# Properties

 Label 4.4.16357.1-15.1-d Base field 4.4.16357.1 Weight $[2, 2, 2, 2]$ Level norm $15$ Level $[15, 15, -w^{3} + 5w + 1]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.16357.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[15, 15, -w^{3} + 5w + 1]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $22$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} - 2x^{3} - 16x^{2} + 36x - 12$$
Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}1$
5 $[5, 5, -w^{3} + 5w + 2]$ $\phantom{-}e$
5 $[5, 5, w - 1]$ $\phantom{-}1$
11 $[11, 11, -w^{3} + 5w]$ $\phantom{-}\frac{1}{2}e^{3} - 8e + 6$
13 $[13, 13, -w^{3} + w^{2} + 6w - 3]$ $\phantom{-}4$
16 $[16, 2, 2]$ $-\frac{1}{2}e^{2} - e + 4$
19 $[19, 19, 2w^{3} - w^{2} - 11w + 2]$ $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + 8e - 7$
25 $[25, 5, -w^{2} + w + 3]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - 9e + 13$
27 $[27, 3, w^{3} - w^{2} - 5w + 4]$ $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + 7e - 11$
31 $[31, 31, -w - 3]$ $\phantom{-}\frac{1}{2}e^{3} - e^{2} - 9e + 10$
37 $[37, 37, -w^{3} - w^{2} + 6w + 4]$ $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + 7e + 1$
41 $[41, 41, w^{3} + w^{2} - 6w - 5]$ $\phantom{-}0$
43 $[43, 43, w^{3} - 7w - 2]$ $\phantom{-}2e + 2$
47 $[47, 47, -2w^{3} + 11w + 2]$ $-\frac{1}{2}e^{2} + e + 3$
61 $[61, 61, w^{2} - 3]$ $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + 9e - 7$
67 $[67, 67, w^{2} + w - 4]$ $-\frac{1}{2}e^{3} + e^{2} + 9e - 14$
79 $[79, 79, -4w^{3} + 2w^{2} + 22w - 9]$ $\phantom{-}e^{2} + e - 10$
97 $[97, 97, -3w^{3} + 2w^{2} + 19w - 6]$ $\phantom{-}e^{2} + 2e - 8$
97 $[97, 97, -w^{3} + 6w - 3]$ $-e^{2} + 10$
97 $[97, 97, -3w^{3} + 16w]$ $\phantom{-}\frac{3}{2}e^{3} - e^{2} - 22e + 16$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w + 1]$ $-1$
$5$ $[5, 5, w - 1]$ $-1$