Properties

Label 525.4.q
Level $525$
Weight $4$
Character orbit 525.q
Rep. character $\chi_{525}(299,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $280$
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.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(320\)

Dimensions

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

Total New Old
Modular forms 504 296 208
Cusp forms 456 280 176
Eisenstein series 48 16 32

Trace form

\( 280q - 540q^{4} - 2q^{9} + O(q^{10}) \) \( 280q - 540q^{4} - 2q^{9} - 2020q^{16} - 96q^{19} - 582q^{21} - 252q^{24} - 840q^{31} + 1008q^{36} - 120q^{39} + 1792q^{46} - 1108q^{49} + 198q^{51} - 4398q^{54} + 420q^{61} + 12752q^{64} + 168q^{66} + 1120q^{79} - 4342q^{81} + 9222q^{84} + 7740q^{91} - 9132q^{94} + 7758q^{96} + 764q^{99} + O(q^{100}) \)

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