Properties

Base field \(\Q(\zeta_{7})^+\)
Weight [2, 2, 2]
Level norm 113
Level $[113, 113, 3w^{2} + w - 8]$
Label 3.3.49.1-113.1-a
Dimension 1
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 $[113, 113, 3w^{2} + w - 8]$
Label 3.3.49.1-113.1-a
Dimension 1
Is CM no
Is base change no
Parent newspace dimension 1

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
7 $[7, 7, 2w^{2} - w - 3]$ $\phantom{-}0$
8 $[8, 2, 2]$ $-3$
13 $[13, 13, -w^{2} - w + 3]$ $\phantom{-}2$
13 $[13, 13, -w^{2} + 2w + 2]$ $-2$
13 $[13, 13, -2w^{2} + w + 2]$ $\phantom{-}6$
27 $[27, 3, 3]$ $-8$
29 $[29, 29, 3w^{2} - 2w - 4]$ $-6$
29 $[29, 29, 2w^{2} + w - 4]$ $-2$
29 $[29, 29, -w^{2} + 3w + 1]$ $\phantom{-}2$
41 $[41, 41, w^{2} - w - 5]$ $\phantom{-}2$
41 $[41, 41, 2w^{2} - 3w - 4]$ $\phantom{-}2$
41 $[41, 41, -3w^{2} + w + 3]$ $-6$
43 $[43, 43, w^{2} + 2w - 5]$ $\phantom{-}4$
43 $[43, 43, 2w^{2} + w - 5]$ $\phantom{-}4$
43 $[43, 43, 3w^{2} - 2w - 3]$ $-4$
71 $[71, 71, 4w^{2} - 3w - 5]$ $\phantom{-}12$
71 $[71, 71, 3w^{2} - 4w - 5]$ $-16$
71 $[71, 71, -4w^{2} + w + 5]$ $\phantom{-}0$
83 $[83, 83, w^{2} + w - 7]$ $-8$
83 $[83, 83, w^{2} - 2w - 6]$ $-4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
113 $[113, 113, 3w^{2} + w - 8]$ $-1$