# Properties

 Label 320.4.d Level $320$ Weight $4$ Character orbit 320.d Rep. character $\chi_{320}(161,\cdot)$ Character field $\Q$ Dimension $24$ Newform subspaces $4$ Sturm bound $192$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$320 = 2^{6} \cdot 5$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 320.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$192$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$3$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(320, [\chi])$$.

Total New Old
Modular forms 156 24 132
Cusp forms 132 24 108
Eisenstein series 24 0 24

## Trace form

 $$24 q - 216 q^{9} + O(q^{10})$$ $$24 q - 216 q^{9} - 600 q^{25} + 1392 q^{33} - 240 q^{41} - 264 q^{49} + 2736 q^{57} - 864 q^{73} - 7272 q^{81} + 2544 q^{89} + 3168 q^{97} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(320, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
320.4.d.a $4$ $18.881$ $$\Q(i, \sqrt{19})$$ None $$0$$ $$0$$ $$0$$ $$-20$$ $$q+(-3\beta _{1}+\beta _{3})q^{3}+5\beta _{1}q^{5}+(-5+\cdots)q^{7}+\cdots$$
320.4.d.b $4$ $18.881$ $$\Q(i, \sqrt{19})$$ None $$0$$ $$0$$ $$0$$ $$20$$ $$q+(-3\beta _{1}+\beta _{3})q^{3}-5\beta _{1}q^{5}+(5-5\beta _{2}+\cdots)q^{7}+\cdots$$
320.4.d.c $8$ $18.881$ 8.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$-64$$ $$q-\beta _{1}q^{3}-5\beta _{2}q^{5}+(-8+\beta _{4}-3\beta _{6}+\cdots)q^{7}+\cdots$$
320.4.d.d $8$ $18.881$ 8.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$64$$ $$q-\beta _{1}q^{3}+5\beta _{2}q^{5}+(8-\beta _{4}+3\beta _{6}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(320, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(320, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(8, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(32, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(64, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(160, [\chi])$$$$^{\oplus 2}$$