Properties

Label 4.4.19773.1-13.1-f
Base field 4.4.19773.1
Weight $[2, 2, 2, 2]$
Level norm $13$
Level $[13, 13, w^{3} - 2w^{2} - 6w + 1]$
Dimension $8$
CM no
Base change no

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Base field 4.4.19773.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[13, 13, w^{3} - 2w^{2} - 6w + 1]$
Dimension: $8$
CM: no
Base change: no
Newspace dimension: $40$

Hecke eigenvalues ($q$-expansion)

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

\(x^{8} - 100x^{6} + 3344x^{4} - 44800x^{2} + 200704\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w^{3} - 2w^{2} - 8w - 3]$ $\phantom{-}\frac{5}{2688}e^{6} - \frac{97}{672}e^{4} + \frac{527}{168}e^{2} - \frac{62}{3}$
3 $[3, 3, w^{3} - 3w^{2} - 5w + 2]$ $\phantom{-}\frac{3}{896}e^{6} - \frac{61}{224}e^{4} + \frac{347}{56}e^{2} - 40$
13 $[13, 13, w^{3} - 2w^{2} - 6w + 1]$ $\phantom{-}1$
16 $[16, 2, 2]$ $-\frac{1}{192}e^{6} + \frac{5}{12}e^{4} - \frac{28}{3}e^{2} + \frac{167}{3}$
17 $[17, 17, -2w^{3} + 5w^{2} + 14w - 1]$ $\phantom{-}e$
17 $[17, 17, -w^{3} + 3w^{2} + 5w - 4]$ $-\frac{5}{5376}e^{7} + \frac{97}{1344}e^{5} - \frac{485}{336}e^{3} + \frac{19}{3}e$
17 $[17, 17, -w^{3} + 2w^{2} + 8w + 1]$ $-e$
17 $[17, 17, w - 1]$ $\phantom{-}\frac{5}{5376}e^{7} - \frac{97}{1344}e^{5} + \frac{485}{336}e^{3} - \frac{19}{3}e$
23 $[23, 23, 2w^{3} - 6w^{2} - 11w + 7]$ $\phantom{-}\frac{13}{10752}e^{7} - \frac{269}{2688}e^{5} + \frac{1597}{672}e^{3} - \frac{101}{6}e$
23 $[23, 23, w^{3} - 3w^{2} - 7w + 4]$ $-\frac{13}{10752}e^{7} + \frac{269}{2688}e^{5} - \frac{1597}{672}e^{3} + \frac{101}{6}e$
23 $[23, 23, -w^{2} + 2w + 5]$ $\phantom{-}\frac{1}{5376}e^{7} - \frac{11}{1344}e^{5} - \frac{29}{336}e^{3} + \frac{17}{6}e$
23 $[23, 23, 3w^{3} - 8w^{2} - 20w + 5]$ $-\frac{1}{5376}e^{7} + \frac{11}{1344}e^{5} + \frac{29}{336}e^{3} - \frac{17}{6}e$
61 $[61, 61, -w^{3} + 2w^{2} + 9w + 1]$ $-\frac{1}{336}e^{6} + \frac{43}{168}e^{4} - \frac{535}{84}e^{2} + \frac{116}{3}$
61 $[61, 61, -2w^{3} + 5w^{2} + 13w - 2]$ $-\frac{1}{448}e^{6} + \frac{9}{56}e^{4} - \frac{83}{28}e^{2} + 8$
61 $[61, 61, w^{3} - 2w^{2} - 9w - 2]$ $-\frac{1}{336}e^{6} + \frac{43}{168}e^{4} - \frac{535}{84}e^{2} + \frac{116}{3}$
61 $[61, 61, 2w^{3} - 5w^{2} - 13w + 1]$ $-\frac{1}{448}e^{6} + \frac{9}{56}e^{4} - \frac{83}{28}e^{2} + 8$
79 $[79, 79, 4w^{3} - 10w^{2} - 28w + 5]$ $\phantom{-}\frac{1}{2688}e^{6} - \frac{53}{672}e^{4} + \frac{559}{168}e^{2} - \frac{88}{3}$
79 $[79, 79, w^{3} - 3w^{2} - 4w + 4]$ $\phantom{-}\frac{1}{2688}e^{6} - \frac{53}{672}e^{4} + \frac{559}{168}e^{2} - \frac{88}{3}$
79 $[79, 79, w^{3} - 4w^{2} - 2w + 10]$ $-\frac{5}{896}e^{6} + \frac{111}{224}e^{4} - \frac{709}{56}e^{2} + 90$
79 $[79, 79, 2w^{3} - 6w^{2} - 10w + 5]$ $-\frac{5}{896}e^{6} + \frac{111}{224}e^{4} - \frac{709}{56}e^{2} + 90$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13, 13, w^{3} - 2w^{2} - 6w + 1]$ $-1$