Properties

Base field 3.3.1849.1
Weight [2, 2, 2]
Level norm 8
Level $[8, 4, -w]$
Label 3.3.1849.1-8.2-b
Dimension 5
CM no
Base change no

Related objects

Downloads

Learn more about

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 $[8, 4, -w]$
Label 3.3.1849.1-8.2-b
Dimension 5
Is CM no
Is base change no
Parent newspace dimension 6

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} - x^{4} - 8x^{3} + 8x^{2} + 11x - 9\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -\frac{1}{2}w^{2} + \frac{1}{2}w + 8]$ $\phantom{-}0$
2 $[2, 2, \frac{1}{2}w^{2} - \frac{3}{2}w - 1]$ $-1$
2 $[2, 2, w + 3]$ $\phantom{-}e$
11 $[11, 11, -w^{2} + 3w + 7]$ $\phantom{-}e^{3} - 5e$
11 $[11, 11, -2w - 1]$ $-e^{4} + 8e^{2} - 9$
11 $[11, 11, -w^{2} + w + 11]$ $-e^{4} + 6e^{2} - 3$
27 $[27, 3, 3]$ $-e^{3} + 7e - 2$
41 $[41, 41, 2w + 5]$ $\phantom{-}2e^{4} - 12e^{2} + 2e + 6$
41 $[41, 41, -w^{2} + 3w + 3]$ $\phantom{-}e^{3} - 2e^{2} - 7e + 6$
41 $[41, 41, -w^{2} + w + 15]$ $-2e^{4} + 14e^{2} - 18$
43 $[43, 43, -3w^{2} + 11w + 11]$ $-2e^{4} - e^{3} + 16e^{2} + 5e - 22$
47 $[47, 47, -w^{2} - w + 5]$ $\phantom{-}e^{4} + 2e^{3} - 6e^{2} - 8e + 3$
47 $[47, 47, w^{2} - 5w - 3]$ $\phantom{-}2e^{4} + 2e^{3} - 16e^{2} - 8e + 24$
47 $[47, 47, -2w^{2} + 4w + 23]$ $-e^{4} + e^{3} + 8e^{2} - 3e - 15$
59 $[59, 59, -w^{2} + w + 13]$ $\phantom{-}2e^{3} + 2e^{2} - 10e - 6$
59 $[59, 59, w^{2} - 3w - 5]$ $-e^{4} + 8e^{2} - 2e - 9$
59 $[59, 59, -2w - 3]$ $-3e^{4} - e^{3} + 22e^{2} + e - 21$
97 $[97, 97, 7w^{2} - 11w - 91]$ $\phantom{-}2e^{4} - 16e^{2} + 20$
97 $[97, 97, -2w^{2} - 8w - 5]$ $\phantom{-}e^{4} + 2e^{3} - 8e^{2} - 10e + 17$
97 $[97, 97, 5w^{2} - 19w - 15]$ $\phantom{-}e^{4} - 2e^{3} - 8e^{2} + 14e + 11$
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 $[2, 2, \frac{1}{2}w^{2} - \frac{3}{2}w - 1]$ $1$