Properties

Label 4.4.19525.1-25.1-e
Base field 4.4.19525.1
Weight $[2, 2, 2, 2]$
Level norm $25$
Level $[25, 5, -\frac{2}{3}w^{2} + \frac{5}{3}w + 5]$
Dimension $4$
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: $[25, 5, -\frac{2}{3}w^{2} + \frac{5}{3}w + 5]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $44$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 20x^{2} + 54\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, \frac{2}{3}w^{2} + \frac{1}{3}w - 5]$ $\phantom{-}0$
5 $[5, 5, \frac{2}{3}w^{2} - \frac{5}{3}w - 4]$ $\phantom{-}e$
9 $[9, 3, -w + 3]$ $\phantom{-}4$
9 $[9, 3, w + 2]$ $-4$
11 $[11, 11, \frac{2}{3}w^{2} + \frac{1}{3}w - 4]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{14}{3}e$
16 $[16, 2, 2]$ $\phantom{-}e^{2} - 11$
19 $[19, 19, \frac{1}{3}w^{3} - \frac{10}{3}w - 3]$ $\phantom{-}e$
19 $[19, 19, \frac{1}{3}w^{3} - w^{2} - \frac{7}{3}w + 6]$ $-e$
29 $[29, 29, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{8}{3}w - 2]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{14}{3}e$
29 $[29, 29, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ $-\frac{1}{3}e^{3} + \frac{14}{3}e$
31 $[31, 31, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w + 1]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{17}{3}e$
31 $[31, 31, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{8}{3}w - 4]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{17}{3}e$
49 $[49, 7, \frac{1}{3}w^{3} - \frac{10}{3}w - 1]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{11}{3}e$
49 $[49, 7, -\frac{1}{3}w^{3} + w^{2} + \frac{7}{3}w - 4]$ $-\frac{1}{3}e^{3} + \frac{11}{3}e$
59 $[59, 59, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{5}{3}w - 11]$ $\phantom{-}e^{2} - 12$
59 $[59, 59, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 5w - 13]$ $-e^{2} + 12$
61 $[61, 61, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{2}{3}w - 9]$ $\phantom{-}8$
61 $[61, 61, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 4w + 2]$ $-\frac{1}{3}e^{3} + \frac{11}{3}e$
61 $[61, 61, \frac{2}{3}w^{2} - \frac{5}{3}w - 1]$ $-\frac{1}{3}e^{3} + \frac{11}{3}e$
61 $[61, 61, -\frac{1}{3}w^{2} + \frac{4}{3}w + 6]$ $\phantom{-}8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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