Properties

Base field \(\Q(\zeta_{11})^+\)
Weight [2, 2, 2, 2, 2]
Level norm 89
Level $[89,89,-2w^{4} + w^{3} + 7w^{2} - 3w - 2]$
Label 5.5.14641.1-89.2-a
Dimension 3
CM no
Base change no

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Base field \(\Q(\zeta_{11})^+\)

Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x - 1\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2, 2, 2]
Level $[89,89,-2w^{4} + w^{3} + 7w^{2} - 3w - 2]$
Label 5.5.14641.1-89.2-a
Dimension 3
Is CM no
Is base change no
Parent newspace dimension 3

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} \) \(\mathstrut -\mathstrut 16x \) \(\mathstrut -\mathstrut 16\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
11 $[11, 11, w^{4} + w^{3} - 4w^{2} - 3w + 2]$ $\phantom{-}e$
23 $[23, 23, -w^{4} + 3w^{2} + 1]$ $-e^{2} + 3e + 12$
23 $[23, 23, -w^{4} + 3w^{2} + w - 2]$ $\phantom{-}\frac{1}{4}e^{2} - \frac{5}{2}e - 2$
23 $[23, 23, w^{4} - w^{3} - 3w^{2} + 3w + 2]$ $-\frac{1}{4}e^{2} + \frac{1}{2}e + 4$
23 $[23, 23, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ $\phantom{-}\frac{1}{2}e^{2} - 8$
23 $[23, 23, -w^{2} + w + 3]$ $-\frac{1}{4}e^{2}$
32 $[32, 2, 2]$ $\phantom{-}\frac{5}{4}e^{2} - 2e - 13$
43 $[43, 43, -2w^{4} + w^{3} + 6w^{2} - 2w - 1]$ $\phantom{-}\frac{3}{4}e^{2} - 4$
43 $[43, 43, -w^{4} + 2w^{2} + w + 1]$ $-e^{2} + 8$
43 $[43, 43, w^{3} + w^{2} - 4w - 2]$ $\phantom{-}\frac{1}{4}e^{2} - \frac{1}{2}e + 4$
43 $[43, 43, 2w^{4} - w^{3} - 7w^{2} + 3w + 3]$ $-\frac{1}{2}e^{2} - e + 8$
43 $[43, 43, w^{4} - w^{3} - 4w^{2} + 4w + 2]$ $-\frac{1}{2}e^{2} + e + 4$
67 $[67, 67, 2w^{4} - 7w^{2} + 2]$ $\phantom{-}\frac{7}{4}e^{2} - \frac{1}{2}e - 18$
67 $[67, 67, w^{4} - 2w^{3} - 3w^{2} + 6w + 2]$ $-\frac{1}{2}e^{2} + e + 8$
67 $[67, 67, 2w^{4} - 7w^{2} - w + 4]$ $\phantom{-}\frac{3}{4}e^{2} + \frac{1}{2}e - 6$
67 $[67, 67, w^{4} - 2w^{3} - 4w^{2} + 6w + 2]$ $\phantom{-}\frac{3}{4}e^{2} - \frac{7}{2}e - 8$
67 $[67, 67, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ $\phantom{-}\frac{1}{2}e^{2} - 2e$
89 $[89, 89, w^{3} + w^{2} - 4w - 1]$ $-e^{2} + 14$
89 $[89, 89, -2w^{4} + w^{3} + 7w^{2} - 3w - 2]$ $\phantom{-}1$
89 $[89, 89, -w^{4} + w^{3} + 4w^{2} - 4w - 3]$ $-\frac{5}{4}e^{2} + \frac{1}{2}e + 14$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
89 $[89,89,-2w^{4} + w^{3} + 7w^{2} - 3w - 2]$ $-1$