Properties

Label 4.4.8957.1-27.1-f
Base field 4.4.8957.1
Weight $[2, 2, 2, 2]$
Level norm $27$
Level $[27, 3, -w^{3} + 2w^{2} + 3w - 1]$
Dimension $3$
CM no
Base change no

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Base field 4.4.8957.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[27, 3, -w^{3} + 2w^{2} + 3w - 1]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $15$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{3} + 2x^{2} - 5x - 2\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w^{3} + w^{2} + 5w]$ $\phantom{-}e$
3 $[3, 3, w - 1]$ $\phantom{-}1$
9 $[9, 3, w^{3} - w^{2} - 4w]$ $-1$
13 $[13, 13, -2w^{3} + w^{2} + 11w + 3]$ $\phantom{-}e^{2} + 2e - 4$
13 $[13, 13, w^{3} - 2w^{2} - 4w + 3]$ $-\frac{1}{2}e^{2} - \frac{3}{2}e - 3$
16 $[16, 2, 2]$ $-\frac{1}{2}e^{2} - \frac{5}{2}e$
23 $[23, 23, -w^{2} + 2]$ $\phantom{-}e - 2$
23 $[23, 23, -w^{3} + 2w^{2} + 4w - 4]$ $-\frac{3}{2}e^{2} - \frac{7}{2}e + 3$
49 $[49, 7, -w^{3} + 2w^{2} + 5w - 2]$ $\phantom{-}e + 4$
49 $[49, 7, 2w^{3} - 2w^{2} - 9w - 1]$ $\phantom{-}\frac{5}{2}e^{2} + \frac{7}{2}e - 9$
53 $[53, 53, w^{3} - 3w^{2} + 3]$ $\phantom{-}2e^{2} + e - 12$
53 $[53, 53, 2w^{3} - w^{2} - 8w - 3]$ $\phantom{-}5e + 4$
53 $[53, 53, -w^{3} + w^{2} + 6w - 1]$ $-\frac{3}{2}e^{2} - \frac{9}{2}e + 5$
61 $[61, 61, -w - 3]$ $-3e^{2} - 4e + 10$
61 $[61, 61, -w^{3} + w^{2} + 5w - 4]$ $\phantom{-}e^{2} + 3e - 8$
79 $[79, 79, w^{3} - 2w^{2} - 4w + 1]$ $\phantom{-}2e^{2} + 5e - 8$
79 $[79, 79, w^{2} - 5]$ $\phantom{-}2e^{2} + 3e$
101 $[101, 101, w^{3} - 6w]$ $-4e^{2} - 4e + 14$
101 $[101, 101, w^{2} - 2w - 4]$ $-\frac{1}{2}e^{2} - \frac{11}{2}e + 1$
103 $[103, 103, 4w^{3} - 3w^{2} - 20w - 3]$ $\phantom{-}\frac{1}{2}e^{2} + \frac{5}{2}e - 1$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w - 1]$ $-1$
$9$ $[9, 3, w^{3} - w^{2} - 4w]$ $1$