Properties

 Label 525.2.w Level 525 Weight 2 Character orbit w Rep. character $$\chi_{525}(104,\cdot)$$ Character field $$\Q(\zeta_{10})$$ Dimension 304 Newform subspaces 1 Sturm bound 160 Trace bound 0

Related objects

Defining parameters

 Level: $$N$$ = $$525 = 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 525.w (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$525$$ Character field: $$\Q(\zeta_{10})$$ Newform subspaces: $$1$$ Sturm bound: $$160$$ Trace bound: $$0$$

Dimensions

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

Total New Old
Modular forms 336 336 0
Cusp forms 304 304 0
Eisenstein series 32 32 0

Trace form

 $$304q - 84q^{4} - 6q^{9} + O(q^{10})$$ $$304q - 84q^{4} - 6q^{9} - 36q^{15} - 60q^{16} - 18q^{21} - 40q^{22} - 8q^{25} + 60q^{28} + 14q^{30} + 28q^{36} - 20q^{37} - 2q^{39} - 35q^{42} - 24q^{46} - 20q^{49} - 52q^{51} - 80q^{58} + 4q^{60} + 55q^{63} - 76q^{64} - 20q^{67} + 6q^{70} + 30q^{72} - 40q^{78} - 68q^{79} - 10q^{81} + 80q^{84} - 88q^{85} - 20q^{88} - 82q^{91} - 36q^{99} + O(q^{100})$$

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.w.a $$304$$ $$4.192$$ None $$0$$ $$0$$ $$0$$ $$0$$

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database