# Properties

 Label 136.2.n Level $136$ Weight $2$ Character orbit 136.n Rep. character $\chi_{136}(9,\cdot)$ Character field $\Q(\zeta_{8})$ Dimension $20$ Newform subspaces $3$ Sturm bound $36$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$136 = 2^{3} \cdot 17$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 136.n (of order $$8$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$17$$ Character field: $$\Q(\zeta_{8})$$ Newform subspaces: $$3$$ Sturm bound: $$36$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(136, [\chi])$$.

Total New Old
Modular forms 88 20 68
Cusp forms 56 20 36
Eisenstein series 32 0 32

## Trace form

 $$20 q - 12 q^{9} + O(q^{10})$$ $$20 q - 12 q^{9} + 4 q^{11} + 8 q^{17} - 16 q^{25} + 12 q^{27} - 16 q^{29} - 16 q^{31} - 64 q^{35} - 16 q^{39} - 16 q^{41} + 4 q^{43} - 40 q^{45} + 8 q^{49} + 24 q^{53} + 52 q^{59} + 24 q^{61} + 96 q^{63} + 8 q^{65} - 24 q^{67} + 80 q^{69} + 24 q^{71} + 16 q^{73} + 100 q^{75} + 40 q^{79} + 20 q^{83} + 24 q^{85} - 96 q^{87} - 16 q^{91} - 80 q^{93} - 8 q^{95} - 52 q^{97} - 72 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(136, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
136.2.n.a $4$ $1.086$ $$\Q(\zeta_{8})$$ None $$0$$ $$-4$$ $$4$$ $$-4$$ $$q+(-1-\zeta_{8})q^{3}+(1-\zeta_{8})q^{5}+(-1+\cdots)q^{7}+\cdots$$
136.2.n.b $4$ $1.086$ $$\Q(\zeta_{8})$$ None $$0$$ $$4$$ $$-8$$ $$4$$ $$q+(1+\zeta_{8}-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(-2+2\zeta_{8}+\cdots)q^{5}+\cdots$$
136.2.n.c $12$ $1.086$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+\beta _{2}q^{3}+\beta _{8}q^{5}+(1-\beta _{3}-\beta _{6}-\beta _{8}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(136, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(136, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(17, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(34, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(68, [\chi])$$$$^{\oplus 2}$$