Properties

Label 525.4.bh
Level $525$
Weight $4$
Character orbit 525.bh
Rep. character $\chi_{525}(13,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $960$
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.bh (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(320\)

Dimensions

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

Total New Old
Modular forms 1952 960 992
Cusp forms 1888 960 928
Eisenstein series 64 0 64

Trace form

\( 960q - 4q^{7} + 168q^{8} + O(q^{10}) \) \( 960q - 4q^{7} + 168q^{8} - 168q^{15} + 3840q^{16} + 912q^{22} + 480q^{23} - 520q^{25} - 1772q^{28} + 160q^{29} - 192q^{30} + 1344q^{32} + 1328q^{35} + 8640q^{36} + 456q^{37} - 1068q^{42} + 928q^{43} + 14112q^{50} - 4192q^{53} - 696q^{57} - 3016q^{58} - 840q^{60} + 36q^{63} - 19320q^{64} + 4720q^{65} + 4784q^{67} + 2100q^{70} + 1512q^{72} - 2352q^{77} - 1416q^{78} + 19440q^{81} - 11280q^{84} + 472q^{85} - 6088q^{88} - 10600q^{92} - 5472q^{93} + 19552q^{95} + 31048q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database