# Properties

 Base field 4.4.16997.1 Weight [2, 2, 2, 2] Level norm 5 Level $[5, 5, w]$ Label 4.4.16997.1-5.1-b Dimension 5 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.16997.1

Generator $$w$$, with minimal polynomial $$x^{4} - 6x^{2} - x + 5$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[5, 5, w]$ Label 4.4.16997.1-5.1-b Dimension 5 Is CM no Is base change no Parent newspace dimension 6

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{5} - 13x^{3} + 14x^{2} + 15x - 18$$
Norm Prime Eigenvalue
5 $[5, 5, w]$ $-1$
5 $[5, 5, -w^{2} + w + 2]$ $\phantom{-}e$
7 $[7, 7, -w^{2} + 2]$ $\phantom{-}\frac{5}{3}e^{4} + 2e^{3} - \frac{56}{3}e^{2} + \frac{4}{3}e + 21$
13 $[13, 13, -w^{2} + 3]$ $-\frac{4}{3}e^{4} - 2e^{3} + \frac{43}{3}e^{2} + \frac{4}{3}e - 18$
13 $[13, 13, w^{2} - w - 4]$ $\phantom{-}\frac{1}{3}e^{4} - \frac{13}{3}e^{2} + \frac{11}{3}e + 5$
16 $[16, 2, 2]$ $-\frac{1}{3}e^{4} - e^{3} + \frac{7}{3}e^{2} + \frac{16}{3}e - 3$
19 $[19, 19, -w^{2} + w + 1]$ $\phantom{-}\frac{4}{3}e^{4} + 2e^{3} - \frac{40}{3}e^{2} - \frac{4}{3}e + 14$
23 $[23, 23, -w^{3} + 4w + 2]$ $-3e^{4} - 4e^{3} + 34e^{2} + 4e - 42$
25 $[25, 5, -w^{3} + w^{2} + 3w - 1]$ $\phantom{-}\frac{5}{3}e^{4} + 2e^{3} - \frac{59}{3}e^{2} - \frac{2}{3}e + 27$
29 $[29, 29, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}3e^{4} + 4e^{3} - 33e^{2} - 2e + 39$
29 $[29, 29, -w + 3]$ $\phantom{-}2e^{4} + 2e^{3} - 24e^{2} + 2e + 30$
31 $[31, 31, -w^{3} + w^{2} + 5w - 2]$ $-\frac{13}{3}e^{4} - 6e^{3} + \frac{148}{3}e^{2} + \frac{22}{3}e - 66$
37 $[37, 37, w^{3} - 4w - 1]$ $\phantom{-}\frac{4}{3}e^{4} + 2e^{3} - \frac{40}{3}e^{2} + \frac{2}{3}e + 8$
37 $[37, 37, w^{3} - 3w + 1]$ $\phantom{-}\frac{10}{3}e^{4} + 4e^{3} - \frac{112}{3}e^{2} + \frac{2}{3}e + 44$
53 $[53, 53, -w^{3} + 2w^{2} + 4w - 6]$ $-e^{4} - 2e^{3} + 11e^{2} + 8e - 15$
59 $[59, 59, w^{2} + w - 4]$ $\phantom{-}2e + 6$
61 $[61, 61, -2w^{2} + w + 8]$ $\phantom{-}\frac{4}{3}e^{4} + 2e^{3} - \frac{46}{3}e^{2} - \frac{22}{3}e + 26$
73 $[73, 73, -w^{3} + 5w - 1]$ $-\frac{8}{3}e^{4} - 4e^{3} + \frac{86}{3}e^{2} + \frac{14}{3}e - 34$
79 $[79, 79, 2w^{2} + w - 6]$ $\phantom{-}\frac{20}{3}e^{4} + 9e^{3} - \frac{224}{3}e^{2} - \frac{23}{3}e + 96$
79 $[79, 79, 2w^{3} - w^{2} - 9w + 3]$ $-\frac{8}{3}e^{4} - 4e^{3} + \frac{83}{3}e^{2} + \frac{8}{3}e - 28$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, w]$ $1$