# Properties

 Label 576.3.e Level $576$ Weight $3$ Character orbit 576.e Rep. character $\chi_{576}(449,\cdot)$ Character field $\Q$ Dimension $16$ Newform subspaces $8$ Sturm bound $288$ Trace bound $13$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$576 = 2^{6} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 576.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ Newform subspaces: $$8$$ Sturm bound: $$288$$ Trace bound: $$13$$ Distinguishing $$T_p$$: $$5$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(576, [\chi])$$.

Total New Old
Modular forms 216 16 200
Cusp forms 168 16 152
Eisenstein series 48 0 48

## Trace form

 $$16 q + O(q^{10})$$ $$16 q + 32 q^{13} - 80 q^{25} - 160 q^{37} + 112 q^{49} + 160 q^{61} + 320 q^{85} - 64 q^{97} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(576, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
576.3.e.a $$2$$ $$15.695$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$-24$$ $$q+5\beta q^{5}-12q^{7}+4\beta q^{11}+8q^{13}+\cdots$$
576.3.e.b $$2$$ $$15.695$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$-16$$ $$q+\beta q^{5}-8q^{7}-8\beta q^{11}+8q^{13}+9\beta q^{17}+\cdots$$
576.3.e.c $$2$$ $$15.695$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$-8$$ $$q+\beta q^{5}-4q^{7}-4\beta q^{11}-8q^{13}-3\beta q^{17}+\cdots$$
576.3.e.d $$2$$ $$15.695$$ $$\Q(\sqrt{-2})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta q^{5}-24q^{13}-23\beta q^{17}+23q^{25}+\cdots$$
576.3.e.e $$2$$ $$15.695$$ $$\Q(\sqrt{-2})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+7\beta q^{5}+24q^{13}+7\beta q^{17}-73q^{25}+\cdots$$
576.3.e.f $$2$$ $$15.695$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$8$$ $$q+\beta q^{5}+4q^{7}+4\beta q^{11}-8q^{13}-3\beta q^{17}+\cdots$$
576.3.e.g $$2$$ $$15.695$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$16$$ $$q+\beta q^{5}+8q^{7}+8\beta q^{11}+8q^{13}+9\beta q^{17}+\cdots$$
576.3.e.h $$2$$ $$15.695$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$24$$ $$q+5\beta q^{5}+12q^{7}-4\beta q^{11}+8q^{13}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(576, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(576, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(12, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(24, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(72, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(96, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(144, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(192, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(288, [\chi])$$$$^{\oplus 2}$$