Properties

Label 6.6.371293.1-53.5-a
Base field \(\Q(\zeta_{13})^+\)
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $53$
Level $[53,53,-w^{5} + 5w^{3} + w^{2} - 5w]$
Dimension $1$
CM no
Base change no

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Base field \(\Q(\zeta_{13})^+\)

Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 5x^{4} + 4x^{3} + 6x^{2} - 3x - 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[53,53,-w^{5} + 5w^{3} + w^{2} - 5w]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $6$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
13 $[13, 13, w^{5} - 5w^{3} + 4w]$ $-2$
25 $[25, 5, w^{5} - 5w^{3} + 6w - 1]$ $-8$
25 $[25, 5, -w^{3} + w^{2} + 3w - 1]$ $\phantom{-}1$
25 $[25, 5, w^{5} - 4w^{3} - w^{2} + 3w + 2]$ $-5$
27 $[27, 3, w^{4} - w^{3} - 4w^{2} + 2w + 2]$ $-4$
27 $[27, 3, w^{4} - w^{3} - 4w^{2} + 2w + 3]$ $\phantom{-}2$
53 $[53, 53, -w^{4} + w^{3} + 3w^{2} - 2w + 1]$ $\phantom{-}0$
53 $[53, 53, -w^{4} + w^{3} + 4w^{2} - 3w - 4]$ $\phantom{-}6$
53 $[53, 53, -w^{5} + w^{4} + 4w^{3} - 4w^{2} - 3w + 1]$ $-9$
53 $[53, 53, w^{3} - 2w - 2]$ $-9$
53 $[53, 53, w^{5} - 5w^{3} - w^{2} + 5w]$ $\phantom{-}1$
53 $[53, 53, -w^{4} + 4w^{2} + w - 4]$ $-6$
64 $[64, 2, -2]$ $-11$
79 $[79, 79, -2w^{5} + w^{4} + 9w^{3} - 3w^{2} - 9w + 2]$ $\phantom{-}1$
79 $[79, 79, -w^{5} - w^{4} + 5w^{3} + 4w^{2} - 6w - 1]$ $-17$
79 $[79, 79, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}1$
79 $[79, 79, -2w^{5} + 2w^{4} + 9w^{3} - 7w^{2} - 9w + 3]$ $\phantom{-}1$
79 $[79, 79, -2w^{4} + w^{3} + 7w^{2} - 3w - 3]$ $\phantom{-}4$
79 $[79, 79, -w^{5} + 6w^{3} - w^{2} - 8w + 1]$ $-8$
103 $[103, 103, 2w^{4} - 7w^{2} - w + 3]$ $-16$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$53$ $[53,53,-w^{5} + 5w^{3} + w^{2} - 5w]$ $-1$