Properties

Label 3150.2.bx
Level 3150
Weight 2
Character orbit bx
Rep. character \(\chi_{3150}(629,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 320
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.bx (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 525 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 2944 320 2624
Cusp forms 2816 320 2496
Eisenstein series 128 0 128

Trace form

\( 320q - 80q^{4} + O(q^{10}) \) \( 320q - 80q^{4} - 80q^{16} - 40q^{22} + 20q^{28} + 24q^{46} - 8q^{49} - 80q^{64} + 60q^{70} - 16q^{79} + 40q^{88} - 104q^{91} + O(q^{100}) \)

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