Properties

Label 6.6.1075648.1-29.3-a
Base field \(\Q(\zeta_{28})^+\)
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $29$
Level $[29,29,-w^{5} - w^{4} + 5w^{3} + 4w^{2} - 5w - 3]$
Dimension $1$
CM no
Base change no

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Base field \(\Q(\zeta_{28})^+\)

Generator \(w\), with minimal polynomial \(x^{6} - 7x^{4} + 14x^{2} - 7\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[29,29,-w^{5} - w^{4} + 5w^{3} + 4w^{2} - 5w - 3]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $16$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
7 $[7, 7, w]$ $-2$
8 $[8, 2, w^{3} + w^{2} - 2w - 1]$ $\phantom{-}4$
27 $[27, 3, -w^{5} - w^{4} + 5w^{3} + 5w^{2} - 5w - 6]$ $-2$
27 $[27, 3, w^{4} - 4w^{2} - w + 1]$ $\phantom{-}8$
29 $[29, 29, w^{2} + w - 3]$ $\phantom{-}10$
29 $[29, 29, -w^{4} - w^{3} + 5w^{2} + 3w - 4]$ $\phantom{-}0$
29 $[29, 29, w^{5} + w^{4} - 5w^{3} - 4w^{2} + 5w + 3]$ $-1$
29 $[29, 29, -w^{5} + w^{4} + 5w^{3} - 4w^{2} - 5w + 3]$ $\phantom{-}10$
29 $[29, 29, w^{4} - w^{3} - 5w^{2} + 3w + 4]$ $\phantom{-}0$
29 $[29, 29, -w^{2} + w + 3]$ $\phantom{-}0$
83 $[83, 83, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ $\phantom{-}14$
83 $[83, 83, w^{5} - w^{4} - 4w^{3} + 6w^{2} + 3w - 5]$ $\phantom{-}4$
83 $[83, 83, -w^{5} - w^{4} + 5w^{3} + 5w^{2} - 4w - 6]$ $\phantom{-}4$
83 $[83, 83, w^{5} - w^{4} - 5w^{3} + 5w^{2} + 4w - 6]$ $\phantom{-}4$
83 $[83, 83, -w^{5} + w^{4} + 6w^{3} - 3w^{2} - 9w + 2]$ $\phantom{-}4$
83 $[83, 83, -w^{4} - w^{3} + 4w^{2} + 2w - 1]$ $-6$
113 $[113, 113, -w^{5} - w^{4} + 5w^{3} + 3w^{2} - 5w - 1]$ $-6$
113 $[113, 113, 2w^{4} - w^{3} - 9w^{2} + 3w + 6]$ $-6$
113 $[113, 113, w^{4} - 6w^{2} - w + 8]$ $\phantom{-}14$
113 $[113, 113, w^{4} - 6w^{2} + w + 8]$ $\phantom{-}14$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$29$ $[29,29,-w^{5} - w^{4} + 5w^{3} + 4w^{2} - 5w - 3]$ $1$