Properties

Label 6.6.1279733.1-49.1-d
Base field 6.6.1279733.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $49$
Level $[49, 7, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 5w - 1]$
Dimension $1$
CM no
Base change no

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Base field 6.6.1279733.1

Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 6x^{4} + 10x^{3} + 10x^{2} - 11x - 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[49, 7, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 5w - 1]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $30$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
7 $[7, 7, w^{4} - 2w^{3} - 3w^{2} + 6w - 1]$ $\phantom{-}0$
7 $[7, 7, -w^{4} + w^{3} + 4w^{2} - w - 1]$ $\phantom{-}2$
13 $[13, 13, w^{5} - 2w^{4} - 4w^{3} + 7w^{2} + 3w - 3]$ $-4$
29 $[29, 29, -w^{4} + w^{3} + 4w^{2} - 3w - 2]$ $\phantom{-}2$
29 $[29, 29, w^{4} - 5w^{2} - 2w + 4]$ $-5$
29 $[29, 29, -w^{4} + w^{3} + 3w^{2} - w + 2]$ $-3$
29 $[29, 29, -w^{2} + w + 1]$ $\phantom{-}4$
41 $[41, 41, -w^{5} + w^{4} + 4w^{3} - w^{2} - 3w - 1]$ $-6$
43 $[43, 43, 2w^{3} - 2w^{2} - 7w + 3]$ $\phantom{-}4$
43 $[43, 43, w^{3} - w^{2} - 2w + 1]$ $-1$
64 $[64, 2, -2]$ $-5$
71 $[71, 71, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 8w - 3]$ $-9$
71 $[71, 71, w^{5} - 2w^{4} - 2w^{3} + 5w^{2} - 3w - 1]$ $-1$
83 $[83, 83, -2w^{4} + 3w^{3} + 6w^{2} - 7w + 2]$ $-16$
83 $[83, 83, w^{4} - w^{3} - 5w^{2} + 2w + 3]$ $\phantom{-}12$
83 $[83, 83, -w^{5} + 3w^{4} + w^{3} - 9w^{2} + 5w + 3]$ $\phantom{-}9$
83 $[83, 83, w^{5} - 7w^{3} + 10w - 1]$ $-3$
97 $[97, 97, w^{5} - 2w^{4} - 3w^{3} + 5w^{2} - w - 1]$ $-2$
97 $[97, 97, w^{5} - 5w^{3} - w^{2} + 3w - 3]$ $\phantom{-}16$
113 $[113, 113, w^{4} - w^{3} - 4w^{2} + w + 4]$ $-10$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$7$ $[7, 7, w^{4} - 2w^{3} - 3w^{2} + 6w - 1]$ $-1$