Properties

Label 4.4.18097.1-1.1-a
Base field 4.4.18097.1
Weight $[2, 2, 2, 2]$
Level norm $1$
Level $[1, 1, 1]$
Dimension $8$
CM no
Base change no

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Base field 4.4.18097.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + 6x + 4\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[1, 1, 1]$
Dimension: $8$
CM: no
Base change: no
Newspace dimension: $8$

Hecke eigenvalues ($q$-expansion)

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

\(x^{8} - 21x^{6} + 127x^{4} - 180x^{2} + 64\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w + 1]$ $\phantom{-}e$
4 $[4, 2, w]$ $-\frac{5}{48}e^{7} + \frac{97}{48}e^{5} - \frac{499}{48}e^{3} + \frac{83}{12}e$
4 $[4, 2, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{7}{2}w - 3]$ $-\frac{1}{48}e^{7} + \frac{29}{48}e^{5} - \frac{215}{48}e^{3} + \frac{67}{12}e$
7 $[7, 7, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{5}{2}w - 2]$ $-\frac{1}{6}e^{6} + \frac{17}{6}e^{4} - \frac{77}{6}e^{2} + \frac{32}{3}$
13 $[13, 13, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - 1]$ $\phantom{-}\frac{1}{6}e^{6} - \frac{17}{6}e^{4} + \frac{71}{6}e^{2} - \frac{14}{3}$
17 $[17, 17, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w]$ $\phantom{-}\frac{1}{8}e^{7} - \frac{21}{8}e^{5} + \frac{119}{8}e^{3} - \frac{27}{2}e$
27 $[27, 3, -w^{3} + 7w + 1]$ $\phantom{-}e^{3} - 9e$
31 $[31, 31, w + 3]$ $\phantom{-}\frac{1}{6}e^{6} - \frac{23}{6}e^{4} + \frac{143}{6}e^{2} - \frac{56}{3}$
31 $[31, 31, -w^{2} + 5]$ $-\frac{1}{12}e^{7} + \frac{17}{12}e^{5} - \frac{83}{12}e^{3} + \frac{28}{3}e$
37 $[37, 37, w^{2} - 3]$ $-\frac{1}{24}e^{7} + \frac{29}{24}e^{5} - \frac{215}{24}e^{3} + \frac{61}{6}e$
41 $[41, 41, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{3}{2}w - 2]$ $-\frac{1}{8}e^{7} + \frac{21}{8}e^{5} - \frac{127}{8}e^{3} + \frac{41}{2}e$
47 $[47, 47, w^{3} - 5w - 3]$ $\phantom{-}\frac{1}{4}e^{7} - \frac{21}{4}e^{5} + \frac{119}{4}e^{3} - 24e$
53 $[53, 53, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w]$ $\phantom{-}\frac{1}{8}e^{7} - \frac{21}{8}e^{5} + \frac{127}{8}e^{3} - \frac{41}{2}e$
61 $[61, 61, w^{3} - w^{2} - 5w + 3]$ $\phantom{-}\frac{1}{3}e^{6} - \frac{17}{3}e^{4} + \frac{71}{3}e^{2} - \frac{22}{3}$
83 $[83, 83, w^{3} + w^{2} - 6w - 7]$ $\phantom{-}\frac{1}{2}e^{7} - \frac{19}{2}e^{5} + \frac{97}{2}e^{3} - 35e$
83 $[83, 83, -w^{3} + 5w + 1]$ $\phantom{-}\frac{1}{2}e^{6} - \frac{19}{2}e^{4} + \frac{99}{2}e^{2} - 36$
83 $[83, 83, 2w - 1]$ $\phantom{-}\frac{1}{2}e^{7} - \frac{19}{2}e^{5} + \frac{97}{2}e^{3} - 35e$
83 $[83, 83, -\frac{3}{2}w^{3} - \frac{1}{2}w^{2} + \frac{19}{2}w + 2]$ $-e^{4} + 10e^{2} - 12$
89 $[89, 89, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w - 2]$ $\phantom{-}2e^{4} - 22e^{2} + 26$
89 $[89, 89, w^{3} - 5w + 5]$ $-6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

This form has no Atkin-Lehner eigenvalues since the level is \((1)\).