Properties

Label 3150.2.cr
Level $3150$
Weight $2$
Character orbit 3150.cr
Rep. character $\chi_{3150}(361,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $800$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3150.cr (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3150, [\chi])\).

Total New Old
Modular forms 5888 800 5088
Cusp forms 5632 800 4832
Eisenstein series 256 0 256

Trace form

\( 800 q + 100 q^{4} - 2 q^{5} + O(q^{10}) \) \( 800 q + 100 q^{4} - 2 q^{5} + 2 q^{10} + 6 q^{11} + 100 q^{16} + 4 q^{19} + 4 q^{20} - 32 q^{22} - 14 q^{23} + 48 q^{26} - 2 q^{28} + 24 q^{29} - 6 q^{31} - 16 q^{34} - 24 q^{35} - 20 q^{37} - 8 q^{38} + 2 q^{40} - 4 q^{41} - 72 q^{43} - 4 q^{44} + 12 q^{46} + 20 q^{47} - 16 q^{50} - 16 q^{53} + 24 q^{55} + 8 q^{58} + 8 q^{61} - 200 q^{64} + 18 q^{65} + 32 q^{67} - 40 q^{68} + 46 q^{70} + 4 q^{71} - 36 q^{73} + 16 q^{74} + 32 q^{76} - 8 q^{77} - 2 q^{80} - 64 q^{82} + 40 q^{83} + 12 q^{85} - 12 q^{86} - 14 q^{88} - 54 q^{89} - 4 q^{91} - 32 q^{92} + 32 q^{94} - 32 q^{95} + 132 q^{97} + 32 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3150, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3150, [\chi])\) into lower level spaces

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