Properties

Label 3150.2.ed
Level 3150
Weight 2
Character orbit ed
Rep. character \(\chi_{3150}(53,\cdot)\)
Character field \(\Q(\zeta_{60})\)
Dimension 1280
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.ed (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 525 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 11776 1280 10496
Cusp forms 11264 1280 9984
Eisenstein series 512 0 512

Trace form

\( 1280q + 8q^{7} + O(q^{10}) \) \( 1280q + 8q^{7} + 8q^{10} - 160q^{16} + 112q^{22} - 16q^{25} - 32q^{28} - 16q^{37} - 32q^{43} - 32q^{55} - 8q^{58} - 32q^{67} + 136q^{70} - 64q^{73} - 128q^{82} + 64q^{85} + 24q^{88} + 128q^{97} + O(q^{100}) \)

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