Properties

Label 525.4.j
Level $525$
Weight $4$
Character orbit 525.j
Rep. character $\chi_{525}(218,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $216$
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.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Sturm bound: \(320\)

Dimensions

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

Total New Old
Modular forms 504 216 288
Cusp forms 456 216 240
Eisenstein series 48 0 48

Trace form

\( 216q - 8q^{3} + O(q^{10}) \) \( 216q - 8q^{3} + 128q^{12} + 144q^{13} - 2544q^{16} - 460q^{18} - 224q^{21} - 576q^{22} + 592q^{27} + 1920q^{31} + 56q^{33} - 1856q^{36} - 2088q^{37} + 140q^{42} - 240q^{43} - 1056q^{46} - 3208q^{48} + 1720q^{51} - 240q^{52} + 1112q^{57} - 840q^{58} + 3648q^{61} + 1064q^{63} + 2576q^{66} + 2832q^{67} + 296q^{72} - 1776q^{73} - 14592q^{76} + 4500q^{78} + 4288q^{81} - 1680q^{82} + 392q^{87} + 5352q^{88} - 2016q^{91} + 5488q^{93} + 576q^{96} + 7872q^{97} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database