# Properties

 Label 501.2.c Level $501$ Weight $2$ Character orbit 501.c Rep. character $\chi_{501}(500,\cdot)$ Character field $\Q$ Dimension $54$ Newform subspaces $2$ Sturm bound $112$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$501 = 3 \cdot 167$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 501.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$501$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$112$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(501, [\chi])$$.

Total New Old
Modular forms 58 58 0
Cusp forms 54 54 0
Eisenstein series 4 4 0

## Trace form

 $$54q - 2q^{3} - 60q^{4} + 4q^{6} - 4q^{7} - 2q^{9} + O(q^{10})$$ $$54q - 2q^{3} - 60q^{4} + 4q^{6} - 4q^{7} - 2q^{9} - 10q^{12} + 64q^{16} + 2q^{18} - 28q^{21} - 4q^{22} + 30q^{24} + 38q^{25} - 26q^{27} + 4q^{28} - 24q^{31} - 20q^{33} - 24q^{36} + 5q^{42} - 11q^{48} + 62q^{49} + 23q^{54} - 40q^{57} + 56q^{58} - 40q^{61} - 6q^{63} - 140q^{64} - 4q^{66} - 19q^{72} + 56q^{75} + 40q^{76} - 42q^{81} + 81q^{84} - 2q^{87} - 64q^{88} - 36q^{93} + 20q^{94} - 82q^{96} + 32q^{97} + 100q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(501, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
501.2.c.a $$22$$ $$4.001$$ $$\Q(\sqrt{-167})$$ $$0$$ $$0$$ $$0$$ $$0$$
501.2.c.b $$32$$ $$4.001$$ None $$0$$ $$-2$$ $$0$$ $$-4$$

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database