Properties

Label 4.4.8525.1-11.3-b
Base field 4.4.8525.1
Weight $[2, 2, 2, 2]$
Level norm $11$
Level $[11,11,w^{2} - 5]$
Dimension $3$
CM no
Base change no

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Base field 4.4.8525.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 8x^{2} + 9x + 19\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[11,11,w^{2} - 5]$
Dimension: $3$
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:

\(x^{3} + 2x^{2} - 14x - 32\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, w + 1]$ $-\frac{1}{2}e^{2} + 5$
5 $[5, 5, -w + 2]$ $\phantom{-}e$
11 $[11, 11, w^{2} - 2w - 4]$ $\phantom{-}\frac{1}{2}e^{2} - e - 9$
11 $[11, 11, -w^{2} + 3]$ $\phantom{-}e^{2} - 10$
11 $[11, 11, w^{2} - 5]$ $\phantom{-}1$
16 $[16, 2, 2]$ $-e^{2} + 9$
19 $[19, 19, -w]$ $-\frac{3}{2}e^{2} + e + 13$
19 $[19, 19, -w + 1]$ $\phantom{-}2e^{2} - 2e - 26$
31 $[31, 31, -w^{3} + 3w^{2} + 2w - 9]$ $-e^{2} + 14$
31 $[31, 31, -w^{2} + 2w + 7]$ $-e^{2} + 4$
31 $[31, 31, -w^{3} + 5w + 5]$ $\phantom{-}e^{2} - 2e - 16$
41 $[41, 41, -w^{3} + 2w^{2} + 4w - 2]$ $-2e^{2} + 2e + 28$
41 $[41, 41, -w^{3} + w^{2} + 5w - 3]$ $-\frac{1}{2}e^{2} - e + 3$
59 $[59, 59, -w^{3} + w^{2} + 6w - 2]$ $-\frac{7}{2}e^{2} + 3e + 41$
59 $[59, 59, -w^{3} + w^{2} + 4w + 5]$ $-\frac{1}{2}e^{2} - e + 7$
59 $[59, 59, w^{3} - 5w^{2} - w + 18]$ $\phantom{-}5e^{2} - 6e - 62$
59 $[59, 59, w^{3} - 2w^{2} - 5w + 4]$ $\phantom{-}2e^{2} - 2e - 28$
81 $[81, 3, -3]$ $\phantom{-}\frac{3}{2}e^{2} - e - 19$
89 $[89, 89, -w^{3} + 3w^{2} - 3]$ $-\frac{7}{2}e^{2} + 2e + 41$
89 $[89, 89, -4w^{2} + 5w + 20]$ $\phantom{-}3e - 4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$11$ $[11,11,w^{2} - 5]$ $-1$