# Properties

 Label 572.2.b Level $572$ Weight $2$ Character orbit 572.b Rep. character $\chi_{572}(571,\cdot)$ Character field $\Q$ Dimension $80$ Newform subspaces $3$ Sturm bound $168$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$572 = 2^{2} \cdot 11 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 572.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$572$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$168$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(572, [\chi])$$.

Total New Old
Modular forms 88 88 0
Cusp forms 80 80 0
Eisenstein series 8 8 0

## Trace form

 $$80q - 4q^{4} - 80q^{9} + O(q^{10})$$ $$80q - 4q^{4} - 80q^{9} - 4q^{14} + 12q^{16} - 16q^{22} - 72q^{25} + 4q^{26} + 14q^{36} + 14q^{38} + 38q^{42} - 14q^{48} - 80q^{49} - 16q^{53} + 6q^{56} - 4q^{64} + 34q^{66} - 16q^{69} + 44q^{77} - 22q^{78} + 64q^{81} - 60q^{82} + 76q^{88} - 18q^{92} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(572, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
572.2.b.a $$4$$ $$4.567$$ $$\Q(\sqrt{-2}, \sqrt{-13})$$ $$\Q(\sqrt{-13})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}-2q^{4}+\beta _{2}q^{7}+2\beta _{2}q^{8}+\cdots$$
572.2.b.b $$20$$ $$4.567$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ $$\Q(\sqrt{-143})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{14}q^{2}-\beta _{9}q^{3}+\beta _{12}q^{4}+(-\beta _{3}+\cdots)q^{6}+\cdots$$
572.2.b.c $$56$$ $$4.567$$ None $$0$$ $$0$$ $$0$$ $$0$$