Properties

Label 3.3.1901.1-4.1-b
Base field 3.3.1901.1
Weight $[2, 2, 2]$
Level norm $4$
Level $[4, 2, -w^{2} + 3w + 3]$
Dimension $3$
CM no
Base change no

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Base field 3.3.1901.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x - 4\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[4, 2, -w^{2} + 3w + 3]$
Dimension: $3$
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:

\(x^{3} + x^{2} - 5x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w + 2]$ $\phantom{-}e$
3 $[3, 3, w + 1]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{5}{2}$
4 $[4, 2, -w^{2} + 3w + 3]$ $-1$
9 $[9, 3, -w^{2} + 2w + 7]$ $\phantom{-}\frac{1}{2}e^{2} + 2e - \frac{3}{2}$
13 $[13, 13, w + 3]$ $\phantom{-}\frac{1}{2}e^{2} + e + \frac{3}{2}$
13 $[13, 13, -w + 3]$ $-e - 2$
13 $[13, 13, -w + 1]$ $-\frac{1}{2}e^{2} - 2e - \frac{1}{2}$
17 $[17, 17, -w^{2} - 2w + 1]$ $-3$
23 $[23, 23, w^{2} - 2w - 5]$ $-\frac{1}{2}e^{2} - e - \frac{1}{2}$
31 $[31, 31, 2w + 3]$ $\phantom{-}2e - 2$
31 $[31, 31, -2w^{2} + 3w + 15]$ $-e^{2} + 7$
31 $[31, 31, 3w + 7]$ $-\frac{1}{2}e^{2} + \frac{13}{2}$
37 $[37, 37, 3w^{2} - 4w - 27]$ $\phantom{-}2e^{2} + e - 9$
41 $[41, 41, -2w^{2} + 7w + 1]$ $-2e^{2} - 3e + 2$
59 $[59, 59, w^{2} - 3]$ $\phantom{-}\frac{1}{2}e^{2} - 2e - \frac{5}{2}$
61 $[61, 61, 4w^{2} - 12w - 11]$ $\phantom{-}\frac{3}{2}e^{2} - e - \frac{15}{2}$
71 $[71, 71, w^{2} - 2w - 11]$ $\phantom{-}e^{2} + 1$
97 $[97, 97, 3w + 5]$ $\phantom{-}\frac{1}{2}e^{2} - e - \frac{17}{2}$
101 $[101, 101, 2w^{2} - 6w - 7]$ $-\frac{1}{2}e^{2} - 6e - \frac{9}{2}$
103 $[103, 103, 2w^{2} - 3w - 19]$ $\phantom{-}\frac{5}{2}e^{2} - \frac{17}{2}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, -w^{2} + 3w + 3]$ $1$