Properties

Label 6.6.1997632.1-13.2-b
Base field 6.6.1997632.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $13$
Level $[13, 13, -w^{2} + w + 3]$
Dimension $8$
CM no
Base change no

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Base field 6.6.1997632.1

Generator \(w\), with minimal polynomial \(x^{6} - 8x^{4} + 19x^{2} - 13\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[13, 13, -w^{2} + w + 3]$
Dimension: $8$
CM: no
Base change: no
Newspace dimension: $16$

Hecke eigenvalues ($q$-expansion)

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

\(x^{8} + 12x^{7} + 44x^{6} - 4x^{5} - 368x^{4} - 663x^{3} + 195x^{2} + 1348x + 832\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
8 $[8, 2, w^{4} - 5w^{2} - w + 4]$ $\phantom{-}e$
13 $[13, 13, w]$ $-5e^{7} - 43e^{6} - 75e^{5} + 268e^{4} + 930e^{3} + 213e^{2} - 1643e - 1256$
13 $[13, 13, -w^{2} + w + 3]$ $\phantom{-}1$
13 $[13, 13, w^{2} + w - 3]$ $-2e^{7} - 18e^{6} - 35e^{5} + 107e^{4} + 416e^{3} + 132e^{2} - 736e - 590$
27 $[27, 3, w^{5} - 6w^{3} + w^{2} + 8w - 2]$ $-e^{7} + 36e^{5} + 47e^{4} - 256e^{3} - 384e^{2} + 431e + 566$
27 $[27, 3, w^{5} - 6w^{3} - w^{2} + 8w + 2]$ $-e^{7} - 16e^{6} - 59e^{5} + 59e^{4} + 567e^{3} + 410e^{2} - 983e - 950$
29 $[29, 29, w^{4} - 6w^{2} + w + 8]$ $\phantom{-}11e^{7} + 95e^{6} + 168e^{5} - 588e^{4} - 2073e^{3} - 504e^{2} + 3665e + 2818$
29 $[29, 29, -w^{4} + 6w^{2} + w - 8]$ $-11e^{7} - 93e^{6} - 156e^{5} + 587e^{4} + 1969e^{3} + 401e^{2} - 3485e - 2630$
41 $[41, 41, w^{3} - w^{2} - 3w + 4]$ $\phantom{-}16e^{7} + 139e^{6} + 250e^{5} - 853e^{4} - 3064e^{3} - 799e^{2} + 5413e + 4222$
41 $[41, 41, w^{5} + w^{4} - 6w^{3} - 5w^{2} + 8w + 3]$ $\phantom{-}2e^{7} + 17e^{6} + 29e^{5} - 106e^{4} - 363e^{3} - 85e^{2} + 641e + 496$
41 $[41, 41, -w^{5} + w^{4} + 6w^{3} - 5w^{2} - 8w + 3]$ $-2e^{7} - 11e^{6} + 7e^{5} + 103e^{4} + 51e^{3} - 227e^{2} - 107e + 92$
41 $[41, 41, w^{5} - w^{4} - 6w^{3} + 5w^{2} + 8w - 6]$ $\phantom{-}4e^{7} + 32e^{6} + 45e^{5} - 215e^{4} - 613e^{3} - 30e^{2} + 1085e + 740$
43 $[43, 43, -w^{4} + 6w^{2} - w - 9]$ $\phantom{-}5e^{7} + 44e^{6} + 81e^{5} - 269e^{4} - 983e^{3} - 260e^{2} + 1739e + 1346$
43 $[43, 43, -w^{4} + 6w^{2} + w - 9]$ $\phantom{-}5e^{7} + 43e^{6} + 75e^{5} - 268e^{4} - 930e^{3} - 214e^{2} + 1642e + 1260$
49 $[49, 7, w^{4} - 5w^{2} + 7]$ $-5e^{7} - 46e^{6} - 94e^{5} + 266e^{4} + 1094e^{3} + 395e^{2} - 1924e - 1586$
97 $[97, 97, w^{4} + w^{3} - 5w^{2} - 3w + 4]$ $-9e^{7} - 68e^{6} - 79e^{5} + 476e^{4} + 1190e^{3} - 84e^{2} - 2129e - 1384$
97 $[97, 97, w^{4} + w^{3} - 5w^{2} - 3w + 3]$ $-7e^{7} - 62e^{6} - 115e^{5} + 379e^{4} + 1389e^{3} + 368e^{2} - 2452e - 1902$
97 $[97, 97, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ $\phantom{-}3e^{7} + 24e^{6} + 33e^{5} - 164e^{4} - 453e^{3} + e^{2} + 798e + 514$
97 $[97, 97, -w^{4} + w^{3} + 5w^{2} - 3w - 4]$ $\phantom{-}16e^{7} + 130e^{6} + 196e^{5} - 849e^{4} - 2597e^{3} - 324e^{2} + 4617e + 3314$
113 $[113, 113, w^{5} - w^{4} - 6w^{3} + 6w^{2} + 7w - 9]$ $\phantom{-}11e^{7} + 95e^{6} + 168e^{5} - 588e^{4} - 2073e^{3} - 505e^{2} + 3664e + 2826$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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