# Properties

 Label 160.3.e Level $160$ Weight $3$ Character orbit 160.e Rep. character $\chi_{160}(79,\cdot)$ Character field $\Q$ Dimension $10$ Newform subspaces $3$ Sturm bound $72$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$160 = 2^{5} \cdot 5$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 160.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$40$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$72$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$3$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(160, [\chi])$$.

Total New Old
Modular forms 56 14 42
Cusp forms 40 10 30
Eisenstein series 16 4 12

## Trace form

 $$10 q - 22 q^{9} + O(q^{10})$$ $$10 q - 22 q^{9} + 4 q^{11} - 28 q^{19} + 10 q^{25} + 100 q^{35} + 36 q^{41} - 18 q^{49} - 128 q^{51} + 68 q^{59} - 60 q^{65} - 320 q^{75} - 6 q^{81} + 148 q^{89} + 392 q^{91} + 164 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(160, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
160.3.e.a $1$ $4.360$ $$\Q$$ $$\Q(\sqrt{-10})$$ $$0$$ $$0$$ $$-5$$ $$6$$ $$q-5q^{5}+6q^{7}+9q^{9}+18q^{11}+6q^{13}+\cdots$$
160.3.e.b $1$ $4.360$ $$\Q$$ $$\Q(\sqrt{-10})$$ $$0$$ $$0$$ $$5$$ $$-6$$ $$q+5q^{5}-6q^{7}+9q^{9}+18q^{11}-6q^{13}+\cdots$$
160.3.e.c $8$ $4.360$ 8.0.$$\cdots$$.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{3}+\beta _{3}q^{5}+(-\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(160, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(160, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 3}$$