Properties

Label 4.4.2048.1-79.1-b
Base field \(\Q(\zeta_{16})^+\)
Weight $[2, 2, 2, 2]$
Level norm $79$
Level $[79, 79, -w^{3} - w^{2} + 4w - 1]$
Dimension $5$
CM no
Base change no

Related objects

Downloads

Learn more

Base field \(\Q(\zeta_{16})^+\)

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[79, 79, -w^{3} - w^{2} + 4w - 1]$
Dimension: $5$
CM: no
Base change: no
Newspace dimension: $6$

Hecke eigenvalues ($q$-expansion)

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

\(x^{5} - 2x^{4} - 6x^{3} + 10x^{2} + 5x - 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}e$
17 $[17, 17, -w^{2} - w + 3]$ $-\frac{1}{2}e^{4} + e^{3} + \frac{3}{2}e^{2} - 3e + 2$
17 $[17, 17, -w^{3} - w^{2} + 3w + 1]$ $-e^{4} + \frac{1}{2}e^{3} + 6e^{2} - \frac{3}{2}e - 4$
17 $[17, 17, w^{3} - w^{2} - 3w + 1]$ $\phantom{-}\frac{3}{2}e^{4} - 2e^{3} - \frac{17}{2}e^{2} + 7e + 6$
17 $[17, 17, w^{2} - w - 3]$ $-e^{4} + e^{3} + 7e^{2} - 5e - 6$
31 $[31, 31, w^{3} + w^{2} - 2w - 3]$ $-\frac{1}{2}e^{3} - \frac{1}{2}e + 2$
31 $[31, 31, -w^{3} + w^{2} + 4w - 1]$ $-e^{4} + \frac{3}{2}e^{3} + 5e^{2} - \frac{13}{2}e + 2$
31 $[31, 31, w^{3} + w^{2} - 4w - 1]$ $\phantom{-}\frac{1}{2}e^{4} - e^{3} - \frac{7}{2}e^{2} + 4e + 8$
31 $[31, 31, -w^{3} + w^{2} + 2w - 3]$ $-e^{3} + 2e^{2} + 5e - 4$
47 $[47, 47, -2w^{3} + w^{2} + 5w - 1]$ $-\frac{1}{2}e^{4} + 2e^{3} + \frac{3}{2}e^{2} - 8e$
47 $[47, 47, 2w^{3} + w^{2} - 6w - 1]$ $-e^{4} + 2e^{3} + 7e^{2} - 10e - 8$
47 $[47, 47, -2w^{3} + w^{2} + 6w - 1]$ $-2e + 4$
47 $[47, 47, 2w^{3} + w^{2} - 5w - 1]$ $\phantom{-}e^{4} - \frac{3}{2}e^{3} - 6e^{2} + \frac{17}{2}e + 6$
49 $[49, 7, w^{2} + 1]$ $\phantom{-}e^{4} - 2e^{3} - 5e^{2} + 10e - 2$
49 $[49, 7, -2w^{2} + 3]$ $\phantom{-}e^{4} - 9e^{2} + 10$
79 $[79, 79, -w^{3} - w^{2} + 4w - 1]$ $-1$
79 $[79, 79, -w^{3} + w^{2} + 2w - 5]$ $\phantom{-}\frac{1}{2}e^{4} - 4e^{3} - \frac{3}{2}e^{2} + 19e + 4$
79 $[79, 79, w^{3} + w^{2} - 2w - 5]$ $\phantom{-}\frac{1}{2}e^{4} - e^{3} - \frac{7}{2}e^{2} + 5e + 8$
79 $[79, 79, w^{3} - w^{2} - 4w - 1]$ $-\frac{5}{2}e^{4} + 4e^{3} + \frac{27}{2}e^{2} - 16e - 4$
81 $[81, 3, -3]$ $\phantom{-}\frac{1}{2}e^{4} - 2e^{3} - \frac{7}{2}e^{2} + 13e - 2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$79$ $[79, 79, -w^{3} - w^{2} + 4w - 1]$ $1$