# Properties

 Label 4.4.9792.1-17.1-c Base field 4.4.9792.1 Weight $[2, 2, 2, 2]$ Level norm $17$ Level $[17, 17, 2w^{3} - 6w^{2} - 7w + 8]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.9792.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 7x^{2} + 2x + 7$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[17, 17, 2w^{3} - 6w^{2} - 7w + 8]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $10$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

 $$x^{4} + 3x^{3} - 10x^{2} - 9x - 1$$
Norm Prime Eigenvalue
4 $[4, 2, w^{3} - 3w^{2} - 3w + 4]$ $\phantom{-}\frac{3}{8}e^{3} + e^{2} - \frac{15}{4}e - \frac{9}{8}$
7 $[7, 7, w]$ $\phantom{-}e$
7 $[7, 7, w^{3} - 3w^{2} - 4w + 5]$ $\phantom{-}\frac{9}{8}e^{3} + 3e^{2} - \frac{49}{4}e - \frac{51}{8}$
9 $[9, 3, w^{3} - 4w^{2} - w + 9]$ $\phantom{-}\frac{3}{8}e^{3} + e^{2} - \frac{15}{4}e + \frac{7}{8}$
17 $[17, 17, 2w^{3} - 6w^{2} - 7w + 8]$ $-1$
17 $[17, 17, -w^{3} + 3w^{2} + 4w - 3]$ $\phantom{-}\frac{1}{2}e^{3} + e^{2} - 6e + \frac{1}{2}$
17 $[17, 17, -w + 2]$ $\phantom{-}\frac{1}{4}e^{3} + e^{2} - \frac{3}{2}e - \frac{7}{4}$
23 $[23, 23, 2w^{3} - 7w^{2} - 4w + 12]$ $\phantom{-}\frac{5}{4}e^{3} + 3e^{2} - \frac{25}{2}e - \frac{7}{4}$
23 $[23, 23, -w^{2} + 2w + 3]$ $\phantom{-}\frac{17}{8}e^{3} + 6e^{2} - \frac{85}{4}e - \frac{83}{8}$
31 $[31, 31, -2w^{3} + 7w^{2} + 5w - 12]$ $-\frac{11}{8}e^{3} - 3e^{2} + \frac{71}{4}e + \frac{49}{8}$
31 $[31, 31, -w^{3} + 4w^{2} + 2w - 8]$ $\phantom{-}\frac{11}{8}e^{3} + 3e^{2} - \frac{71}{4}e - \frac{17}{8}$
41 $[41, 41, 3w^{3} - 10w^{2} - 7w + 16]$ $-\frac{3}{4}e^{3} - e^{2} + \frac{19}{2}e - \frac{3}{4}$
41 $[41, 41, 2w^{3} - 7w^{2} - 5w + 10]$ $-\frac{9}{8}e^{3} - 4e^{2} + \frac{37}{4}e + \frac{99}{8}$
49 $[49, 7, 2w^{3} - 6w^{2} - 6w + 9]$ $-\frac{9}{4}e^{3} - 6e^{2} + \frac{45}{2}e + \frac{15}{4}$
71 $[71, 71, w^{2} - 2w - 2]$ $-\frac{5}{8}e^{3} - 2e^{2} + \frac{17}{4}e - \frac{1}{8}$
71 $[71, 71, 2w^{3} - 7w^{2} - 4w + 13]$ $-2e^{3} - 5e^{2} + 22e + 4$
73 $[73, 73, 3w^{3} - 11w^{2} - 5w + 19]$ $\phantom{-}\frac{3}{2}e^{3} + 3e^{2} - 20e - \frac{7}{2}$
73 $[73, 73, -4w^{3} + 13w^{2} + 10w - 17]$ $-\frac{3}{2}e^{3} - 3e^{2} + 20e + \frac{5}{2}$
79 $[79, 79, 3w^{3} - 9w^{2} - 10w + 13]$ $-\frac{17}{8}e^{3} - 5e^{2} + \frac{105}{4}e + \frac{43}{8}$
79 $[79, 79, -2w^{3} + 6w^{2} + 5w - 8]$ $\phantom{-}\frac{7}{4}e^{3} + 4e^{2} - \frac{45}{2}e - \frac{37}{4}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$17$ $[17, 17, 2w^{3} - 6w^{2} - 7w + 8]$ $1$