# Properties

 Label 576.2.l Level 576 Weight 2 Character orbit l Rep. character $$\chi_{576}(143,\cdot)$$ Character field $$\Q(\zeta_{4})$$ Dimension 16 Newforms 1 Sturm bound 192 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$576 = 2^{6} \cdot 3^{2}$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 576.l (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$48$$ Character field: $$\Q(i)$$ Newforms: $$1$$ Sturm bound: $$192$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(576, [\chi])$$.

Total New Old
Modular forms 224 16 208
Cusp forms 160 16 144
Eisenstein series 64 0 64

## Trace form

 $$16q + O(q^{10})$$ $$16q - 16q^{19} + 32q^{43} + 16q^{49} + 64q^{55} - 32q^{61} + 16q^{67} - 32q^{85} - 48q^{91} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(576, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
576.2.l.a $$16$$ $$4.599$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{5}-\beta _{9}q^{7}+(\beta _{2}+\beta _{14})q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(576, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(576, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(144, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(192, [\chi])$$$$^{\oplus 2}$$