# Properties

 Label 175.2.t Level 175 Weight 2 Character orbit t Rep. character $$\chi_{175}(4,\cdot)$$ Character field $$\Q(\zeta_{30})$$ Dimension 144 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.t (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$175$$ Character field: $$\Q(\zeta_{30})$$ 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 176 176 0
Cusp forms 144 144 0
Eisenstein series 32 32 0

## Trace form

 $$144q - 5q^{2} - 5q^{3} - 19q^{4} - 3q^{5} - 12q^{6} - 50q^{8} - 17q^{9} + O(q^{10})$$ $$144q - 5q^{2} - 5q^{3} - 19q^{4} - 3q^{5} - 12q^{6} - 50q^{8} - 17q^{9} - q^{10} - 5q^{12} - 20q^{13} - 18q^{14} + 12q^{15} + 5q^{16} + 5q^{17} - 11q^{19} - 24q^{20} - 9q^{21} - 60q^{22} + 25q^{23} + 50q^{24} - 11q^{25} - 60q^{26} + 40q^{27} - 24q^{29} + 53q^{30} + 15q^{31} + 20q^{33} - 20q^{34} - 14q^{35} + 16q^{36} - 5q^{37} - 20q^{38} + 13q^{39} + 7q^{40} - 62q^{41} + 40q^{42} - 15q^{44} - 41q^{45} - 27q^{46} - 5q^{47} - 38q^{49} + 54q^{50} - 8q^{51} - 130q^{52} + 25q^{53} - 29q^{54} - 20q^{55} + 32q^{56} - 65q^{58} - 39q^{59} + 79q^{60} + 7q^{61} - 20q^{62} - 45q^{63} + 34q^{64} - 13q^{65} + 11q^{66} + 25q^{67} + 74q^{69} + 85q^{70} - 46q^{71} + 60q^{72} + 35q^{73} + 6q^{74} - 107q^{75} + 180q^{76} - 5q^{77} + 10q^{78} + 9q^{79} + 88q^{80} - 59q^{81} + 90q^{83} - 51q^{84} - 6q^{85} + 11q^{86} - 5q^{87} + 140q^{88} - 42q^{89} + 4q^{90} + 22q^{91} + 10q^{92} + 5q^{94} + 13q^{95} + 53q^{96} + 120q^{97} - 180q^{98} - 44q^{99} + O(q^{100})$$

## 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.t.a $$144$$ $$1.397$$ None $$-5$$ $$-5$$ $$-3$$ $$0$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database