Properties

Base field \(\Q(\zeta_{7})^+\)
Weight [2, 2, 2]
Level norm 167
Level $[167, 167, w^{2} + w - 8]$
Label 3.3.49.1-167.1-a
Dimension 3
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 $[167, 167, w^{2} + w - 8]$
Label 3.3.49.1-167.1-a
Dimension 3
Is CM no
Is base change no
Parent newspace dimension 3

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} \) \(\mathstrut -\mathstrut x^{2} \) \(\mathstrut -\mathstrut 4x \) \(\mathstrut -\mathstrut 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
7 $[7, 7, 2w^{2} - w - 3]$ $\phantom{-}e$
8 $[8, 2, 2]$ $\phantom{-}2e^{2} - 4e - 4$
13 $[13, 13, -w^{2} - w + 3]$ $\phantom{-}2e - 2$
13 $[13, 13, -w^{2} + 2w + 2]$ $-e^{2} - e + 3$
13 $[13, 13, -2w^{2} + w + 2]$ $-3e^{2} + 4e + 8$
27 $[27, 3, 3]$ $-3e^{2} + 6e + 6$
29 $[29, 29, 3w^{2} - 2w - 4]$ $\phantom{-}4e^{2} - 6e - 12$
29 $[29, 29, 2w^{2} + w - 4]$ $-e^{2} + e + 3$
29 $[29, 29, -w^{2} + 3w + 1]$ $\phantom{-}4e - 2$
41 $[41, 41, w^{2} - w - 5]$ $\phantom{-}3e^{2} - 7e - 11$
41 $[41, 41, 2w^{2} - 3w - 4]$ $\phantom{-}4e^{2} - 5e - 8$
41 $[41, 41, -3w^{2} + w + 3]$ $-2e^{2} + 4$
43 $[43, 43, w^{2} + 2w - 5]$ $-2e^{2} + 6$
43 $[43, 43, 2w^{2} + w - 5]$ $\phantom{-}4e^{2} - 4e - 14$
43 $[43, 43, 3w^{2} - 2w - 3]$ $-6e^{2} + 10e + 16$
71 $[71, 71, 4w^{2} - 3w - 5]$ $-5e^{2} + 6e + 12$
71 $[71, 71, 3w^{2} - 4w - 5]$ $\phantom{-}3e^{2} - 5e + 3$
71 $[71, 71, -4w^{2} + w + 5]$ $-2e^{2} + 4e + 2$
83 $[83, 83, w^{2} + w - 7]$ $\phantom{-}2e^{2} - 4e - 12$
83 $[83, 83, w^{2} - 2w - 6]$ $\phantom{-}4e^{2} + e - 14$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
167 $[167, 167, w^{2} + w - 8]$ $-1$