Properties

Label 3150.2.cr
Level 3150
Weight 2
Character orbit 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

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

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database