# Properties

 Label 175.2.x Level 175 Weight 2 Character orbit x Rep. character $$\chi_{175}(3,\cdot)$$ Character field $$\Q(\zeta_{60})$$ Dimension 288 Newform subspaces 1 Sturm bound 40 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$175 = 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 175.x (of order $$60$$ and degree $$16$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$175$$ Character field: $$\Q(\zeta_{60})$$ Newform subspaces: $$1$$ Sturm bound: $$40$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(175, [\chi])$$.

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

## Trace form

 $$288q - 8q^{2} - 24q^{3} - 10q^{4} - 30q^{5} - 10q^{7} - 36q^{8} - 10q^{9} + O(q^{10})$$ $$288q - 8q^{2} - 24q^{3} - 10q^{4} - 30q^{5} - 10q^{7} - 36q^{8} - 10q^{9} - 36q^{10} - 6q^{11} - 36q^{12} - 20q^{14} - 28q^{15} - 30q^{16} - 42q^{17} - 14q^{18} - 30q^{19} - 12q^{21} + 32q^{22} - 40q^{23} + 2q^{25} - 48q^{26} + 22q^{28} - 58q^{30} - 18q^{31} + 8q^{32} - 30q^{33} - 2q^{35} + 40q^{36} - 10q^{37} + 72q^{38} + 30q^{39} - 48q^{40} + 6q^{42} - 108q^{43} - 10q^{44} + 186q^{45} - 6q^{46} - 54q^{47} - 248q^{50} - 16q^{51} + 216q^{52} + 50q^{53} - 30q^{54} + 4q^{56} - 216q^{57} - 4q^{58} + 90q^{59} + 96q^{60} - 18q^{61} - 66q^{63} - 100q^{64} + 14q^{65} - 90q^{66} + 4q^{67} + 342q^{68} - 60q^{70} - 24q^{71} + 58q^{72} - 6q^{73} + 216q^{75} - 80q^{77} - 132q^{78} - 10q^{79} - 6q^{80} - 10q^{81} + 216q^{82} + 20q^{84} - 48q^{85} - 6q^{86} - 48q^{87} - 122q^{88} + 120q^{89} - 12q^{91} - 4q^{92} + 106q^{93} - 30q^{94} - 98q^{95} - 90q^{96} + 222q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(175, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
175.2.x.a $$288$$ $$1.397$$ None $$-8$$ $$-24$$ $$-30$$ $$-10$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database