Properties

Base field 3.3.940.1
Weight [2, 2, 2]
Level norm 16
Level $[16, 4, w^{2} - 7]$
Label 3.3.940.1-16.2-d
Dimension 5
CM no
Base change no

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Base field 3.3.940.1

Generator \(w\), with minimal polynomial \(x^{3} - 7x - 4\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2]
Level $[16, 4, w^{2} - 7]$
Label 3.3.940.1-16.2-d
Dimension 5
Is CM no
Is base change no
Parent newspace dimension 11

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} + 2x^{4} - 7x^{3} - 13x^{2} + 4x + 5\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $\phantom{-}e$
2 $[2, 2, -w - 1]$ $\phantom{-}0$
5 $[5, 5, -w^{2} + w + 7]$ $\phantom{-}\frac{1}{2}e^{4} + \frac{1}{2}e^{3} - 4e^{2} - \frac{5}{2}e + \frac{7}{2}$
5 $[5, 5, -w^{2} + w + 5]$ $-\frac{1}{2}e^{4} - \frac{1}{2}e^{3} + 3e^{2} + \frac{7}{2}e + \frac{1}{2}$
17 $[17, 17, -w^{2} + 3w + 1]$ $-\frac{3}{2}e^{4} - \frac{3}{2}e^{3} + 11e^{2} + \frac{17}{2}e - \frac{13}{2}$
23 $[23, 23, -w^{2} + w + 3]$ $\phantom{-}e^{4} - 7e^{2} + 6$
27 $[27, 3, 3]$ $-e^{3} + e^{2} + 7e - 3$
29 $[29, 29, -w^{2} + 3w - 1]$ $\phantom{-}\frac{1}{2}e^{4} + \frac{1}{2}e^{3} - 4e^{2} - \frac{9}{2}e + \frac{11}{2}$
37 $[37, 37, w^{2} + w + 1]$ $\phantom{-}\frac{3}{2}e^{4} + \frac{1}{2}e^{3} - 9e^{2} - \frac{5}{2}e - \frac{1}{2}$
41 $[41, 41, w^{2} - w - 9]$ $\phantom{-}\frac{1}{2}e^{4} + \frac{3}{2}e^{3} - e^{2} - \frac{19}{2}e - \frac{11}{2}$
43 $[43, 43, -3w^{2} + 3w + 17]$ $-e^{4} + e^{3} + 8e^{2} - 5e - 7$
47 $[47, 47, 2w^{2} - 2w - 13]$ $\phantom{-}e^{4} + 3e^{3} - 6e^{2} - 17e + 3$
47 $[47, 47, -2w + 5]$ $-2e^{3} + 14e + 4$
53 $[53, 53, 3w^{2} - w - 19]$ $\phantom{-}\frac{3}{2}e^{4} + \frac{5}{2}e^{3} - 10e^{2} - \frac{23}{2}e + \frac{15}{2}$
59 $[59, 59, 2w - 1]$ $\phantom{-}e^{4} - 9e^{2} - 2e + 14$
67 $[67, 67, w^{2} + w - 5]$ $-e^{3} - e^{2} + 7e + 7$
71 $[71, 71, -3w^{2} + w + 21]$ $\phantom{-}e^{4} - 9e^{2} - 4e + 12$
79 $[79, 79, 3w^{2} - w - 23]$ $-e^{4} - 2e^{3} + 7e^{2} + 12e$
89 $[89, 89, 2w^{2} - 4w - 7]$ $-\frac{1}{2}e^{4} - \frac{3}{2}e^{3} + 4e^{2} + \frac{17}{2}e - \frac{1}{2}$
89 $[89, 89, -2w^{2} - 2w + 5]$ $\phantom{-}\frac{1}{2}e^{4} + \frac{3}{2}e^{3} - 5e^{2} - \frac{23}{2}e + \frac{17}{2}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w - 1]$ $-1$