Properties

Base field 3.3.1849.1
Weight [2, 2, 2]
Level norm 8
Level $[8,8,w^{2} - 2w - 11]$
Label 3.3.1849.1-8.9-b
Dimension 5
CM no
Base change no

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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 $[8,8,w^{2} - 2w - 11]$
Label 3.3.1849.1-8.9-b
Dimension 5
Is CM no
Is base change no
Parent newspace dimension 18

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} + x^{4} - 5x^{3} - 4x^{2} + 4x + 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -\frac{1}{2}w^{2} + \frac{1}{2}w + 8]$ $\phantom{-}e$
2 $[2, 2, \frac{1}{2}w^{2} - \frac{3}{2}w - 1]$ $-e^{2} + 2$
2 $[2, 2, w + 3]$ $\phantom{-}0$
11 $[11, 11, -w^{2} + 3w + 7]$ $\phantom{-}e^{3} - 3e$
11 $[11, 11, -2w - 1]$ $\phantom{-}2e^{4} + e^{3} - 9e^{2} - 5e + 5$
11 $[11, 11, -w^{2} + w + 11]$ $-e^{4} - e^{3} + 5e^{2} + 5e - 4$
27 $[27, 3, 3]$ $-2e^{3} + 2e^{2} + 8e - 2$
41 $[41, 41, 2w + 5]$ $-3e^{4} - 3e^{3} + 14e^{2} + 7e - 9$
41 $[41, 41, -w^{2} + 3w + 3]$ $\phantom{-}3e^{4} + e^{3} - 16e^{2} - 7e + 11$
41 $[41, 41, -w^{2} + w + 15]$ $-e^{4} - e^{3} + 4e^{2} + 5e - 3$
43 $[43, 43, -3w^{2} + 11w + 11]$ $-2e^{4} + 10e^{2} - 2e - 8$
47 $[47, 47, -w^{2} - w + 5]$ $-e^{4} + 3e^{3} + 2e^{2} - 11e + 5$
47 $[47, 47, w^{2} - 5w - 3]$ $-e^{4} - e^{3} + 2e^{2} + 5e - 1$
47 $[47, 47, -2w^{2} + 4w + 23]$ $-5e^{4} - 3e^{3} + 22e^{2} + 11e - 11$
59 $[59, 59, -w^{2} + w + 13]$ $\phantom{-}e^{4} - 2e^{2} - 9$
59 $[59, 59, w^{2} - 3w - 5]$ $\phantom{-}3e^{4} - 2e^{3} - 11e^{2} + 4e - 4$
59 $[59, 59, -2w - 3]$ $-4e^{4} - 4e^{3} + 17e^{2} + 10e - 9$
97 $[97, 97, 7w^{2} - 11w - 91]$ $\phantom{-}e^{4} - e^{3} - 4e^{2} + e + 3$
97 $[97, 97, -2w^{2} - 8w - 5]$ $-5e^{4} - e^{3} + 24e^{2} + 5e - 19$
97 $[97, 97, 5w^{2} - 19w - 15]$ $-3e^{4} + e^{3} + 14e^{2} - 3e - 9$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2,2,w + 3]$ $1$