# Properties

 Label 75.2.l Level 75 Weight 2 Character orbit l Rep. character $$\chi_{75}(2,\cdot)$$ Character field $$\Q(\zeta_{20})$$ Dimension 64 Newform subspaces 1 Sturm bound 20 Trace bound 0

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## Defining parameters

 Level: $$N$$ = $$75 = 3 \cdot 5^{2}$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 75.l (of order $$20$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$75$$ Character field: $$\Q(\zeta_{20})$$ Newform subspaces: $$1$$ Sturm bound: $$20$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(75, [\chi])$$.

Total New Old
Modular forms 96 96 0
Cusp forms 64 64 0
Eisenstein series 32 32 0

## Trace form

 $$64q - 10q^{3} - 20q^{4} - 6q^{6} - 20q^{7} - 10q^{9} + O(q^{10})$$ $$64q - 10q^{3} - 20q^{4} - 6q^{6} - 20q^{7} - 10q^{9} - 20q^{10} - 10q^{12} - 20q^{13} - 10q^{15} - 8q^{16} - 10q^{18} - 6q^{21} + 20q^{22} + 40q^{25} - 10q^{27} + 40q^{28} - 10q^{30} - 12q^{31} - 10q^{33} + 20q^{34} - 22q^{36} - 20q^{37} + 30q^{39} - 20q^{40} + 90q^{42} - 20q^{43} + 70q^{45} - 12q^{46} + 100q^{48} - 16q^{51} + 20q^{52} + 120q^{54} - 20q^{55} + 70q^{57} - 20q^{58} + 50q^{60} - 12q^{61} - 20q^{63} - 100q^{64} - 30q^{66} - 60q^{67} - 80q^{69} - 100q^{70} - 150q^{72} - 60q^{73} - 90q^{75} - 64q^{76} - 80q^{78} - 60q^{79} + 14q^{81} - 60q^{82} - 130q^{84} + 60q^{85} - 60q^{87} + 20q^{88} - 70q^{90} - 12q^{91} - 20q^{93} + 260q^{94} + 42q^{96} + 120q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(75, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
75.2.l.a $$64$$ $$0.599$$ None $$0$$ $$-10$$ $$0$$ $$-20$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database