Properties

Label 3.3.1425.1-3.2-c
Base field 3.3.1425.1
Weight $[2, 2, 2]$
Level norm $3$
Level $[3, 3, w + 1]$
Dimension $4$
CM no
Base change no

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Base field 3.3.1425.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x - 3\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[3, 3, w + 1]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $6$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - x^{3} - 11x^{2} + 5x + 22\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
3 $[3, 3, w + 1]$ $\phantom{-}1$
5 $[5, 5, w^{2} - w - 7]$ $-\frac{1}{4}e^{3} + \frac{7}{4}e + \frac{1}{2}$
8 $[8, 2, 2]$ $-\frac{1}{4}e^{3} + \frac{1}{2}e^{2} + \frac{5}{4}e - \frac{5}{2}$
11 $[11, 11, w - 1]$ $-\frac{1}{4}e^{3} + \frac{1}{2}e^{2} + \frac{9}{4}e - \frac{7}{2}$
13 $[13, 13, w^{2} - 2w - 8]$ $\phantom{-}\frac{3}{2}e^{2} - \frac{1}{2}e - 8$
17 $[17, 17, w^{2} - 2w - 7]$ $-\frac{3}{4}e^{3} + \frac{21}{4}e + \frac{3}{2}$
19 $[19, 19, -w^{2} + 2w + 4]$ $\phantom{-}\frac{1}{4}e^{3} - e^{2} - \frac{3}{4}e + \frac{17}{2}$
19 $[19, 19, -2w^{2} + 3w + 16]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{11}{4}e + \frac{1}{2}$
23 $[23, 23, -w^{2} + 2w + 2]$ $\phantom{-}\frac{1}{4}e^{3} + e^{2} - \frac{15}{4}e - \frac{15}{2}$
31 $[31, 31, 2w^{2} - 3w - 13]$ $-e^{3} + e^{2} + 6e - 2$
37 $[37, 37, w^{2} - w - 10]$ $\phantom{-}\frac{1}{4}e^{3} - e^{2} - \frac{11}{4}e + \frac{11}{2}$
43 $[43, 43, 3w^{2} - 5w - 19]$ $\phantom{-}\frac{3}{4}e^{3} - 2e^{2} - \frac{25}{4}e + \frac{19}{2}$
43 $[43, 43, w^{2} - w - 4]$ $\phantom{-}\frac{1}{2}e^{2} + \frac{3}{2}e + 1$
43 $[43, 43, 2w^{2} - 2w - 17]$ $\phantom{-}\frac{1}{2}e^{3} - e^{2} - \frac{5}{2}e + 9$
47 $[47, 47, w^{2} - 2]$ $-\frac{1}{4}e^{3} + \frac{19}{4}e + \frac{3}{2}$
67 $[67, 67, w^{2} - 3w - 5]$ $-\frac{1}{2}e^{3} + e^{2} + \frac{1}{2}e - 5$
79 $[79, 79, -w^{2} + 3w - 1]$ $-\frac{1}{2}e^{2} + \frac{1}{2}e - 1$
83 $[83, 83, w^{2} + w - 4]$ $\phantom{-}\frac{5}{4}e^{3} - 3e^{2} - \frac{35}{4}e + \frac{29}{2}$
97 $[97, 97, w^{2} - 11]$ $\phantom{-}\frac{1}{4}e^{3} - 4e^{2} - \frac{7}{4}e + \frac{45}{2}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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