Properties

Label 3.3.49.1-169.6-a
Base field \(\Q(\zeta_{7})^+\)
Weight $[2, 2, 2]$
Level norm $169$
Level $[169,169,-w + 6]$
Dimension $2$
CM no
Base change no

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Base field \(\Q(\zeta_{7})^+\)

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

Form

Weight: $[2, 2, 2]$
Level: $[169,169,-w + 6]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $2$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 12\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
7 $[7, 7, 2w^{2} - w - 3]$ $\phantom{-}e$
8 $[8, 2, 2]$ $-\frac{1}{2}e$
13 $[13, 13, -w^{2} - w + 3]$ $\phantom{-}0$
13 $[13, 13, -w^{2} + 2w + 2]$ $-\frac{3}{2}e$
13 $[13, 13, -2w^{2} + w + 2]$ $\phantom{-}1$
27 $[27, 3, 3]$ $\phantom{-}2$
29 $[29, 29, 3w^{2} - 2w - 4]$ $-9$
29 $[29, 29, 2w^{2} + w - 4]$ $\phantom{-}\frac{1}{2}e$
29 $[29, 29, -w^{2} + 3w + 1]$ $\phantom{-}\frac{1}{2}e$
41 $[41, 41, w^{2} - w - 5]$ $\phantom{-}3$
41 $[41, 41, 2w^{2} - 3w - 4]$ $\phantom{-}3$
41 $[41, 41, -3w^{2} + w + 3]$ $\phantom{-}2e$
43 $[43, 43, w^{2} + 2w - 5]$ $-e$
43 $[43, 43, 2w^{2} + w - 5]$ $-8$
43 $[43, 43, 3w^{2} - 2w - 3]$ $-e$
71 $[71, 71, 4w^{2} - 3w - 5]$ $-6$
71 $[71, 71, 3w^{2} - 4w - 5]$ $-4e$
71 $[71, 71, -4w^{2} + w + 5]$ $-6$
83 $[83, 83, w^{2} + w - 7]$ $\phantom{-}6$
83 $[83, 83, w^{2} - 2w - 6]$ $\phantom{-}4e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13,13,-w^{2} - w + 3]$ $-1$