Properties

Label 4.4.14197.1-7.1-f
Base field 4.4.14197.1
Weight $[2, 2, 2, 2]$
Level norm $7$
Level $[7, 7, w - 1]$
Dimension $2$
CM no
Base change no

Related objects

Downloads

Learn more

Base field 4.4.14197.1

Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - 3x + 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[7, 7, w - 1]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $8$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 4x + 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
7 $[7, 7, w - 1]$ $-1$
9 $[9, 3, w^{3} - 5w - 2]$ $\phantom{-}e$
9 $[9, 3, w^{3} - w^{2} - 4w]$ $\phantom{-}4$
13 $[13, 13, -w + 2]$ $-e + 4$
16 $[16, 2, 2]$ $\phantom{-}3$
17 $[17, 17, w^{3} - w^{2} - 5w]$ $-1$
19 $[19, 19, -w^{3} + w^{2} + 6w]$ $-2$
23 $[23, 23, -w^{2} + w + 3]$ $\phantom{-}2e$
29 $[29, 29, w^{3} - 5w]$ $\phantom{-}e - 8$
31 $[31, 31, w^{3} - 6w - 1]$ $-2e + 8$
31 $[31, 31, w^{2} - 2]$ $-2e$
37 $[37, 37, -w - 3]$ $\phantom{-}4e - 7$
37 $[37, 37, w^{3} - 4w - 1]$ $\phantom{-}e - 4$
37 $[37, 37, w^{3} - 7w - 4]$ $-4e + 7$
37 $[37, 37, w^{2} - 3]$ $\phantom{-}4e - 4$
43 $[43, 43, w^{2} + w - 3]$ $-2e$
43 $[43, 43, w^{3} - w^{2} - 5w - 1]$ $-2$
47 $[47, 47, -w^{3} + w^{2} + 5w - 4]$ $\phantom{-}2$
53 $[53, 53, w^{3} - 6w]$ $-5e + 12$
61 $[61, 61, w^{3} - w^{2} - 7w - 2]$ $\phantom{-}8e - 15$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$7$ $[7, 7, w - 1]$ $1$