Properties

Label 3.3.993.1-21.2-b
Base field 3.3.993.1
Weight $[2, 2, 2]$
Level norm $21$
Level $[21, 21, w^{2} - 2w - 3]$
Dimension $3$
CM no
Base change no

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Base field 3.3.993.1

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

Form

Weight: $[2, 2, 2]$
Level: $[21, 21, w^{2} - 2w - 3]$
Dimension: $3$
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:

\(x^{3} - 3x^{2} - 9x + 13\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w]$ $-1$
3 $[3, 3, w - 1]$ $-1$
5 $[5, 5, -w + 2]$ $\phantom{-}e$
7 $[7, 7, w + 1]$ $-1$
8 $[8, 2, 2]$ $\phantom{-}\frac{1}{3}e^{2} - \frac{1}{3}e - \frac{5}{3}$
13 $[13, 13, w^{2} - w - 4]$ $-\frac{1}{3}e^{2} - \frac{2}{3}e + \frac{11}{3}$
17 $[17, 17, -w^{2} + 2w + 1]$ $\phantom{-}\frac{1}{3}e^{2} - \frac{4}{3}e - \frac{5}{3}$
25 $[25, 5, -w^{2} - w + 4]$ $-\frac{2}{3}e^{2} + \frac{2}{3}e + \frac{10}{3}$
31 $[31, 31, w^{2} - w - 1]$ $-e^{2} + e + 5$
31 $[31, 31, 2w^{2} - w - 14]$ $\phantom{-}\frac{2}{3}e^{2} - \frac{5}{3}e - \frac{10}{3}$
31 $[31, 31, w^{2} - 2]$ $\phantom{-}\frac{2}{3}e^{2} - \frac{8}{3}e - \frac{13}{3}$
37 $[37, 37, -3w^{2} + w + 19]$ $-8$
49 $[49, 7, w^{2} - 2w - 4]$ $-e^{2} + 2e + 5$
53 $[53, 53, -w - 4]$ $-\frac{4}{3}e^{2} + \frac{4}{3}e + \frac{29}{3}$
61 $[61, 61, 2w^{2} + w - 7]$ $-\frac{2}{3}e^{2} + \frac{5}{3}e + \frac{4}{3}$
71 $[71, 71, 2w^{2} - 2w - 13]$ $-2e - 2$
73 $[73, 73, w - 5]$ $-e^{2} + 3e + 5$
83 $[83, 83, w^{2} - 3w - 2]$ $\phantom{-}\frac{1}{3}e^{2} - \frac{10}{3}e - \frac{23}{3}$
89 $[89, 89, w^{2} + 2w - 4]$ $-\frac{2}{3}e^{2} + \frac{14}{3}e + \frac{16}{3}$
97 $[97, 97, -w^{2} + 2w + 7]$ $\phantom{-}\frac{2}{3}e^{2} + \frac{10}{3}e - \frac{28}{3}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, -w]$ $1$
$7$ $[7, 7, w + 1]$ $1$