# Properties

 Label 1152.3.g Level $1152$ Weight $3$ Character orbit 1152.g Rep. character $\chi_{1152}(127,\cdot)$ Character field $\Q$ Dimension $40$ Newform subspaces $6$ Sturm bound $576$ Trace bound $13$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1152 = 2^{7} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 1152.g (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$4$$ Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$576$$ Trace bound: $$13$$ Distinguishing $$T_p$$: $$5$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(1152, [\chi])$$.

Total New Old
Modular forms 416 40 376
Cusp forms 352 40 312
Eisenstein series 64 0 64

## Trace form

 $$40q + O(q^{10})$$ $$40q - 16q^{17} + 248q^{25} - 176q^{41} - 344q^{49} + 160q^{65} - 464q^{73} + 48q^{89} + 368q^{97} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(1152, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1152.3.g.a $$4$$ $$31.390$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$-8$$ $$0$$ $$q+(-2+\zeta_{8}^{3})q^{5}+(-\zeta_{8}-\zeta_{8}^{2})q^{7}+\cdots$$
1152.3.g.b $$4$$ $$31.390$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$8$$ $$0$$ $$q+(2+\zeta_{8}^{2})q^{5}+(-\zeta_{8}-\zeta_{8}^{3})q^{7}+(-\zeta_{8}+\cdots)q^{11}+\cdots$$
1152.3.g.c $$8$$ $$31.390$$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$-16$$ $$0$$ $$q+(-2+\zeta_{24})q^{5}-\zeta_{24}^{6}q^{7}+(\zeta_{24}^{3}+\cdots)q^{11}+\cdots$$
1152.3.g.d $$8$$ $$31.390$$ 8.0.157351936.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{5}-\beta _{5}q^{7}+\beta _{1}q^{11}+(-6+\beta _{7})q^{13}+\cdots$$
1152.3.g.e $$8$$ $$31.390$$ 8.0.157351936.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{5}-\beta _{5}q^{7}+\beta _{1}q^{11}+(6-\beta _{7})q^{13}+\cdots$$
1152.3.g.f $$8$$ $$31.390$$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$16$$ $$0$$ $$q+(2-\zeta_{24}^{2})q^{5}-\zeta_{24}^{4}q^{7}+(\zeta_{24}-\zeta_{24}^{4}+\cdots)q^{11}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(1152, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(1152, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(12, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(16, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(32, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(64, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(96, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(128, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(144, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(192, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(288, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(384, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(576, [\chi])$$$$^{\oplus 2}$$