# Properties

 Label 525.4.bg Level $525$ Weight $4$ Character orbit 525.bg Rep. character $\chi_{525}(16,\cdot)$ Character field $\Q(\zeta_{15})$ Dimension $960$ Sturm bound $320$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$525 = 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 525.bg (of order $$15$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$175$$ Character field: $$\Q(\zeta_{15})$$ 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

 $$960q + 480q^{4} + 8q^{5} + 48q^{6} - 4q^{7} + 252q^{8} + 1080q^{9} + O(q^{10})$$ $$960q + 480q^{4} + 8q^{5} + 48q^{6} - 4q^{7} + 252q^{8} + 1080q^{9} - 6q^{10} + 84q^{11} + 132q^{14} + 84q^{15} + 1920q^{16} - 384q^{17} - 304q^{19} - 952q^{20} - 96q^{22} + 96q^{23} + 1152q^{24} - 86q^{25} + 1460q^{28} - 96q^{29} - 768q^{30} - 330q^{31} + 672q^{32} - 36q^{33} + 800q^{34} - 1220q^{35} - 8640q^{36} + 552q^{37} + 1846q^{38} + 438q^{40} + 576q^{41} - 1272q^{42} - 48q^{43} - 896q^{44} + 72q^{45} - 228q^{46} - 848q^{47} + 1056q^{48} + 516q^{49} + 10180q^{50} - 2142q^{52} + 960q^{53} - 216q^{54} + 452q^{55} - 2700q^{56} - 1392q^{57} + 508q^{58} + 984q^{59} + 1194q^{60} - 2120q^{61} + 6048q^{62} + 108q^{63} - 19284q^{64} + 140q^{65} - 1056q^{66} + 2852q^{67} + 7044q^{68} + 2208q^{69} + 1494q^{70} + 1472q^{71} - 1134q^{72} + 1392q^{73} + 2988q^{74} + 312q^{75} - 25544q^{76} - 3656q^{77} - 1488q^{78} + 1084q^{79} + 708q^{80} + 9720q^{81} - 3684q^{82} - 15536q^{83} + 6768q^{84} + 3544q^{85} - 336q^{86} - 12q^{87} - 354q^{88} + 648q^{90} - 1884q^{91} - 4924q^{92} + 5472q^{93} - 3104q^{94} + 1152q^{95} + 1182q^{96} + 12372q^{97} - 5664q^{98} + 1008q^{99} + O(q^{100})$$

## 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