# Properties

 Label 320.3.h Level $320$ Weight $3$ Character orbit 320.h Rep. character $\chi_{320}(319,\cdot)$ Character field $\Q$ Dimension $22$ Newform subspaces $7$ Sturm bound $144$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$320 = 2^{6} \cdot 5$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 320.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$20$$ Character field: $$\Q$$ Newform subspaces: $$7$$ Sturm bound: $$144$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(320, [\chi])$$.

Total New Old
Modular forms 108 26 82
Cusp forms 84 22 62
Eisenstein series 24 4 20

## Trace form

 $$22 q + 2 q^{5} + 50 q^{9} + O(q^{10})$$ $$22 q + 2 q^{5} + 50 q^{9} + 40 q^{21} - 26 q^{25} + 4 q^{29} - 84 q^{41} + 22 q^{45} + 66 q^{49} - 28 q^{61} + 424 q^{69} + 46 q^{81} - 192 q^{85} + 12 q^{89} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(320, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
320.3.h.a $1$ $8.719$ $$\Q$$ $$\Q(\sqrt{-5})$$ $$0$$ $$-4$$ $$5$$ $$-4$$ $$q-4q^{3}+5q^{5}-4q^{7}+7q^{9}-20q^{15}+\cdots$$
320.3.h.b $1$ $8.719$ $$\Q$$ $$\Q(\sqrt{-5})$$ $$0$$ $$4$$ $$5$$ $$4$$ $$q+4q^{3}+5q^{5}+4q^{7}+7q^{9}+20q^{15}+\cdots$$
320.3.h.c $2$ $8.719$ $$\Q(\sqrt{5})$$ $$\Q(\sqrt{-5})$$ $$0$$ $$0$$ $$-10$$ $$0$$ $$q-\beta q^{3}-5q^{5}-3\beta q^{7}+11q^{9}+5\beta q^{15}+\cdots$$
320.3.h.d $2$ $8.719$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$-6$$ $$0$$ $$q+(-3+i)q^{5}-9q^{9}-6iq^{13}-4iq^{17}+\cdots$$
320.3.h.e $4$ $8.719$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+\beta _{1}q^{3}+(1+\beta _{2})q^{5}-3\beta _{1}q^{7}-q^{9}+\cdots$$
320.3.h.f $6$ $8.719$ 6.0.1827904.1 None $$0$$ $$-4$$ $$2$$ $$12$$ $$q+(-1-\beta _{1})q^{3}+\beta _{3}q^{5}+(2+\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots$$
320.3.h.g $6$ $8.719$ 6.0.1827904.1 None $$0$$ $$4$$ $$2$$ $$-12$$ $$q+(1+\beta _{1})q^{3}+(1+\beta _{1}+\beta _{3})q^{5}+(-2+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(320, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(320, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(20, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(80, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(160, [\chi])$$$$^{\oplus 2}$$