# Properties

 Label 1152.3.m Level $1152$ Weight $3$ Character orbit 1152.m Rep. character $\chi_{1152}(415,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $76$ Newform subspaces $6$ Sturm bound $576$ Trace bound $19$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1152 = 2^{7} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 1152.m (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$16$$ Character field: $$\Q(i)$$ Newform subspaces: $$6$$ Sturm bound: $$576$$ Trace bound: $$19$$ Distinguishing $$T_p$$: $$5$$, $$7$$

## Dimensions

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

Total New Old
Modular forms 832 84 748
Cusp forms 704 76 628
Eisenstein series 128 8 120

## Trace form

 $$76q - 4q^{5} + O(q^{10})$$ $$76q - 4q^{5} + 4q^{13} + 8q^{17} + 28q^{29} - 92q^{37} + 356q^{49} - 164q^{53} + 68q^{61} + 40q^{65} + 24q^{77} - 216q^{85} - 8q^{97} + O(q^{100})$$

## 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.m.a $$6$$ $$31.390$$ 6.0.399424.1 None $$0$$ $$0$$ $$-2$$ $$-4$$ $$q+(-1+\beta _{1}-\beta _{2}-\beta _{4})q^{5}+(\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots$$
1152.3.m.b $$6$$ $$31.390$$ 6.0.399424.1 None $$0$$ $$0$$ $$-2$$ $$4$$ $$q+(-1+\beta _{1}-\beta _{2}-\beta _{4})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$$
1152.3.m.c $$16$$ $$31.390$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{11}q^{5}-\beta _{3}q^{7}+(-2-2\beta _{2}+\beta _{5}+\cdots)q^{11}+\cdots$$
1152.3.m.d $$16$$ $$31.390$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{5}-\beta _{8}q^{7}+(\beta _{4}+\beta _{14})q^{11}+\cdots$$
1152.3.m.e $$16$$ $$31.390$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{5}+\beta _{8}q^{7}+(-\beta _{4}-\beta _{14})q^{11}+\cdots$$
1152.3.m.f $$16$$ $$31.390$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{11}q^{5}+\beta _{3}q^{7}+(2+2\beta _{2}-\beta _{5}+\cdots)q^{11}+\cdots$$

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

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