# Properties

 Label 1152.3.o Level $1152$ Weight $3$ Character orbit 1152.o Rep. character $\chi_{1152}(511,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $192$ Sturm bound $576$

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## Defining parameters

 Level: $$N$$ $$=$$ $$1152 = 2^{7} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 1152.o (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$36$$ Character field: $$\Q(\zeta_{6})$$ Sturm bound: $$576$$

## Dimensions

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

Total New Old
Modular forms 800 192 608
Cusp forms 736 192 544
Eisenstein series 64 0 64

## Trace form

 $$192q + O(q^{10})$$ $$192q - 480q^{25} - 64q^{33} + 96q^{41} + 672q^{49} + 160q^{57} - 160q^{81} - 384q^{89} + O(q^{100})$$

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

The newforms in this space have not yet been added to the LMFDB.

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

$$S_{3}^{\mathrm{old}}(1152, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(144, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(288, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(576, [\chi])$$$$^{\oplus 2}$$