# Properties

 Label 4.4.19429.1-15.1-e Base field 4.4.19429.1 Weight $[2, 2, 2, 2]$ Level norm $15$ Level $[15, 15, w^{2} - 2w - 5]$ Dimension $6$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.19429.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 7x^{2} - x + 5$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[15, 15, w^{2} - 2w - 5]$ Dimension: $6$ CM: no Base change: no Newspace dimension: $25$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{6} - x^{5} - 21x^{4} + 34x^{3} + 23x^{2} - 32x - 16$$
Norm Prime Eigenvalue
3 $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ $-1$
5 $[5, 5, w]$ $-1$
7 $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$ $\phantom{-}e$
13 $[13, 13, -w^{2} + w + 4]$ $\phantom{-}\frac{5}{2}e^{5} + \frac{1}{2}e^{4} - \frac{101}{2}e^{3} + 24e^{2} + \frac{117}{2}e + 14$
13 $[13, 13, -w^{3} + 2w^{2} + 5w - 2]$ $\phantom{-}e^{5} - 20e^{3} + 14e^{2} + 17e + 2$
16 $[16, 2, 2]$ $\phantom{-}\frac{1}{4}e^{5} + \frac{3}{4}e^{4} - \frac{21}{4}e^{3} - \frac{23}{2}e^{2} + \frac{79}{4}e + 12$
17 $[17, 17, -w + 2]$ $\phantom{-}\frac{7}{2}e^{5} + \frac{3}{2}e^{4} - \frac{141}{2}e^{3} + 18e^{2} + \frac{181}{2}e + 32$
19 $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}\frac{1}{4}e^{5} - \frac{1}{4}e^{4} - \frac{21}{4}e^{3} + \frac{17}{2}e^{2} + \frac{19}{4}e - 7$
27 $[27, 3, w^{3} - 3w^{2} - 4w + 7]$ $\phantom{-}\frac{25}{4}e^{5} + \frac{15}{4}e^{4} - \frac{505}{4}e^{3} + \frac{21}{2}e^{2} + \frac{727}{4}e + 73$
31 $[31, 31, w^{3} - 3w^{2} - 3w + 7]$ $-e$
31 $[31, 31, -w^{3} + w^{2} + 6w + 1]$ $-e^{4} + 20e^{2} - 12e - 18$
41 $[41, 41, w^{2} - w - 1]$ $\phantom{-}4e^{5} + 3e^{4} - 81e^{3} - 6e^{2} + 127e + 64$
43 $[43, 43, 2w^{3} - 5w^{2} - 6w + 4]$ $\phantom{-}\frac{25}{4}e^{5} + \frac{7}{4}e^{4} - \frac{505}{4}e^{3} + \frac{101}{2}e^{2} + \frac{607}{4}e + 37$
47 $[47, 47, -w^{3} + 2w^{2} + 5w - 1]$ $-5e^{5} - 2e^{4} + 101e^{3} - 29e^{2} - 131e - 36$
53 $[53, 53, -w - 3]$ $-\frac{3}{4}e^{5} - \frac{1}{4}e^{4} + \frac{63}{4}e^{3} - \frac{9}{2}e^{2} - \frac{113}{4}e - 3$
53 $[53, 53, -w^{3} + 3w^{2} + 3w - 6]$ $-\frac{3}{2}e^{5} - \frac{5}{2}e^{4} + \frac{61}{2}e^{3} + 30e^{2} - \frac{139}{2}e - 50$
59 $[59, 59, 2w^{2} - 3w - 6]$ $\phantom{-}4e^{5} + 3e^{4} - 81e^{3} - 6e^{2} + 127e + 58$
59 $[59, 59, w^{3} - w^{2} - 7w - 3]$ $-\frac{3}{2}e^{5} + \frac{1}{2}e^{4} + \frac{61}{2}e^{3} - 30e^{2} - \frac{55}{2}e + 4$
79 $[79, 79, 2w^{3} - 4w^{2} - 8w + 3]$ $-4e^{5} - 2e^{4} + 81e^{3} - 14e^{2} - 113e - 42$
79 $[79, 79, w^{2} - 2w - 1]$ $\phantom{-}\frac{11}{4}e^{5} + \frac{5}{4}e^{4} - \frac{223}{4}e^{3} + \frac{25}{2}e^{2} + \frac{313}{4}e + 29$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ $1$
$5$ $[5, 5, w]$ $1$