Properties

 Label 864.2.i Level $864$ Weight $2$ Character orbit 864.i Rep. character $\chi_{864}(289,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $24$ Newform subspaces $6$ Sturm bound $288$ Trace bound $7$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$864 = 2^{5} \cdot 3^{3}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 864.i (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$6$$ Sturm bound: $$288$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$5$$, $$7$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(864, [\chi])$$.

Total New Old
Modular forms 336 24 312
Cusp forms 240 24 216
Eisenstein series 96 0 96

Trace form

 $$24 q + O(q^{10})$$ $$24 q - 8 q^{17} - 12 q^{25} + 8 q^{29} - 12 q^{41} - 12 q^{49} + 48 q^{53} + 16 q^{65} + 24 q^{73} + 16 q^{77} + 64 q^{89} - 12 q^{97} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(864, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
864.2.i.a $2$ $6.899$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$4$$ $$-2$$ $$q+4\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(5-5\zeta_{6})q^{11}+\cdots$$
864.2.i.b $2$ $6.899$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$4$$ $$2$$ $$q+4\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(-5+5\zeta_{6})q^{11}+\cdots$$
864.2.i.c $4$ $6.899$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$-2$$ $$-2$$ $$q-\beta _{1}q^{5}+(-1+\beta _{1}-\beta _{2}+\beta _{3})q^{7}+\cdots$$
864.2.i.d $4$ $6.899$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-1+\zeta_{12})q^{5}-\zeta_{12}^{2}q^{7}-\zeta_{12}^{2}q^{11}+\cdots$$
864.2.i.e $4$ $6.899$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$-2$$ $$2$$ $$q-\beta _{1}q^{5}+(1-\beta _{1}+\beta _{2}-\beta _{3})q^{7}+(1+\cdots)q^{11}+\cdots$$
864.2.i.f $8$ $6.899$ 8.0.170772624.1 None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+\beta _{6}q^{5}+(\beta _{1}-\beta _{7})q^{7}-\beta _{3}q^{11}+(-2\beta _{4}+\cdots)q^{13}+\cdots$$

Decomposition of $$S_{2}^{\mathrm{old}}(864, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(864, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(54, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(72, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(108, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(144, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(216, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(288, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(432, [\chi])$$$$^{\oplus 2}$$