Properties

Label 3.3.1556.1-3.1-b
Base field 3.3.1556.1
Weight $[2, 2, 2]$
Level norm $3$
Level $[3, 3, w - 2]$
Dimension $4$
CM no
Base change no

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Base field 3.3.1556.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x + 11\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[3, 3, w - 2]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $8$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} + x^{3} - 6x^{2} - 6x + 2\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w - 1]$ $\phantom{-}e$
3 $[3, 3, w - 2]$ $-1$
9 $[9, 3, w^{2} + w - 7]$ $-e^{3} + e^{2} + 4e - 4$
11 $[11, 11, w]$ $-e^{2} + 2$
11 $[11, 11, -2w + 3]$ $\phantom{-}e^{3} - 6e - 2$
11 $[11, 11, -w^{2} + 3w - 1]$ $\phantom{-}e^{3} - 6e - 2$
17 $[17, 17, w + 2]$ $\phantom{-}e^{2} - 2e - 4$
17 $[17, 17, -2w + 5]$ $-e^{2} + 2e + 4$
17 $[17, 17, -w^{2} - w + 5]$ $-e^{3} - e^{2} + 6e$
23 $[23, 23, w - 4]$ $-2e^{3} - e^{2} + 8e + 6$
29 $[29, 29, w^{2} - 6]$ $\phantom{-}e^{3} - e^{2} - 4e + 2$
31 $[31, 31, w^{2} - w - 1]$ $\phantom{-}2e$
37 $[37, 37, -w^{2} - 2w + 6]$ $-2e^{3} + e^{2} + 10e - 4$
43 $[43, 43, w^{2} - 3w + 3]$ $\phantom{-}e^{3} - e^{2} - 4e$
47 $[47, 47, 3w^{2} - 28]$ $\phantom{-}2e^{3} - 2e^{2} - 10e + 4$
53 $[53, 53, w^{2} - w - 3]$ $\phantom{-}e^{2} - 6$
61 $[61, 61, -5w + 6]$ $\phantom{-}e^{2} - 4$
71 $[71, 71, w^{2} - w - 7]$ $\phantom{-}e^{3} + 3e^{2} - 4e - 8$
83 $[83, 83, -2w^{2} - w + 14]$ $\phantom{-}2e^{3} - 8e$
89 $[89, 89, w^{2} + 3w - 3]$ $-e^{3} + 3e^{2} + 8e - 10$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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