Properties

Label 3.3.1396.1-2.1-b
Base field 3.3.1396.1
Weight $[2, 2, 2]$
Level norm $2$
Level $[2, 2, -w + 1]$
Dimension $2$
CM no
Base change no

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Base field 3.3.1396.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x + 5\); narrow class number \(2\) and class number \(1\).

Form

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

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} + x - 10\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 1]$ $\phantom{-}1$
5 $[5, 5, w]$ $-2$
5 $[5, 5, -w^{2} + 6]$ $-2$
5 $[5, 5, -w + 2]$ $\phantom{-}e$
7 $[7, 7, w + 2]$ $\phantom{-}e + 2$
11 $[11, 11, 2w - 1]$ $-e + 2$
13 $[13, 13, w^{2} + w - 3]$ $\phantom{-}e$
27 $[27, 3, 3]$ $-e + 2$
41 $[41, 41, w^{2} - w - 1]$ $-e - 8$
41 $[41, 41, 3w^{2} - w - 23]$ $\phantom{-}10$
41 $[41, 41, w^{2} - 2]$ $\phantom{-}2e + 6$
43 $[43, 43, w^{2} - w - 3]$ $-4$
47 $[47, 47, -w - 4]$ $-2e - 4$
49 $[49, 7, 3w^{2} - 2w - 24]$ $-2e + 6$
53 $[53, 53, 2w^{2} - w - 12]$ $-2e - 6$
59 $[59, 59, w^{2} - 2w - 4]$ $\phantom{-}2e$
61 $[61, 61, -w^{2} + 3w - 3]$ $-e + 4$
71 $[71, 71, w^{2} + w - 7]$ $-3e - 6$
79 $[79, 79, 2w + 3]$ $\phantom{-}2e + 4$
89 $[89, 89, 2w - 7]$ $\phantom{-}3e + 8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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