Properties

Label 3150.2.dl
Level 3150
Weight 2
Character orbit dl
Rep. character \(\chi_{3150}(341,\cdot)\)
Character field \(\Q(\zeta_{30})\)
Dimension 640
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.dl (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 525 \)
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 640 5248
Cusp forms 5632 640 4992
Eisenstein series 256 0 256

Trace form

\( 640q - 80q^{4} - 8q^{7} + O(q^{10}) \) \( 640q - 80q^{4} - 8q^{7} - 12q^{10} + 80q^{16} - 32q^{22} + 4q^{25} - 12q^{28} - 36q^{31} - 16q^{37} - 12q^{40} - 32q^{43} + 24q^{46} + 8q^{49} + 8q^{58} + 160q^{64} - 32q^{67} - 108q^{70} + 192q^{73} - 8q^{79} + 384q^{82} - 80q^{85} + 4q^{88} - 104q^{91} + 96q^{94} + O(q^{100}) \)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database