# Properties

 Base field 4.4.13068.1 Weight [2, 2, 2, 2] Level norm 17 Level $[17, 17, -w^{3} + w^{2} + 6w - 1]$ Label 4.4.13068.1-17.1-f Dimension 9 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.13068.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 6x^{2} - x + 1$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[17, 17, -w^{3} + w^{2} + 6w - 1]$ Label 4.4.13068.1-17.1-f Dimension 9 Is CM no Is base change no Parent newspace dimension 24

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{9}$$ $$\mathstrut -\mathstrut 6x^{8}$$ $$\mathstrut +\mathstrut 5x^{7}$$ $$\mathstrut +\mathstrut 31x^{6}$$ $$\mathstrut -\mathstrut 61x^{5}$$ $$\mathstrut -\mathstrut 9x^{4}$$ $$\mathstrut +\mathstrut 79x^{3}$$ $$\mathstrut -\mathstrut 26x^{2}$$ $$\mathstrut -\mathstrut 21x$$ $$\mathstrut +\mathstrut 9$$
Norm Prime Eigenvalue
2 $[2, 2, w^{3} - w^{2} - 6w - 2]$ $\phantom{-}e$
3 $[3, 3, -w^{3} + 2w^{2} + 4w - 2]$ $-\frac{1}{3}e^{8} + e^{7} + \frac{7}{3}e^{6} - \frac{22}{3}e^{5} - \frac{14}{3}e^{4} + 14e^{3} + \frac{14}{3}e^{2} - \frac{22}{3}e - 1$
4 $[4, 2, w^{3} - w^{2} - 5w - 2]$ $\phantom{-}\frac{5}{3}e^{8} - 7e^{7} - \frac{11}{3}e^{6} + \frac{131}{3}e^{5} - \frac{83}{3}e^{4} - 55e^{3} + \frac{128}{3}e^{2} + \frac{50}{3}e - 11$
17 $[17, 17, -w^{3} + w^{2} + 6w - 1]$ $-1$
17 $[17, 17, -w + 2]$ $\phantom{-}2e^{8} - 10e^{7} + 2e^{6} + 57e^{5} - 72e^{4} - 50e^{3} + 95e^{2} + 7e - 21$
29 $[29, 29, -w^{3} + 2w^{2} + 4w - 4]$ $\phantom{-}e^{8} - 5e^{7} + 33e^{5} - 34e^{4} - 50e^{3} + 60e^{2} + 23e - 18$
29 $[29, 29, w^{3} - 2w^{2} - 4w]$ $-2e^{7} + 5e^{6} + 12e^{5} - 29e^{4} - 14e^{3} + 27e^{2} + 7e$
31 $[31, 31, -w^{2} + 2]$ $\phantom{-}\frac{8}{3}e^{8} - 13e^{7} + \frac{1}{3}e^{6} + \frac{233}{3}e^{5} - \frac{248}{3}e^{4} - 84e^{3} + \frac{341}{3}e^{2} + \frac{71}{3}e - 29$
31 $[31, 31, -w^{3} + 7w + 5]$ $\phantom{-}\frac{8}{3}e^{8} - 15e^{7} + \frac{19}{3}e^{6} + \frac{263}{3}e^{5} - \frac{356}{3}e^{4} - 86e^{3} + \frac{458}{3}e^{2} + \frac{44}{3}e - 35$
41 $[41, 41, -2w^{3} + 2w^{2} + 13w - 2]$ $\phantom{-}5e^{8} - 24e^{7} - e^{6} + 146e^{5} - 147e^{4} - 170e^{3} + 214e^{2} + 48e - 57$
41 $[41, 41, 3w^{3} - 4w^{2} - 17w + 5]$ $\phantom{-}e^{8} - 3e^{7} - 5e^{6} + 17e^{5} + 2e^{4} - 13e^{3} - 2e^{2} - e$
67 $[67, 67, 3w^{3} - 4w^{2} - 17w + 1]$ $-\frac{7}{3}e^{8} + 7e^{7} + \frac{37}{3}e^{6} - \frac{124}{3}e^{5} - \frac{35}{3}e^{4} + 41e^{3} + \frac{74}{3}e^{2} - \frac{1}{3}e - 14$
67 $[67, 67, -w^{2} + 4w + 2]$ $-\frac{10}{3}e^{8} + 13e^{7} + \frac{37}{3}e^{6} - \frac{259}{3}e^{5} + \frac{76}{3}e^{4} + 130e^{3} - \frac{157}{3}e^{2} - \frac{148}{3}e + 16$
83 $[83, 83, 2w^{2} - 5w - 2]$ $-7e^{7} + 23e^{6} + 34e^{5} - 146e^{4} - 3e^{3} + 187e^{2} - 13e - 39$
83 $[83, 83, -w^{3} + 8w + 6]$ $-e^{8} + 6e^{7} - 3e^{6} - 37e^{5} + 49e^{4} + 46e^{3} - 62e^{2} - 18e + 12$
83 $[83, 83, w^{3} - 2w^{2} - 2w - 2]$ $-2e^{6} + 3e^{5} + 13e^{4} - 15e^{3} - 14e^{2} + 4e - 3$
83 $[83, 83, w^{3} - 2w^{2} - 6w]$ $-2e^{8} + 13e^{7} - 10e^{6} - 78e^{5} + 129e^{4} + 87e^{3} - 193e^{2} - 29e + 57$
97 $[97, 97, -3w^{3} + 2w^{2} + 17w + 7]$ $\phantom{-}\frac{2}{3}e^{8} + 3e^{7} - \frac{53}{3}e^{6} - \frac{52}{3}e^{5} + \frac{271}{3}e^{4} + 19e^{3} - \frac{322}{3}e^{2} - \frac{46}{3}e + 22$
97 $[97, 97, w^{3} - 4w^{2} + 3w + 1]$ $\phantom{-}\frac{14}{3}e^{8} - 22e^{7} - \frac{14}{3}e^{6} + \frac{419}{3}e^{5} - \frac{347}{3}e^{4} - 186e^{3} + \frac{539}{3}e^{2} + \frac{197}{3}e - 56$
97 $[97, 97, -5w^{3} + 8w^{2} + 24w - 8]$ $-\frac{1}{3}e^{8} + e^{7} + \frac{4}{3}e^{6} - \frac{16}{3}e^{5} + \frac{7}{3}e^{4} + 3e^{3} - \frac{16}{3}e^{2} + \frac{5}{3}e - 5$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
17 $[17, 17, -w^{3} + w^{2} + 6w - 1]$ $1$