Properties

Label 525.4.bf
Level $525$
Weight $4$
Character orbit 525.bf
Rep. character $\chi_{525}(32,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $560$
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.bf (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(320\)

Dimensions

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

Total New Old
Modular forms 1008 592 416
Cusp forms 912 560 352
Eisenstein series 96 32 64

Trace form

\( 560q + 2q^{3} - 48q^{6} - 4q^{7} + O(q^{10}) \) \( 560q + 2q^{3} - 48q^{6} - 4q^{7} + 94q^{12} + 16q^{13} + 4088q^{16} - 14q^{18} + 272q^{21} + 32q^{22} + 32q^{27} - 776q^{28} - 152q^{31} + 430q^{33} + 176q^{36} - 212q^{37} + 910q^{42} + 1360q^{43} - 2024q^{46} - 1604q^{48} + 524q^{51} - 68q^{52} - 3548q^{57} + 1572q^{58} - 968q^{61} + 2974q^{63} + 2764q^{66} + 1012q^{67} - 866q^{72} - 2804q^{73} + 1824q^{76} - 6888q^{78} + 5972q^{81} + 1112q^{82} + 52q^{87} - 1284q^{88} + 7976q^{91} - 3034q^{93} - 492q^{96} - 7496q^{97} + O(q^{100}) \)

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

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

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database