# Properties

 Label 572.2.bg Level $572$ Weight $2$ Character orbit 572.bg Rep. character $\chi_{572}(9,\cdot)$ Character field $\Q(\zeta_{15})$ Dimension $112$ Newform subspaces $1$ Sturm bound $168$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$572 = 2^{2} \cdot 11 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 572.bg (of order $$15$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$143$$ Character field: $$\Q(\zeta_{15})$$ Newform subspaces: $$1$$ Sturm bound: $$168$$ Trace bound: $$0$$

## Dimensions

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

Total New Old
Modular forms 720 112 608
Cusp forms 624 112 512
Eisenstein series 96 0 96

## Trace form

 $$112q + 8q^{9} + O(q^{10})$$ $$112q + 8q^{9} - 10q^{11} + 11q^{13} - 2q^{15} + 4q^{17} - 12q^{19} - 40q^{21} + 10q^{23} - 16q^{25} - 12q^{27} + q^{29} + 4q^{31} + 35q^{33} - 5q^{35} - 12q^{37} + 21q^{39} - 10q^{41} - 32q^{43} + 34q^{45} + 70q^{47} + 16q^{49} - 48q^{51} - 26q^{53} + 10q^{55} - 12q^{57} - 5q^{59} + 28q^{61} + 34q^{63} + 22q^{65} - 68q^{67} - 58q^{69} + 44q^{71} + 42q^{73} - 24q^{75} + 46q^{77} - 24q^{79} + 64q^{81} - 114q^{83} + 4q^{85} - 30q^{87} - 6q^{89} + 77q^{91} - 5q^{93} - 36q^{95} - 15q^{97} - 40q^{99} + O(q^{100})$$

## 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.bg.a $$112$$ $$4.567$$ None $$0$$ $$0$$ $$0$$ $$0$$

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

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