Properties

Label 525.4.t
Level $525$
Weight $4$
Character orbit 525.t
Rep. character $\chi_{525}(26,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $292$
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.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
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 504 316 188
Cusp forms 456 292 164
Eisenstein series 48 24 24

Trace form

\( 292q + 3q^{3} + 562q^{4} - 36q^{7} + 3q^{9} + O(q^{10}) \) \( 292q + 3q^{3} + 562q^{4} - 36q^{7} + 3q^{9} - 138q^{12} - 1950q^{16} + 116q^{18} + 420q^{19} - 165q^{21} - 140q^{22} - 90q^{24} - 98q^{28} - 114q^{31} + 111q^{33} + 1044q^{36} + 552q^{37} + 954q^{39} - 1068q^{42} + 348q^{43} + 824q^{46} - 1204q^{49} - 183q^{51} - 3756q^{52} + 252q^{54} + 1362q^{57} - 710q^{58} + 2778q^{61} + 361q^{63} - 10548q^{64} + 162q^{66} + 1804q^{67} - 2258q^{72} + 2148q^{73} - 504q^{78} - 614q^{79} - 801q^{81} + 792q^{82} + 1374q^{84} + 5118q^{87} - 2782q^{88} - 838q^{91} + 2343q^{93} + 8376q^{94} - 2700q^{96} - 3006q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database