# Properties

 Label 600.1.bj Level 600 Weight 1 Character orbit bj Rep. character $$\chi_{600}(221,\cdot)$$ Character field $$\Q(\zeta_{10})$$ Dimension 8 Newforms 2 Sturm bound 120 Trace bound 2

# Related objects

## Defining parameters

 Level: $$N$$ = $$600 = 2^{3} \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ = $$1$$ Character orbit: $$[\chi]$$ = 600.bj (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$600$$ Character field: $$\Q(\zeta_{10})$$ Newforms: $$2$$ Sturm bound: $$120$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(600, [\chi])$$.

Total New Old
Modular forms 24 24 0
Cusp forms 8 8 0
Eisenstein series 16 16 0

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 8 0 0 0

## Trace form

 $$8q - 2q^{4} - 2q^{6} - 4q^{7} - 2q^{9} + O(q^{10})$$ $$8q - 2q^{4} - 2q^{6} - 4q^{7} - 2q^{9} - 2q^{10} - 2q^{15} - 2q^{16} - 4q^{22} + 8q^{24} - 2q^{25} + 6q^{28} + 6q^{31} - 4q^{33} - 2q^{36} - 2q^{40} + 6q^{42} + 4q^{49} - 2q^{54} - 4q^{55} - 4q^{58} + 8q^{60} - 4q^{63} - 2q^{64} + 6q^{70} - 4q^{73} - 4q^{79} - 2q^{81} - 4q^{87} + 6q^{88} - 2q^{90} - 2q^{96} + 6q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(600, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
600.1.bj.a $$4$$ $$0.299$$ $$\Q(\zeta_{10})$$ $$D_{5}$$ $$\Q(\sqrt{-6})$$ None $$-1$$ $$-1$$ $$-1$$ $$-2$$ $$q-\zeta_{10}q^{2}+\zeta_{10}^{2}q^{3}+\zeta_{10}^{2}q^{4}-\zeta_{10}q^{5}+\cdots$$
600.1.bj.b $$4$$ $$0.299$$ $$\Q(\zeta_{10})$$ $$D_{5}$$ $$\Q(\sqrt{-6})$$ None $$1$$ $$1$$ $$1$$ $$-2$$ $$q+\zeta_{10}q^{2}-\zeta_{10}^{2}q^{3}+\zeta_{10}^{2}q^{4}+\zeta_{10}q^{5}+\cdots$$