# Properties

 Label 525.2.bg Level 525 Weight 2 Character orbit bg Rep. character $$\chi_{525}(16,\cdot)$$ Character field $$\Q(\zeta_{15})$$ Dimension 320 Newform subspaces 2 Sturm bound 160 Trace bound 2

# Related objects

## Defining parameters

 Level: $$N$$ = $$525 = 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 525.bg (of order $$15$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$175$$ Character field: $$\Q(\zeta_{15})$$ Newform subspaces: $$2$$ Sturm bound: $$160$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(525, [\chi])$$.

Total New Old
Modular forms 672 320 352
Cusp forms 608 320 288
Eisenstein series 64 0 64

## Trace form

 $$320q + 40q^{4} - 2q^{5} - 8q^{6} + 8q^{7} - 36q^{8} + 40q^{9} + O(q^{10})$$ $$320q + 40q^{4} - 2q^{5} - 8q^{6} + 8q^{7} - 36q^{8} + 40q^{9} - 8q^{10} + 6q^{11} + 12q^{14} + 4q^{15} + 40q^{16} - 12q^{17} + 16q^{19} - 8q^{20} + 32q^{22} + 12q^{23} - 48q^{24} - 70q^{28} + 24q^{29} + 16q^{30} + 30q^{31} - 24q^{32} - 12q^{33} - 16q^{35} - 80q^{36} - 4q^{37} + 2q^{38} - 12q^{40} - 36q^{41} + 14q^{42} - 136q^{43} - 16q^{44} - 2q^{45} - 32q^{46} - 4q^{47} + 32q^{48} + 16q^{49} - 148q^{50} - 6q^{52} - 60q^{53} + 4q^{54} + 16q^{55} - 16q^{57} - 24q^{58} + 24q^{59} + 26q^{60} + 20q^{61} - 216q^{62} - 14q^{63} - 164q^{64} + 10q^{65} + 16q^{66} + 36q^{67} - 12q^{68} - 32q^{69} - 32q^{71} + 18q^{72} + 44q^{73} - 12q^{74} - 8q^{75} + 344q^{76} - 28q^{77} - 16q^{78} + 4q^{79} + 24q^{80} + 40q^{81} + 68q^{82} - 112q^{83} + 48q^{84} + 132q^{85} - 24q^{86} - 16q^{87} + 72q^{88} - 44q^{90} - 26q^{91} - 92q^{92} - 96q^{93} + 16q^{94} - 102q^{95} + 58q^{96} - 84q^{97} + 192q^{98} + 8q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(525, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
525.2.bg.a $$160$$ $$4.192$$ None $$-2$$ $$-20$$ $$0$$ $$4$$
525.2.bg.b $$160$$ $$4.192$$ None $$2$$ $$20$$ $$-2$$ $$4$$

## Decomposition of $$S_{2}^{\mathrm{old}}(525, [\chi])$$ into lower level spaces

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

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database