Properties

Label 3.3.169.1-53.3-a
Base field 3.3.169.1
Weight $[2, 2, 2]$
Level norm $53$
Level $[53,53,-w^{2} - w + 3]$
Dimension $4$
CM no
Base change no

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Base field 3.3.169.1

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

Form

Weight: $[2, 2, 2]$
Level: $[53,53,-w^{2} - w + 3]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $4$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 4x^{3} - 5x^{2} + 18x + 17\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -w^{2} + 2w + 3]$ $\phantom{-}\frac{2}{3}e^{3} - 2e^{2} - \frac{4}{3}e + \frac{8}{3}$
5 $[5, 5, -w^{2} + w + 2]$ $\phantom{-}e$
5 $[5, 5, -w + 1]$ $-e^{2} + 2e + 4$
8 $[8, 2, 2]$ $\phantom{-}\frac{1}{3}e^{3} - 2e^{2} + \frac{4}{3}e + \frac{16}{3}$
13 $[13, 13, -w^{2} + 3]$ $-\frac{2}{3}e^{3} + e^{2} + \frac{10}{3}e + \frac{7}{3}$
27 $[27, 3, 3]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{11}{3}e - \frac{14}{3}$
31 $[31, 31, -2w^{2} + 3w + 3]$ $\phantom{-}\frac{2}{3}e^{3} - e^{2} - \frac{22}{3}e + \frac{8}{3}$
31 $[31, 31, -w^{2} + 5]$ $-\frac{4}{3}e^{3} + 5e^{2} + \frac{8}{3}e - \frac{31}{3}$
31 $[31, 31, -w^{2} + 3w + 4]$ $-2e^{2} + 3e + 8$
47 $[47, 47, 2w - 3]$ $-2e^{2} + 6e + 6$
47 $[47, 47, 2w^{2} - 4w - 7]$ $\phantom{-}\frac{1}{3}e^{3} + 2e^{2} - \frac{23}{3}e - \frac{20}{3}$
47 $[47, 47, 2w^{2} - 2w - 3]$ $-\frac{2}{3}e^{3} - 2e^{2} + \frac{28}{3}e + \frac{52}{3}$
53 $[53, 53, 3w^{2} - 4w - 8]$ $-2e^{3} + 4e^{2} + 10e - 4$
53 $[53, 53, 4w^{2} - 6w - 11]$ $-\frac{4}{3}e^{3} + 6e^{2} - \frac{4}{3}e - \frac{40}{3}$
53 $[53, 53, 3w^{2} - 5w - 6]$ $\phantom{-}1$
73 $[73, 73, w^{2} - 4w - 4]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{17}{3}e + \frac{4}{3}$
73 $[73, 73, 2w^{2} - w - 8]$ $\phantom{-}\frac{4}{3}e^{3} - 6e^{2} + \frac{4}{3}e + \frac{34}{3}$
73 $[73, 73, 3w^{2} - 5w - 5]$ $\phantom{-}e^{3} - 2e^{2} - 7e - 2$
79 $[79, 79, -3w^{2} + 5w + 4]$ $\phantom{-}2e^{3} - 4e^{2} - 8e - 4$
79 $[79, 79, 2w^{2} - w - 9]$ $\phantom{-}2e^{2} - 6e - 8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$53$ $[53,53,-w^{2} - w + 3]$ $-1$