# Properties

 Label 575.2.b Level $575$ Weight $2$ Character orbit 575.b Rep. character $\chi_{575}(24,\cdot)$ Character field $\Q$ Dimension $34$ Newform subspaces $6$ Sturm bound $120$ Trace bound $4$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$575 = 5^{2} \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 575.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$120$$ Trace bound: $$4$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(575, [\chi])$$.

Total New Old
Modular forms 66 34 32
Cusp forms 54 34 20
Eisenstein series 12 0 12

## Trace form

 $$34q - 36q^{4} + 4q^{6} - 30q^{9} + O(q^{10})$$ $$34q - 36q^{4} + 4q^{6} - 30q^{9} - 8q^{11} + 4q^{14} + 40q^{16} - 4q^{19} + 8q^{21} - 8q^{24} - 24q^{26} - 16q^{29} + 20q^{31} - 4q^{34} + 24q^{36} + 48q^{41} + 52q^{44} + 4q^{46} - 66q^{49} + 16q^{51} + 36q^{54} - 80q^{56} - 12q^{59} + 60q^{61} - 60q^{64} - 16q^{66} - 8q^{69} - 20q^{71} - 28q^{74} + 28q^{76} - 8q^{79} + 34q^{81} + 68q^{84} - 68q^{86} - 56q^{89} - 24q^{91} - 60q^{94} - 140q^{96} + 116q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(575, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
575.2.b.a $$2$$ $$4.591$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{2}-2q^{4}+iq^{7}+3q^{9}+2q^{11}+\cdots$$
575.2.b.b $$2$$ $$4.591$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+q^{4}-iq^{7}+3iq^{8}+3q^{9}+\cdots$$
575.2.b.c $$4$$ $$4.591$$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}-\beta _{3})q^{2}+\beta _{3}q^{3}+3\beta _{2}q^{4}+(1+\cdots)q^{6}+\cdots$$
575.2.b.d $$4$$ $$4.591$$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(2\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots$$
575.2.b.e $$8$$ $$4.591$$ 8.0.$$\cdots$$.11 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{7}q^{3}+(-1+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$$
575.2.b.f $$14$$ $$4.591$$ $$\mathbb{Q}[x]/(x^{14} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{10}q^{3}+(-2+\beta _{2})q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(575, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(575, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(115, [\chi])$$$$^{\oplus 2}$$