# Properties

 Label 576.3.g Level $576$ Weight $3$ Character orbit 576.g Rep. character $\chi_{576}(127,\cdot)$ Character field $\Q$ Dimension $19$ Newform subspaces $10$ Sturm bound $288$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$576 = 2^{6} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 576.g (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$4$$ Character field: $$\Q$$ Newform subspaces: $$10$$ Sturm bound: $$288$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

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

Total New Old
Modular forms 216 21 195
Cusp forms 168 19 149
Eisenstein series 48 2 46

## Trace form

 $$19 q - 2 q^{5} + O(q^{10})$$ $$19 q - 2 q^{5} - 14 q^{13} + 10 q^{17} + 49 q^{25} - 18 q^{29} - 30 q^{37} + 90 q^{41} - 93 q^{49} + 62 q^{53} + 146 q^{61} - 12 q^{65} + 22 q^{73} + 256 q^{77} + 68 q^{85} + 58 q^{89} + 38 q^{97} + O(q^{100})$$

## 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.g.a $$1$$ $$15.695$$ $$\Q$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$-8$$ $$0$$ $$q-8q^{5}+10q^{13}-2^{4}q^{17}+39q^{25}+\cdots$$
576.3.g.b $$1$$ $$15.695$$ $$\Q$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$-6$$ $$0$$ $$q-6q^{5}-10q^{13}+30q^{17}+11q^{25}+\cdots$$
576.3.g.c $$1$$ $$15.695$$ $$\Q$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$8$$ $$0$$ $$q+8q^{5}+10q^{13}+2^{4}q^{17}+39q^{25}+\cdots$$
576.3.g.d $$2$$ $$15.695$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-8$$ $$0$$ $$q-4q^{5}+iq^{7}-4iq^{11}+2q^{13}+24q^{17}+\cdots$$
576.3.g.e $$2$$ $$15.695$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q-2q^{5}-\zeta_{6}q^{7}+\zeta_{6}q^{11}-2q^{13}+\cdots$$
576.3.g.f $$2$$ $$15.695$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{6}q^{7}-22q^{13}+2\zeta_{6}q^{19}-5^{2}q^{25}+\cdots$$
576.3.g.g $$2$$ $$15.695$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+2q^{5}+2iq^{7}+iq^{11}+14q^{13}+\cdots$$
576.3.g.h $$2$$ $$15.695$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$8$$ $$0$$ $$q+4q^{5}+iq^{7}+4iq^{11}+2q^{13}-24q^{17}+\cdots$$
576.3.g.i $$2$$ $$15.695$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$12$$ $$0$$ $$q+6q^{5}-\zeta_{6}q^{7}+3\zeta_{6}q^{11}+14q^{13}+\cdots$$
576.3.g.j $$4$$ $$15.695$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$-8$$ $$0$$ $$q+(-2+\zeta_{12}^{2})q^{5}+(\zeta_{12}-\zeta_{12}^{3})q^{7}+\cdots$$

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

$$S_{3}^{\mathrm{old}}(576, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(12, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(16, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(32, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(64, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(96, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(144, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(192, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(288, [\chi])$$$$^{\oplus 2}$$