# Properties

 Label 572.2.n Level $572$ Weight $2$ Character orbit 572.n Rep. character $\chi_{572}(53,\cdot)$ Character field $\Q(\zeta_{5})$ Dimension $48$ Newform subspaces $2$ 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.n (of order $$5$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$11$$ Character field: $$\Q(\zeta_{5})$$ Newform subspaces: $$2$$ 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 360 48 312
Cusp forms 312 48 264
Eisenstein series 48 0 48

## Trace form

 $$48q + 2q^{3} - 6q^{5} + 14q^{7} - 10q^{9} + O(q^{10})$$ $$48q + 2q^{3} - 6q^{5} + 14q^{7} - 10q^{9} + 2q^{13} - 10q^{15} + 4q^{17} - 14q^{19} - 44q^{21} + 4q^{23} - 38q^{25} + 2q^{27} - 6q^{29} - 6q^{31} - 12q^{33} - 16q^{35} + 30q^{37} + 38q^{41} - 16q^{43} + 28q^{45} + 12q^{47} + 26q^{49} + 14q^{51} + 4q^{53} + 30q^{55} - 22q^{57} - 68q^{59} - 26q^{61} + 60q^{63} - 32q^{65} + 36q^{67} + 6q^{71} - 44q^{73} - 42q^{75} - 60q^{77} + 42q^{79} - 2q^{81} + 2q^{83} + 22q^{85} + 88q^{87} + 80q^{89} - 8q^{91} - 20q^{93} + 14q^{95} - 36q^{97} + 78q^{99} + O(q^{100})$$

## 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.n.a $$20$$ $$4.567$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$1$$ $$1$$ $$3$$ $$q+\beta _{5}q^{3}+(-\beta _{9}-\beta _{10})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots$$
572.2.n.b $$28$$ $$4.567$$ None $$0$$ $$1$$ $$-7$$ $$11$$

## Decomposition of $$S_{2}^{\mathrm{old}}(572, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(572, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(22, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(44, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(143, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(286, [\chi])$$$$^{\oplus 2}$$