# Properties

 Label 127.1.b Level 127 Weight 1 Character orbit b Rep. character $$\chi_{127}(126,\cdot)$$ Character field $$\Q$$ Dimension 2 Newform subspaces 1 Sturm bound 10 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$127$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 127.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$127$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$10$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(127, [\chi])$$.

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

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 2 0 0 0

## Trace form

 $$2q - q^{2} + q^{4} - 2q^{8} + 2q^{9} + O(q^{10})$$ $$2q - q^{2} + q^{4} - 2q^{8} + 2q^{9} - q^{11} - q^{13} - q^{17} - q^{18} - q^{19} - 2q^{22} + 2q^{25} - 2q^{26} - q^{31} + 2q^{32} + 3q^{34} + q^{36} - q^{37} + 3q^{38} - q^{41} + 2q^{44} - q^{47} + 2q^{49} - q^{50} + 2q^{52} - q^{61} + 3q^{62} - q^{64} - 3q^{68} - q^{71} - 2q^{72} - q^{73} + 3q^{74} - 3q^{76} - q^{79} + 2q^{81} - 2q^{82} + q^{88} - 2q^{94} - q^{98} - q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(127, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
127.1.b.a $$2$$ $$0.063$$ $$\Q(\sqrt{5})$$ $$D_{5}$$ $$\Q(\sqrt{-127})$$ None $$-1$$ $$0$$ $$0$$ $$0$$ $$q+(-1+\beta )q^{2}+(1-\beta )q^{4}-q^{8}+q^{9}+\cdots$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$1 + T + T^{2} + T^{3} + T^{4}$$
$3$ $$( 1 - T )^{2}( 1 + T )^{2}$$
$5$ $$( 1 - T )^{2}( 1 + T )^{2}$$
$7$ $$( 1 - T )^{2}( 1 + T )^{2}$$
$11$ $$1 + T + T^{2} + T^{3} + T^{4}$$
$13$ $$1 + T + T^{2} + T^{3} + T^{4}$$
$17$ $$1 + T + T^{2} + T^{3} + T^{4}$$
$19$ $$1 + T + T^{2} + T^{3} + T^{4}$$
$23$ $$( 1 - T )^{2}( 1 + T )^{2}$$
$29$ $$( 1 - T )^{2}( 1 + T )^{2}$$
$31$ $$1 + T + T^{2} + T^{3} + T^{4}$$
$37$ $$1 + T + T^{2} + T^{3} + T^{4}$$
$41$ $$1 + T + T^{2} + T^{3} + T^{4}$$
$43$ $$( 1 - T )^{2}( 1 + T )^{2}$$
$47$ $$1 + T + T^{2} + T^{3} + T^{4}$$
$53$ $$( 1 - T )^{2}( 1 + T )^{2}$$
$59$ $$( 1 - T )^{2}( 1 + T )^{2}$$
$61$ $$1 + T + T^{2} + T^{3} + T^{4}$$
$67$ $$( 1 - T )^{2}( 1 + T )^{2}$$
$71$ $$1 + T + T^{2} + T^{3} + T^{4}$$
$73$ $$1 + T + T^{2} + T^{3} + T^{4}$$
$79$ $$1 + T + T^{2} + T^{3} + T^{4}$$
$83$ $$( 1 - T )^{2}( 1 + T )^{2}$$
$89$ $$( 1 - T )^{2}( 1 + T )^{2}$$
$97$ $$( 1 - T )^{2}( 1 + T )^{2}$$