Properties

Label 4.4.8957.1-13.2-a
Base field 4.4.8957.1
Weight $[2, 2, 2, 2]$
Level norm $13$
Level $[13,13,w^{2} - 3w]$
Dimension $5$
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: $[13,13,w^{2} - 3w]$
Dimension: $5$
CM: no
Base change: no
Newspace dimension: $12$

Hecke eigenvalues ($q$-expansion)

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

\(x^{5} + 3x^{4} - 5x^{3} - 13x^{2} + 6x + 9\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w^{3} + w^{2} + 5w]$ $\phantom{-}e$
3 $[3, 3, w - 1]$ $-\frac{1}{3}e^{4} - e^{3} + \frac{2}{3}e^{2} + \frac{7}{3}e + 1$
9 $[9, 3, w^{3} - w^{2} - 4w]$ $-\frac{1}{3}e^{4} + \frac{11}{3}e^{2} - \frac{2}{3}e - 6$
13 $[13, 13, -2w^{3} + w^{2} + 11w + 3]$ $\phantom{-}\frac{1}{3}e^{4} + e^{3} - \frac{2}{3}e^{2} - \frac{10}{3}e - 3$
13 $[13, 13, w^{3} - 2w^{2} - 4w + 3]$ $\phantom{-}1$
16 $[16, 2, 2]$ $\phantom{-}\frac{1}{3}e^{4} + e^{3} - \frac{2}{3}e^{2} - \frac{7}{3}e - 5$
23 $[23, 23, -w^{2} + 2]$ $\phantom{-}e^{4} + 2e^{3} - 6e^{2} - 7e + 6$
23 $[23, 23, -w^{3} + 2w^{2} + 4w - 4]$ $\phantom{-}\frac{1}{3}e^{4} + e^{3} - \frac{5}{3}e^{2} - \frac{16}{3}e - 2$
49 $[49, 7, -w^{3} + 2w^{2} + 5w - 2]$ $\phantom{-}e^{4} + 2e^{3} - 7e^{2} - 4e + 8$
49 $[49, 7, 2w^{3} - 2w^{2} - 9w - 1]$ $\phantom{-}\frac{1}{3}e^{4} - 2e^{3} - \frac{29}{3}e^{2} + \frac{20}{3}e + 19$
53 $[53, 53, w^{3} - 3w^{2} + 3]$ $\phantom{-}e^{4} + 3e^{3} - 3e^{2} - 12e - 1$
53 $[53, 53, 2w^{3} - w^{2} - 8w - 3]$ $\phantom{-}\frac{1}{3}e^{4} - \frac{5}{3}e^{2} + \frac{8}{3}e - 1$
53 $[53, 53, -w^{3} + w^{2} + 6w - 1]$ $-\frac{4}{3}e^{4} - 3e^{3} + \frac{20}{3}e^{2} + \frac{16}{3}e - 7$
61 $[61, 61, -w - 3]$ $\phantom{-}e^{4} + 2e^{3} - 7e^{2} - 6e + 3$
61 $[61, 61, -w^{3} + w^{2} + 5w - 4]$ $-e^{4} - 4e^{3} + 2e^{2} + 15e$
79 $[79, 79, w^{3} - 2w^{2} - 4w + 1]$ $\phantom{-}2e^{4} + 5e^{3} - 6e^{2} - 10e - 2$
79 $[79, 79, w^{2} - 5]$ $\phantom{-}\frac{2}{3}e^{4} + 2e^{3} - \frac{7}{3}e^{2} - \frac{14}{3}e - 10$
101 $[101, 101, w^{3} - 6w]$ $\phantom{-}2e^{4} + 5e^{3} - 9e^{2} - 10e + 11$
101 $[101, 101, w^{2} - 2w - 4]$ $-\frac{4}{3}e^{4} - 7e^{3} + \frac{2}{3}e^{2} + \frac{79}{3}e + 1$
103 $[103, 103, 4w^{3} - 3w^{2} - 20w - 3]$ $-e^{4} + e^{3} + 12e^{2} - 5e - 14$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13,13,w^{2} - 3w]$ $-1$