# Properties

 Label 864.3.e Level $864$ Weight $3$ Character orbit 864.e Rep. character $\chi_{864}(161,\cdot)$ Character field $\Q$ Dimension $32$ Newform subspaces $6$ Sturm bound $432$ Trace bound $13$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$864 = 2^{5} \cdot 3^{3}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 864.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$432$$ Trace bound: $$13$$ Distinguishing $$T_p$$: $$5$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(864, [\chi])$$.

Total New Old
Modular forms 312 32 280
Cusp forms 264 32 232
Eisenstein series 48 0 48

## Trace form

 $$32 q + O(q^{10})$$ $$32 q + 16 q^{13} - 176 q^{25} - 16 q^{37} + 320 q^{49} - 208 q^{61} - 192 q^{73} + 416 q^{85} + 160 q^{97} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(864, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
864.3.e.a $4$ $23.542$ $$\Q(\sqrt{-2}, \sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$-12$$ $$q-\beta _{3}q^{5}+(-3+\beta _{1})q^{7}+(-\beta _{2}-3\beta _{3})q^{11}+\cdots$$
864.3.e.b $4$ $23.542$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$-12$$ $$q+(\zeta_{8}+\zeta_{8}^{2})q^{5}+(-3-\zeta_{8}^{3})q^{7}+(-\zeta_{8}+\cdots)q^{11}+\cdots$$
864.3.e.c $4$ $23.542$ $$\Q(\sqrt{-2}, \sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$12$$ $$q+\beta _{3}q^{5}+(3+\beta _{1})q^{7}+(\beta _{2}-3\beta _{3})q^{11}+\cdots$$
864.3.e.d $4$ $23.542$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$12$$ $$q+(\zeta_{8}+\zeta_{8}^{2})q^{5}+(3+\zeta_{8}^{3})q^{7}+(\zeta_{8}+\cdots)q^{11}+\cdots$$
864.3.e.e $8$ $23.542$ 8.0.2441150464.4 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{6}q^{5}+\beta _{4}q^{7}+(\beta _{1}+\beta _{2})q^{11}+(-2+\cdots)q^{13}+\cdots$$
864.3.e.f $8$ $23.542$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{24}^{2}q^{5}-\zeta_{24}^{4}q^{7}-\zeta_{24}^{6}q^{11}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(864, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(864, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(12, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(24, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(27, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(54, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(72, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(96, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(108, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(144, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(216, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(288, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(432, [\chi])$$$$^{\oplus 2}$$