Properties

Label 525.4.bc
Level $525$
Weight $4$
Character orbit 525.bc
Rep. character $\chi_{525}(82,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $288$
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.bc (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
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 288 720
Cusp forms 912 288 624
Eisenstein series 96 0 96

Trace form

\( 288q + 4q^{7} - 168q^{8} + O(q^{10}) \) \( 288q + 4q^{7} - 168q^{8} - 112q^{11} + 2080q^{16} + 48q^{21} - 624q^{22} + 64q^{23} - 1824q^{26} - 628q^{28} + 1056q^{31} + 672q^{32} + 108q^{33} - 10368q^{36} + 552q^{37} + 4044q^{38} + 1068q^{42} - 720q^{43} - 680q^{46} - 240q^{47} - 672q^{51} - 4644q^{52} - 1728q^{53} - 9792q^{56} - 1392q^{57} - 512q^{58} - 1296q^{61} + 288q^{63} + 8208q^{66} + 3784q^{67} + 8844q^{68} + 256q^{71} + 756q^{72} + 3312q^{73} + 6600q^{77} + 1200q^{78} + 11664q^{81} - 6084q^{82} - 7784q^{86} - 5652q^{87} - 4844q^{88} - 11976q^{91} + 2152q^{92} - 1368q^{93} - 20184q^{98} + O(q^{100}) \)

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