Properties

Label 4.4.19525.1-16.1-d
Base field 4.4.19525.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 2, 2]$
Dimension $2$
CM no
Base change no

Related objects

Downloads

Learn more about

Base field 4.4.19525.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 14x^{2} + 15x + 45\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[16, 2, 2]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $36$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - x - 10\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, \frac{2}{3}w^{2} + \frac{1}{3}w - 5]$ $\phantom{-}e$
5 $[5, 5, \frac{2}{3}w^{2} - \frac{5}{3}w - 4]$ $-e + 1$
9 $[9, 3, -w + 3]$ $\phantom{-}e + 1$
9 $[9, 3, w + 2]$ $-e + 2$
11 $[11, 11, \frac{2}{3}w^{2} + \frac{1}{3}w - 4]$ $-2$
16 $[16, 2, 2]$ $-1$
19 $[19, 19, \frac{1}{3}w^{3} - \frac{10}{3}w - 3]$ $\phantom{-}e - 1$
19 $[19, 19, \frac{1}{3}w^{3} - w^{2} - \frac{7}{3}w + 6]$ $-e$
29 $[29, 29, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{8}{3}w - 2]$ $\phantom{-}e + 4$
29 $[29, 29, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ $-e + 5$
31 $[31, 31, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w + 1]$ $\phantom{-}4$
31 $[31, 31, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{8}{3}w - 4]$ $\phantom{-}4$
49 $[49, 7, \frac{1}{3}w^{3} - \frac{10}{3}w - 1]$ $-e + 1$
49 $[49, 7, -\frac{1}{3}w^{3} + w^{2} + \frac{7}{3}w - 4]$ $\phantom{-}e$
59 $[59, 59, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{5}{3}w - 11]$ $-e + 6$
59 $[59, 59, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 5w - 13]$ $\phantom{-}e + 5$
61 $[61, 61, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{2}{3}w - 9]$ $-e$
61 $[61, 61, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 4w + 2]$ $-e$
61 $[61, 61, \frac{2}{3}w^{2} - \frac{5}{3}w - 1]$ $\phantom{-}e - 1$
61 $[61, 61, -\frac{1}{3}w^{2} + \frac{4}{3}w + 6]$ $\phantom{-}e - 1$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$16$ $[16, 2, 2]$ $1$