Properties

Label 3150.2.dv
Level 3150
Weight 2
Character orbit dv
Rep. character \(\chi_{3150}(109,\cdot)\)
Character field \(\Q(\zeta_{30})\)
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.dv (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 175 \)
Character field: \(\Q(\zeta_{30})\)
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

\( 800q - 100q^{4} - 2q^{5} + O(q^{10}) \) \( 800q - 100q^{4} - 2q^{5} + 2q^{10} - 6q^{11} + 100q^{16} - 20q^{17} + 4q^{19} - 4q^{20} - 40q^{22} - 30q^{23} - 12q^{25} - 48q^{26} + 10q^{28} + 24q^{29} + 6q^{31} - 16q^{34} - 4q^{35} - 2q^{40} + 4q^{41} - 4q^{44} - 12q^{46} - 16q^{50} - 20q^{53} + 16q^{55} - 8q^{61} + 120q^{62} + 200q^{64} - 34q^{65} - 10q^{70} - 4q^{71} + 40q^{73} + 16q^{74} - 32q^{76} + 80q^{77} - 2q^{80} + 120q^{83} - 68q^{85} + 12q^{86} + 10q^{88} - 54q^{89} + 4q^{91} + 40q^{92} + 32q^{94} + 44q^{95} + 20q^{97} + 40q^{98} + O(q^{100}) \)

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