 40 q^{26} - 200 q^{29} - 64 q^{32} - 100 q^{34} - 140 q^{37} + 144 q^{38} - 8 q^{40} - 160 q^{41} + 248 q^{43} + 104 q^{47} - 92 q^{50} + 24 q^{52} - 68 q^{53} - 88 q^{55} + 16 q^{58} - 600 q^{59} + 240 q^{61} + 128 q^{62} - 1628 q^{65} - 664 q^{67} - 24 q^{68} + 112 q^{70} + 240 q^{71} + 44 q^{73} - 112 q^{77} + 800 q^{79} + 32 q^{80} - 208 q^{82} - 48 q^{83} + 1144 q^{85} - 32 q^{88} + 100 q^{89} + 656 q^{92} - 136 q^{95} - 508 q^{97} + 28 q^{98} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)