# Properties

 Label 1152.3.b Level $1152$ Weight $3$ Character orbit 1152.b Rep. character $\chi_{1152}(703,\cdot)$ Character field $\Q$ Dimension $40$ Newform subspaces $10$ Sturm bound $576$ Trace bound $17$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1152 = 2^{7} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 1152.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$10$$ Sturm bound: $$576$$ Trace bound: $$17$$ Distinguishing $$T_p$$: $$5$$, $$7$$, $$17$$

## 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

 $$40q + O(q^{10})$$ $$40q + 16q^{17} - 152q^{25} + 16q^{41} - 216q^{49} - 64q^{65} - 176q^{73} - 432q^{89} - 240q^{97} + O(q^{100})$$

## 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.b.a $$2$$ $$31.390$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{5}-3iq^{13}-30q^{17}-39q^{25}+\cdots$$
1152.3.b.b $$2$$ $$31.390$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{5}+4iq^{13}-2^{4}q^{17}-11q^{25}+\cdots$$
1152.3.b.c $$2$$ $$31.390$$ $$\Q(\sqrt{2})$$ $$\Q(\sqrt{-2})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta q^{11}+2q^{17}-\beta q^{19}+5^{2}q^{25}+\cdots$$
1152.3.b.d $$2$$ $$31.390$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{5}-4iq^{13}+2^{4}q^{17}-11q^{25}+\cdots$$
1152.3.b.e $$4$$ $$31.390$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}^{2}q^{5}+\zeta_{12}^{3}q^{7}-\zeta_{12}q^{11}+\cdots$$
1152.3.b.f $$4$$ $$31.390$$ $$\Q(i, \sqrt{6})$$ $$\Q(\sqrt{-6})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{5}+\beta _{2}q^{7}+\beta _{3}q^{11}+21q^{25}+\cdots$$
1152.3.b.g $$4$$ $$31.390$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}q^{5}-\zeta_{8}^{3}q^{7}-5\zeta_{8}^{2}q^{11}+5\zeta_{8}q^{13}+\cdots$$
1152.3.b.h $$4$$ $$31.390$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{5}+\zeta_{12}^{3}q^{7}+\zeta_{12}^{2}q^{11}+\cdots$$
1152.3.b.i $$8$$ $$31.390$$ 8.0.157351936.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{5}-\beta _{5}q^{7}-\beta _{3}q^{11}-\beta _{2}q^{13}+\cdots$$
1152.3.b.j $$8$$ $$31.390$$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{24}-\zeta_{24}^{4})q^{5}+\zeta_{24}^{2}q^{7}+(\zeta_{24}^{3}+\cdots)q^{11}+\cdots$$

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

$$S_{3}^{\mathrm{old}}(1152, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(8, [\chi])$$$$^{\oplus 15}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(24, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(32, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(64, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(72, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(96, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(128, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(192, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(288, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(384, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(576, [\chi])$$$$^{\oplus 2}$$