Properties

Label 3.3.621.1-16.1-a
Base field 3.3.621.1
Weight $[2, 2, 2]$
Level norm $16$
Level $[16, 4, -w^{2} - w + 1]$
Dimension $5$
CM no
Base change no

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Base field 3.3.621.1

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

Form

Weight: $[2, 2, 2]$
Level: $[16, 4, -w^{2} - w + 1]$
Dimension: $5$
CM: no
Base change: no
Newspace dimension: $11$

Hecke eigenvalues ($q$-expansion)

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

\(x^{5} + 2x^{4} - 7x^{3} - 12x^{2} + 9x + 9\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}e$
3 $[3, 3, w]$ $-\frac{1}{3}e^{4} + \frac{1}{3}e^{3} + \frac{7}{3}e^{2} - 2e - 3$
4 $[4, 2, -w^{2} + w + 5]$ $\phantom{-}0$
7 $[7, 7, -w + 2]$ $\phantom{-}\frac{1}{3}e^{4} - \frac{1}{3}e^{3} - \frac{10}{3}e^{2} + e + 5$
19 $[19, 19, -2w^{2} + w + 10]$ $\phantom{-}\frac{4}{3}e^{4} + \frac{5}{3}e^{3} - \frac{25}{3}e^{2} - 7e + 5$
23 $[23, 23, -w^{2} + 8]$ $-e^{3} + 5e - 6$
23 $[23, 23, -w^{2} + 2]$ $-e^{2} - e$
29 $[29, 29, -w^{2} + 2w + 4]$ $-2e^{4} - e^{3} + 13e^{2} + 4e - 12$
37 $[37, 37, w^{2} - 2w - 8]$ $-\frac{2}{3}e^{4} - \frac{1}{3}e^{3} + \frac{20}{3}e^{2} - 13$
41 $[41, 41, 4w^{2} - 3w - 20]$ $-2e^{3} - e^{2} + 11e$
43 $[43, 43, -w - 4]$ $\phantom{-}\frac{1}{3}e^{4} - \frac{1}{3}e^{3} - \frac{10}{3}e^{2} + 2e + 2$
47 $[47, 47, 2w - 1]$ $\phantom{-}e^{3} + e^{2} - 8e - 6$
49 $[49, 7, -2w^{2} + 3w + 4]$ $-\frac{2}{3}e^{4} - \frac{1}{3}e^{3} + \frac{17}{3}e^{2} + 2e - 4$
59 $[59, 59, 2w^{2} - 13]$ $-2e^{3} + 11e - 3$
61 $[61, 61, -3w^{2} + 4w + 10]$ $-\frac{2}{3}e^{4} + \frac{2}{3}e^{3} + \frac{20}{3}e^{2} - 3e - 13$
67 $[67, 67, 2w^{2} - 2w - 7]$ $\phantom{-}\frac{7}{3}e^{4} + \frac{2}{3}e^{3} - \frac{43}{3}e^{2} + 14$
71 $[71, 71, -3w - 4]$ $-2e^{3} - 3e^{2} + 9e + 6$
79 $[79, 79, 2w^{2} - 3w - 8]$ $-\frac{5}{3}e^{4} + \frac{5}{3}e^{3} + \frac{35}{3}e^{2} - 8e - 7$
83 $[83, 83, 2w^{2} - w - 14]$ $\phantom{-}e^{4} + e^{3} - 4e^{2} - 2e - 6$
83 $[83, 83, -4w^{2} + 3w + 22]$ $-e^{4} + 7e^{2} + e - 15$
Display number of eigenvalues

Atkin-Lehner eigenvalues

The Atkin-Lehner eigenvalues for this form are not in the database.