# Properties

 Label 136.1.e Level 136 Weight 1 Character orbit e Rep. character $$\chi_{136}(67,\cdot)$$ Character field $$\Q$$ Dimension 1 Newform subspaces 1 Sturm bound 18 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$136 = 2^{3} \cdot 17$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 136.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$136$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$18$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(136, [\chi])$$.

Total New Old
Modular forms 3 3 0
Cusp forms 1 1 0
Eisenstein series 2 2 0

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 1 0 0 0

## Trace form

 $$q - q^{2} + q^{4} - q^{8} + q^{9} + O(q^{10})$$ $$q - q^{2} + q^{4} - q^{8} + q^{9} + q^{16} - q^{17} - q^{18} - 2q^{19} - q^{25} - q^{32} + q^{34} + q^{36} + 2q^{38} + 2q^{43} - q^{49} + q^{50} + 2q^{59} + q^{64} - 2q^{67} - q^{68} - q^{72} - 2q^{76} + q^{81} + 2q^{83} - 2q^{86} - 2q^{89} + q^{98} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(136, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
136.1.e.a $$1$$ $$0.068$$ $$\Q$$ $$D_{2}$$ $$\Q(\sqrt{-2})$$, $$\Q(\sqrt{-34})$$ $$\Q(\sqrt{17})$$ $$-1$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{17}+\cdots$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$1 + T$$
$3$ $$( 1 - T )( 1 + T )$$
$5$ $$1 + T^{2}$$
$7$ $$1 + T^{2}$$
$11$ $$( 1 - T )( 1 + T )$$
$13$ $$( 1 - T )( 1 + T )$$
$17$ $$1 + T$$
$19$ $$( 1 + T )^{2}$$
$23$ $$1 + T^{2}$$
$29$ $$1 + T^{2}$$
$31$ $$1 + T^{2}$$
$37$ $$1 + T^{2}$$
$41$ $$( 1 - T )( 1 + T )$$
$43$ $$( 1 - T )^{2}$$
$47$ $$( 1 - T )( 1 + T )$$
$53$ $$( 1 - T )( 1 + T )$$
$59$ $$( 1 - T )^{2}$$
$61$ $$1 + T^{2}$$
$67$ $$( 1 + T )^{2}$$
$71$ $$1 + T^{2}$$
$73$ $$( 1 - T )( 1 + T )$$
$79$ $$1 + T^{2}$$
$83$ $$( 1 - T )^{2}$$
$89$ $$( 1 + T )^{2}$$
$97$ $$( 1 - T )( 1 + T )$$