Properties

Label 4.4.10273.1-9.1-c
Base field 4.4.10273.1
Weight $[2, 2, 2, 2]$
Level norm $9$
Level $[9, 9, w^{3} - 3w^{2} - 2w + 1]$
Dimension $4$
CM no
Base change no

Related objects

Downloads

Learn more

Base field 4.4.10273.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[9, 9, w^{3} - 3w^{2} - 2w + 1]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $7$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 26x^{2} + 97\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w]$ $-\frac{1}{6}e^{2} + \frac{19}{6}$
3 $[3, 3, w - 1]$ $\phantom{-}0$
8 $[8, 2, w^{3} - 2w^{2} - 5w + 1]$ $\phantom{-}e$
13 $[13, 13, -w^{2} + 2w + 3]$ $\phantom{-}\frac{1}{6}e^{3} - \frac{13}{6}e$
17 $[17, 17, -w^{2} + 3w + 3]$ $-\frac{1}{6}e^{2} + \frac{37}{6}$
17 $[17, 17, -w^{2} + 2w + 1]$ $\phantom{-}\frac{1}{6}e^{3} - \frac{25}{6}e$
27 $[27, 3, w^{3} - w^{2} - 6w - 5]$ $-\frac{1}{3}e^{3} + \frac{19}{3}e$
29 $[29, 29, w^{3} - 2w^{2} - 2w + 1]$ $\phantom{-}\frac{1}{6}e^{2} - \frac{1}{6}$
47 $[47, 47, w^{3} - 2w^{2} - 4w - 3]$ $\phantom{-}2e$
49 $[49, 7, w^{3} - 3w^{2} - 3w + 1]$ $\phantom{-}\frac{1}{6}e^{3} - \frac{13}{6}e$
49 $[49, 7, -2w^{3} + 5w^{2} + 7w - 3]$ $-\frac{1}{3}e^{3} + \frac{19}{3}e$
59 $[59, 59, -2w^{3} + 6w^{2} + 5w - 7]$ $\phantom{-}0$
61 $[61, 61, 2w^{3} - 4w^{2} - 9w - 3]$ $-\frac{7}{6}e^{2} + \frac{103}{6}$
71 $[71, 71, w^{3} - 3w^{2} - 3w + 7]$ $\phantom{-}0$
73 $[73, 73, 2w^{3} - 6w^{2} - 3w + 5]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{25}{3}e$
73 $[73, 73, w^{3} - 3w^{2} - 4w + 5]$ $-\frac{1}{2}e^{3} + \frac{17}{2}e$
83 $[83, 83, -2w^{3} + 5w^{2} + 8w - 3]$ $\phantom{-}\frac{1}{3}e^{2} - \frac{19}{3}$
89 $[89, 89, -2w^{3} + 6w^{2} + 4w - 7]$ $-8$
89 $[89, 89, w^{3} - 2w^{2} - 6w + 3]$ $-e^{2} + 9$
97 $[97, 97, -3w - 1]$ $\phantom{-}\frac{5}{6}e^{2} - \frac{89}{6}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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