Properties

Label 3.3.1300.1-16.1-f
Base field 3.3.1300.1
Weight $[2, 2, 2]$
Level norm $16$
Level $[16, 4, -2w - 4]$
Dimension $5$
CM no
Base change no

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Base field 3.3.1300.1

Generator \(w\), with minimal polynomial \(x^{3} - 10x - 10\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[16, 4, -2w - 4]$
Dimension: $5$
CM: no
Base change: no
Newspace dimension: $15$

Hecke eigenvalues ($q$-expansion)

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

\(x^{5} - 4x^{4} - 9x^{3} + 38x^{2} + 18x - 76\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $\phantom{-}0$
5 $[5, 5, -w^{2} + 2w + 5]$ $\phantom{-}e$
7 $[7, 7, w + 3]$ $\phantom{-}e^{2} - e - 6$
11 $[11, 11, -2w^{2} + 5w + 9]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{3}{2}e^{2} - 3e + 8$
13 $[13, 13, -w^{2} + w + 7]$ $\phantom{-}\frac{1}{4}e^{4} - \frac{3}{4}e^{3} - 2e^{2} + \frac{9}{2}e + 5$
13 $[13, 13, w - 3]$ $-e^{2} + 2e + 6$
17 $[17, 17, -w^{2} + 2w + 7]$ $-\frac{1}{4}e^{4} + \frac{1}{4}e^{3} + \frac{5}{2}e^{2} - \frac{1}{2}e - 3$
17 $[17, 17, -2w^{2} + 5w + 7]$ $-\frac{1}{2}e^{4} + e^{3} + \frac{11}{2}e^{2} - 6e - 12$
17 $[17, 17, -w^{2} + 3w + 3]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{3}{2}e^{2} - 2e + 8$
19 $[19, 19, -w + 1]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{5}{2}e^{2} - 2e + 14$
27 $[27, 3, -3]$ $-\frac{1}{2}e^{4} + \frac{1}{2}e^{3} + 7e^{2} - 3e - 18$
31 $[31, 31, w^{2} - 2w - 9]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{1}{2}e^{3} - 6e^{2} + 2e + 16$
37 $[37, 37, w^{2} - 7]$ $\phantom{-}\frac{3}{4}e^{4} - \frac{5}{4}e^{3} - 10e^{2} + \frac{17}{2}e + 25$
41 $[41, 41, w^{2} - w - 11]$ $-\frac{1}{4}e^{4} + \frac{1}{4}e^{3} + \frac{3}{2}e^{2} + \frac{1}{2}e + 3$
47 $[47, 47, w^{2} - 3]$ $\phantom{-}e^{3} - 2e^{2} - 7e + 10$
49 $[49, 7, w^{2} - 3w - 1]$ $\phantom{-}\frac{1}{4}e^{4} - \frac{7}{4}e^{3} + e^{2} + \frac{21}{2}e - 7$
59 $[59, 59, w^{2} - 4w + 1]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{1}{2}e^{3} - 7e^{2} - e + 26$
67 $[67, 67, w^{2} - 3w - 7]$ $-\frac{1}{2}e^{4} + e^{3} + \frac{11}{2}e^{2} - 6e - 14$
71 $[71, 71, 4w + 9]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{1}{2}e^{3} - 8e^{2} + 28$
73 $[73, 73, -4w^{2} + 8w + 23]$ $\phantom{-}\frac{1}{4}e^{4} - \frac{5}{4}e^{3} - \frac{3}{2}e^{2} + \frac{17}{2}e - 5$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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