Properties

Base field 4.4.8789.1
Weight [2, 2, 2, 2]
Level norm 31
Level $[31, 31, -w^{3} + 2w^{2} + 3w - 2]$
Label 4.4.8789.1-31.1-i
Dimension 4
CM no
Base change no

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Base field 4.4.8789.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} - 2x + 1\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[31, 31, -w^{3} + 2w^{2} + 3w - 2]$
Label 4.4.8789.1-31.1-i
Dimension 4
Is CM no
Is base change no
Parent newspace dimension 21

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + 7x^{3} + 8x^{2} - 19x - 13\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -w^{3} + 2w^{2} + 3w]$ $\phantom{-}e$
7 $[7, 7, w - 1]$ $-1$
11 $[11, 11, -w^{3} + 2w^{2} + 4w]$ $\phantom{-}e^{3} + 3e^{2} - 5e - 3$
13 $[13, 13, -2w^{3} + 3w^{2} + 10w - 2]$ $-\frac{3}{2}e^{3} - 5e^{2} + 5e + \frac{11}{2}$
16 $[16, 2, 2]$ $-\frac{1}{2}e^{3} - 2e^{2} + e + \frac{3}{2}$
17 $[17, 17, -w^{3} + 2w^{2} + 5w - 3]$ $-e^{2} - 3e + 1$
17 $[17, 17, -w^{3} + w^{2} + 5w]$ $\phantom{-}e + 3$
17 $[17, 17, -w^{2} + 2w + 1]$ $\phantom{-}\frac{1}{2}e^{3} + 3e^{2} + 3e - \frac{7}{2}$
19 $[19, 19, w^{2} - w - 2]$ $\phantom{-}\frac{3}{2}e^{3} + 5e^{2} - 6e - \frac{21}{2}$
29 $[29, 29, w^{3} - 2w^{2} - 5w]$ $-\frac{3}{2}e^{3} - 4e^{2} + 7e - \frac{5}{2}$
29 $[29, 29, w^{2} - w - 3]$ $-\frac{1}{2}e^{3} - 3e^{2} - 2e + \frac{17}{2}$
31 $[31, 31, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}1$
43 $[43, 43, 2w^{3} - 3w^{2} - 11w]$ $-\frac{3}{2}e^{3} - 5e^{2} + 5e + \frac{13}{2}$
47 $[47, 47, w^{3} - 7w - 4]$ $-2e^{2} - 5e + 3$
53 $[53, 53, -2w^{3} + 3w^{2} + 9w - 1]$ $\phantom{-}e^{3} + 5e^{2} - e - 9$
61 $[61, 61, -w - 3]$ $\phantom{-}\frac{5}{2}e^{3} + 9e^{2} - 7e - \frac{27}{2}$
73 $[73, 73, -w^{3} + 2w^{2} + 3w - 3]$ $\phantom{-}2e^{3} + 5e^{2} - 13e - 4$
73 $[73, 73, w^{3} - w^{2} - 7w - 1]$ $-\frac{1}{2}e^{3} + 3e - \frac{25}{2}$
81 $[81, 3, -3]$ $-\frac{1}{2}e^{3} - 4e^{2} - 6e + \frac{17}{2}$
83 $[83, 83, -2w^{3} + 3w^{2} + 9w + 1]$ $-e^{3} - 3e^{2} + 9e + 11$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
31 $[31, 31, -w^{3} + 2w^{2} + 3w - 2]$ $-1$