Properties

Label 525.4.g
Level $525$
Weight $4$
Character orbit 525.g
Rep. character $\chi_{525}(524,\cdot)$
Character field $\Q$
Dimension $140$
Sturm bound $320$

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Defining parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 525.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q\)
Sturm bound: \(320\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(525, [\chi])\).

Total New Old
Modular forms 252 148 104
Cusp forms 228 140 88
Eisenstein series 24 8 16

Trace form

\( 140q + 552q^{4} + 92q^{9} + O(q^{10}) \) \( 140q + 552q^{4} + 92q^{9} + 2104q^{16} + 60q^{21} + 1176q^{36} + 384q^{39} + 2480q^{46} - 32q^{49} - 1968q^{51} + 11584q^{64} - 3376q^{79} - 4820q^{81} + 1044q^{84} - 1116q^{91} - 8696q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(525, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(525, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database