Properties

Base field 3.3.1849.1
Weight [2, 2, 2]
Level norm 8
Level $[8, 2, 2]$
Label 3.3.1849.1-8.1-h
Dimension 2
CM no
Base change yes

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Base field 3.3.1849.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 14x - 8\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2]
Level $[8, 2, 2]$
Label 3.3.1849.1-8.1-h
Dimension 2
Is CM no
Is base change yes
Parent newspace dimension 9

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} + x - 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -\frac{1}{2}w^{2} + \frac{1}{2}w + 8]$ $\phantom{-}1$
2 $[2, 2, \frac{1}{2}w^{2} - \frac{3}{2}w - 1]$ $\phantom{-}1$
2 $[2, 2, w + 3]$ $\phantom{-}1$
11 $[11, 11, -w^{2} + 3w + 7]$ $\phantom{-}e$
11 $[11, 11, -2w - 1]$ $\phantom{-}e$
11 $[11, 11, -w^{2} + w + 11]$ $\phantom{-}e$
27 $[27, 3, 3]$ $-4e$
41 $[41, 41, 2w + 5]$ $-3e + 2$
41 $[41, 41, -w^{2} + 3w + 3]$ $-3e + 2$
41 $[41, 41, -w^{2} + w + 15]$ $-3e + 2$
43 $[43, 43, -3w^{2} + 11w + 11]$ $-3e + 4$
47 $[47, 47, -w^{2} - w + 5]$ $-2e - 4$
47 $[47, 47, w^{2} - 5w - 3]$ $-2e - 4$
47 $[47, 47, -2w^{2} + 4w + 23]$ $-2e - 4$
59 $[59, 59, -w^{2} + w + 13]$ $\phantom{-}5e$
59 $[59, 59, w^{2} - 3w - 5]$ $\phantom{-}5e$
59 $[59, 59, -2w - 3]$ $\phantom{-}5e$
97 $[97, 97, 7w^{2} - 11w - 91]$ $\phantom{-}e + 10$
97 $[97, 97, -2w^{2} - 8w - 5]$ $\phantom{-}e + 10$
97 $[97, 97, 5w^{2} - 19w - 15]$ $\phantom{-}e + 10$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -\frac{1}{2}w^{2} + \frac{1}{2}w + 8]$ $-1$
2 $[2, 2, \frac{1}{2}w^{2} - \frac{3}{2}w - 1]$ $-1$
2 $[2, 2, w + 3]$ $-1$