# Properties

 Label 572.2.i Level $572$ Weight $2$ Character orbit 572.i Rep. character $\chi_{572}(133,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $20$ 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.i (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(\zeta_{3})$$ 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 180 20 160
Cusp forms 156 20 136
Eisenstein series 24 0 24

## Trace form

 $$20q + 2q^{3} + 4q^{5} - 6q^{7} - 4q^{9} + O(q^{10})$$ $$20q + 2q^{3} + 4q^{5} - 6q^{7} - 4q^{9} + 12q^{13} + 16q^{15} - 2q^{17} + 10q^{19} - 4q^{21} - 14q^{23} + 24q^{25} - 40q^{27} - 10q^{29} + 20q^{31} + 8q^{35} + 4q^{37} + 24q^{39} + 2q^{41} - 14q^{43} - 16q^{45} + 8q^{47} - 44q^{51} + 4q^{53} + 64q^{57} - 8q^{61} + 10q^{63} - 26q^{65} + 6q^{67} + 26q^{69} + 2q^{71} - 64q^{73} + 42q^{75} - 16q^{77} + 16q^{79} - 18q^{81} - 12q^{83} - 30q^{85} - 12q^{87} + 10q^{89} - 10q^{91} - 46q^{93} + 12q^{95} + 46q^{97} + O(q^{100})$$

## 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.i.a $$4$$ $$4.567$$ $$\Q(\zeta_{12})$$ None $$0$$ $$2$$ $$-4$$ $$-2$$ $$q+(\zeta_{12}-\zeta_{12}^{2})q^{3}-q^{5}+(-1+\zeta_{12}+\cdots)q^{7}+\cdots$$
572.2.i.b $$6$$ $$4.567$$ 6.0.309123.1 None $$0$$ $$-1$$ $$6$$ $$-5$$ $$q+(\beta _{1}-\beta _{5})q^{3}+(1+\beta _{1}-\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots$$
572.2.i.c $$10$$ $$4.567$$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$0$$ $$1$$ $$2$$ $$1$$ $$q+\beta _{1}q^{3}+(-\beta _{2}-\beta _{3}-\beta _{5})q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(572, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(26, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(52, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(143, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(286, [\chi])$$$$^{\oplus 2}$$