Properties

Label 3.3.1929.1-9.2-h
Base field 3.3.1929.1
Weight $[2, 2, 2]$
Level norm $9$
Level $[9, 3, -w^{2} + 10]$
Dimension $4$
CM no
Base change no

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Base field 3.3.1929.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 10x + 13\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[9, 3, -w^{2} + 10]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $14$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} + x^{3} - 14x^{2} - 12x + 16\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w - 2]$ $-1$
3 $[3, 3, w - 1]$ $\phantom{-}1$
7 $[7, 7, w^{2} + w - 7]$ $\phantom{-}e$
7 $[7, 7, -w^{2} + 11]$ $\phantom{-}\frac{1}{4}e^{3} + \frac{1}{4}e^{2} - \frac{5}{2}e - 1$
7 $[7, 7, -w^{2} + 9]$ $\phantom{-}\frac{1}{4}e^{3} + \frac{1}{4}e^{2} - \frac{7}{2}e - 1$
8 $[8, 2, 2]$ $\phantom{-}\frac{1}{4}e^{3} + \frac{1}{4}e^{2} - \frac{7}{2}e - 2$
13 $[13, 13, -w]$ $\phantom{-}\frac{1}{4}e^{3} + \frac{1}{4}e^{2} - \frac{5}{2}e + 1$
19 $[19, 19, -w^{2} - w + 4]$ $-\frac{1}{4}e^{3} - \frac{1}{4}e^{2} + \frac{7}{2}e + 5$
23 $[23, 23, w^{2} + w - 10]$ $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + 5e + 6$
29 $[29, 29, 2w^{2} - 21]$ $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + 6e$
37 $[37, 37, 2w^{2} + w - 17]$ $\phantom{-}e^{2} - 10$
43 $[43, 43, 3w^{2} + 3w - 22]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{7}{4}e^{2} - \frac{7}{2}e + 11$
47 $[47, 47, w^{2} - 6]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - 7e + 2$
47 $[47, 47, w^{2} - 3]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - 7e + 2$
47 $[47, 47, -w^{2} + 12]$ $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + 7e + 2$
53 $[53, 53, w^{2} - w - 4]$ $\phantom{-}e^{2} - 3e - 10$
61 $[61, 61, w^{2} - 5]$ $-\frac{5}{4}e^{3} - \frac{1}{4}e^{2} + \frac{25}{2}e + 3$
67 $[67, 67, w^{2} - w - 7]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{3}{4}e^{2} - \frac{11}{2}e + 7$
73 $[73, 73, 7w^{2} + 3w - 66]$ $-\frac{1}{4}e^{3} + \frac{7}{4}e^{2} + \frac{5}{2}e - 17$
79 $[79, 79, 2w^{2} - 19]$ $\phantom{-}e^{2} + e - 4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w - 2]$ $1$
$3$ $[3, 3, w - 1]$ $-1$