# Properties

 Label 192.5.g Level $192$ Weight $5$ Character orbit 192.g Rep. character $\chi_{192}(127,\cdot)$ Character field $\Q$ Dimension $16$ Newform subspaces $5$ Sturm bound $160$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$192 = 2^{6} \cdot 3$$ Weight: $$k$$ $$=$$ $$5$$ Character orbit: $$[\chi]$$ $$=$$ 192.g (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$4$$ Character field: $$\Q$$ Newform subspaces: $$5$$ Sturm bound: $$160$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{5}(192, [\chi])$$.

Total New Old
Modular forms 140 16 124
Cusp forms 116 16 100
Eisenstein series 24 0 24

## Trace form

 $$16 q - 432 q^{9} + O(q^{10})$$ $$16 q - 432 q^{9} + 352 q^{13} + 480 q^{17} - 288 q^{21} + 1328 q^{25} - 1728 q^{29} + 1568 q^{37} - 1440 q^{41} - 5488 q^{49} - 960 q^{53} + 4512 q^{61} + 5376 q^{65} + 9792 q^{69} + 5280 q^{73} + 4992 q^{77} + 11664 q^{81} - 49792 q^{85} - 6240 q^{89} - 19872 q^{93} - 12640 q^{97} + O(q^{100})$$

## Decomposition of $$S_{5}^{\mathrm{new}}(192, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
192.5.g.a $2$ $19.847$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-12$$ $$0$$ $$q-\zeta_{6}q^{3}-6q^{5}+12\zeta_{6}q^{7}-3^{3}q^{9}+\cdots$$
192.5.g.b $2$ $19.847$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$84$$ $$0$$ $$q-3\zeta_{6}q^{3}+42q^{5}-44\zeta_{6}q^{7}-3^{3}q^{9}+\cdots$$
192.5.g.c $4$ $19.847$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$-88$$ $$0$$ $$q-\zeta_{12}^{2}q^{3}+(-22-\zeta_{12}^{3})q^{5}+(-\zeta_{12}+\cdots)q^{7}+\cdots$$
192.5.g.d $4$ $19.847$ $$\Q(\sqrt{-3}, \sqrt{13})$$ None $$0$$ $$0$$ $$-24$$ $$0$$ $$q+\beta _{1}q^{3}+(-6-\beta _{2})q^{5}+(-\beta _{1}-\beta _{3})q^{7}+\cdots$$
192.5.g.e $4$ $19.847$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$40$$ $$0$$ $$q-3\zeta_{12}^{2}q^{3}+(10-\zeta_{12}^{3})q^{5}+(-11\zeta_{12}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{5}^{\mathrm{old}}(192, [\chi])$$ into lower level spaces

$$S_{5}^{\mathrm{old}}(192, [\chi]) \cong$$ $$S_{5}^{\mathrm{new}}(4, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(12, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(16, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(32, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(64, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(96, [\chi])$$$$^{\oplus 2}$$