Properties

Label 525.4.m
Level $525$
Weight $4$
Character orbit 525.m
Rep. character $\chi_{525}(118,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $144$
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.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
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 504 144 360
Cusp forms 456 144 312
Eisenstein series 48 0 48

Trace form

\( 144q - 4q^{7} + 168q^{8} + O(q^{10}) \) \( 144q - 4q^{7} + 168q^{8} - 224q^{11} - 2752q^{16} - 48q^{21} + 192q^{22} - 400q^{23} - 1052q^{28} + 1344q^{32} - 5184q^{36} + 456q^{37} - 1068q^{42} - 192q^{43} - 4024q^{46} - 1344q^{51} + 1728q^{53} + 96q^{56} - 696q^{57} - 3016q^{58} + 36q^{63} + 4784q^{67} + 6176q^{71} + 1512q^{72} - 2352q^{77} - 1416q^{78} - 11664q^{81} - 11704q^{86} - 2128q^{88} + 9528q^{91} - 10600q^{92} + 1368q^{93} + 3888q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database