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Properties

Label 3150.3.du
Level $3150$
Weight $3$
Character orbit 3150.du
Rep. character $\chi_{3150}(271,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1600$
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.du (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
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 11648 1600 10048
Cusp forms 11392 1600 9792
Eisenstein series 256 0 256

Trace form

\( 1600 q + 400 q^{4} + 6 q^{5} - 20 q^{7} + O(q^{10}) \) \( 1600 q + 400 q^{4} + 6 q^{5} - 20 q^{7} + 24 q^{10} + 30 q^{11} + 800 q^{16} - 108 q^{17} + 16 q^{22} + 12 q^{23} - 14 q^{25} + 72 q^{28} - 120 q^{29} + 180 q^{31} - 220 q^{35} - 100 q^{37} - 96 q^{38} - 48 q^{40} - 536 q^{43} - 40 q^{44} - 120 q^{46} - 156 q^{47} + 20 q^{49} - 288 q^{50} - 408 q^{53} - 64 q^{58} - 360 q^{59} + 180 q^{61} - 3200 q^{64} + 176 q^{65} - 80 q^{67} - 864 q^{68} + 360 q^{70} - 380 q^{71} - 420 q^{73} - 160 q^{74} + 108 q^{77} + 40 q^{79} - 24 q^{80} + 1536 q^{82} - 800 q^{85} - 120 q^{86} + 64 q^{88} + 1350 q^{89} - 380 q^{91} + 192 q^{92} - 480 q^{94} + 178 q^{95} - 256 q^{98} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)