Properties

Label 6.6.703493.1-13.4-b
Base field 6.6.703493.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $13$
Level $[13,13,w^{2} - 3]$
Dimension $3$
CM no
Base change no

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Base field 6.6.703493.1

Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 5x^{4} + 11x^{3} + 2x^{2} - 9x + 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[13,13,w^{2} - 3]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $4$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{3} - 3x^{2} - 5x + 3\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
13 $[13, 13, 3w^{5} - 2w^{4} - 17w^{3} + 10w^{2} + 16w - 3]$ $\phantom{-}e$
13 $[13, 13, w^{5} - w^{4} - 5w^{3} + 5w^{2} + 3w - 3]$ $-e^{2} + e + 6$
13 $[13, 13, 2w^{5} - w^{4} - 12w^{3} + 4w^{2} + 13w]$ $-e + 1$
13 $[13, 13, -w^{2} + 3]$ $-1$
41 $[41, 41, -2w^{5} + w^{4} + 11w^{3} - 4w^{2} - 10w - 1]$ $\phantom{-}e^{2} - e - 4$
41 $[41, 41, -4w^{5} + 3w^{4} + 23w^{3} - 14w^{2} - 22w + 4]$ $-\frac{5}{2}e^{2} + 7e + \frac{13}{2}$
41 $[41, 41, w^{5} - 6w^{3} + w^{2} + 7w - 2]$ $\phantom{-}e + 1$
41 $[41, 41, -3w^{5} + w^{4} + 18w^{3} - 4w^{2} - 20w - 1]$ $\phantom{-}e + 1$
43 $[43, 43, 3w^{5} - 2w^{4} - 17w^{3} + 11w^{2} + 16w - 6]$ $-e + 5$
43 $[43, 43, -2w^{5} + w^{4} + 12w^{3} - 6w^{2} - 14w + 5]$ $-\frac{3}{2}e^{2} + 7e + \frac{7}{2}$
49 $[49, 7, 2w^{5} - w^{4} - 12w^{3} + 5w^{2} + 13w - 4]$ $\phantom{-}2e - 6$
64 $[64, 2, -2]$ $\phantom{-}\frac{5}{2}e^{2} - 7e - \frac{17}{2}$
71 $[71, 71, -2w^{5} + w^{4} + 12w^{3} - 4w^{2} - 12w - 1]$ $-3e + 7$
71 $[71, 71, -3w^{5} + 2w^{4} + 17w^{3} - 9w^{2} - 15w]$ $\phantom{-}2e^{2} - 3e - 5$
83 $[83, 83, 4w^{5} - 2w^{4} - 24w^{3} + 9w^{2} + 26w - 1]$ $\phantom{-}\frac{3}{2}e^{2} - 6e + \frac{7}{2}$
83 $[83, 83, -4w^{5} + 2w^{4} + 23w^{3} - 9w^{2} - 23w]$ $\phantom{-}3e^{2} - 13e - 10$
97 $[97, 97, -w^{5} + 7w^{3} + w^{2} - 11w - 3]$ $\phantom{-}\frac{3}{2}e^{2} - 6e - \frac{21}{2}$
97 $[97, 97, -2w^{5} + w^{4} + 11w^{3} - 6w^{2} - 9w + 3]$ $-e^{2} + e + 9$
113 $[113, 113, -4w^{5} + 2w^{4} + 24w^{3} - 9w^{2} - 27w + 2]$ $\phantom{-}\frac{5}{2}e^{2} - 8e + \frac{5}{2}$
113 $[113, 113, 3w^{5} - 2w^{4} - 18w^{3} + 10w^{2} + 20w - 6]$ $\phantom{-}\frac{5}{2}e^{2} - 11e - \frac{21}{2}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13,13,w^{2} - 3]$ $1$