Properties

 Label 175.2.s Level 175 Weight 2 Character orbit s Rep. character $$\chi_{175}(13,\cdot)$$ Character field $$\Q(\zeta_{20})$$ 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.s (of order $$20$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$175$$ Character field: $$\Q(\zeta_{20})$$ 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

 $$144q - 16q^{2} - 20q^{4} - 14q^{7} - 12q^{8} - 20q^{9} + O(q^{10})$$ $$144q - 16q^{2} - 20q^{4} - 14q^{7} - 12q^{8} - 20q^{9} - 12q^{11} - 10q^{14} - 20q^{15} + 12q^{16} - 28q^{18} - 6q^{21} + 16q^{22} - 8q^{23} - 20q^{25} - 70q^{28} + 40q^{30} - 20q^{32} - 40q^{35} - 28q^{36} + 4q^{37} - 60q^{39} - 30q^{42} + 72q^{43} - 20q^{44} - 12q^{46} + 140q^{50} - 32q^{51} - 104q^{53} - 22q^{56} + 120q^{57} - 32q^{58} - 120q^{60} + 48q^{63} + 40q^{64} - 20q^{65} - 16q^{67} + 90q^{70} - 12q^{71} - 64q^{72} + 74q^{77} + 60q^{78} - 20q^{79} - 8q^{81} + 190q^{84} - 12q^{86} + 92q^{88} - 6q^{91} - 20q^{92} - 160q^{93} + 80q^{95} + 162q^{98} + O(q^{100})$$

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.s.a $$144$$ $$1.397$$ None $$-16$$ $$0$$ $$0$$ $$-14$$

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database