# Properties

 Base field $$\Q(\zeta_{11})^+$$ Weight [2, 2, 2, 2, 2] Level norm 109 Level $[109, 109, -w^{3} + 2w^{2} + 3w - 3]$ Label 5.5.14641.1-109.1-a Dimension 4 CM no Base change no

# Related objects

• L-function not available

## Base field $$\Q(\zeta_{11})^+$$

Generator $$w$$, with minimal polynomial $$x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x - 1$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2, 2] Level $[109, 109, -w^{3} + 2w^{2} + 3w - 3]$ Label 5.5.14641.1-109.1-a Dimension 4 Is CM no Is base change no Parent newspace dimension 4

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4}$$ $$\mathstrut -\mathstrut 2x^{3}$$ $$\mathstrut -\mathstrut 17x^{2}$$ $$\mathstrut +\mathstrut 36x$$ $$\mathstrut -\mathstrut 9$$
Norm Prime Eigenvalue
11 $[11, 11, w^{4} + w^{3} - 4w^{2} - 3w + 2]$ $\phantom{-}e$
23 $[23, 23, -w^{4} + 3w^{2} + 1]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{19}{3}e + 4$
23 $[23, 23, -w^{4} + 3w^{2} + w - 2]$ $\phantom{-}\frac{1}{3}e^{2} + \frac{2}{3}e - 2$
23 $[23, 23, w^{4} - w^{3} - 3w^{2} + 3w + 2]$ $\phantom{-}\frac{2}{3}e^{3} - \frac{2}{3}e^{2} - 12e + 12$
23 $[23, 23, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ $\phantom{-}2e$
23 $[23, 23, -w^{2} + w + 3]$ $-\frac{1}{3}e^{2} - \frac{2}{3}e + 5$
32 $[32, 2, 2]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{2}{3}e^{2} - \frac{20}{3}e + 8$
43 $[43, 43, -2w^{4} + w^{3} + 6w^{2} - 2w - 1]$ $-\frac{2}{3}e^{3} + \frac{2}{3}e^{2} + 10e - 10$
43 $[43, 43, -w^{4} + 2w^{2} + w + 1]$ $-\frac{2}{3}e^{3} + \frac{2}{3}e^{2} + 10e - 10$
43 $[43, 43, w^{3} + w^{2} - 4w - 2]$ $-\frac{2}{3}e^{3} + \frac{38}{3}e - 6$
43 $[43, 43, 2w^{4} - w^{3} - 7w^{2} + 3w + 3]$ $\phantom{-}\frac{2}{3}e^{3} - \frac{2}{3}e^{2} - 10e + 8$
43 $[43, 43, w^{4} - w^{3} - 4w^{2} + 4w + 2]$ $-\frac{1}{3}e^{3} + \frac{13}{3}e - 2$
67 $[67, 67, 2w^{4} - 7w^{2} + 2]$ $\phantom{-}\frac{2}{3}e^{3} - \frac{35}{3}e + 16$
67 $[67, 67, w^{4} - 2w^{3} - 3w^{2} + 6w + 2]$ $-\frac{2}{3}e^{3} - \frac{2}{3}e^{2} + \frac{28}{3}e + 4$
67 $[67, 67, 2w^{4} - 7w^{2} - w + 4]$ $-\frac{2}{3}e^{3} + e^{2} + \frac{32}{3}e - 12$
67 $[67, 67, w^{4} - 2w^{3} - 4w^{2} + 6w + 2]$ $-\frac{1}{3}e^{3} + \frac{2}{3}e^{2} + \frac{11}{3}e - 6$
67 $[67, 67, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ $-2e + 2$
89 $[89, 89, w^{3} + w^{2} - 4w - 1]$ $-\frac{2}{3}e^{3} + \frac{1}{3}e^{2} + \frac{34}{3}e - 7$
89 $[89, 89, -2w^{4} + w^{3} + 7w^{2} - 3w - 2]$ $\phantom{-}2e^{2} - 18$
89 $[89, 89, -w^{4} + w^{3} + 4w^{2} - 4w - 3]$ $-e^{2} + 9$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
109 $[109, 109, -w^{3} + 2w^{2} + 3w - 3]$ $-1$