Properties

Label 4.4.17609.1-7.1-a
Base field 4.4.17609.1
Weight $[2, 2, 2, 2]$
Level norm $7$
Level $[7, 7, -w^{3} + 6w - 2]$
Dimension $8$
CM no
Base change no

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Base field 4.4.17609.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + 10x - 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[7, 7, -w^{3} + 6w - 2]$
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:

\(x^{8} - 3x^{7} - 9x^{6} + 30x^{5} + 19x^{4} - 89x^{3} + 7x^{2} + 80x - 32\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 1]$ $\phantom{-}e$
5 $[5, 5, w^{3} + w^{2} - 4w + 1]$ $-\frac{1}{4}e^{7} + \frac{1}{4}e^{6} + \frac{13}{4}e^{5} - 3e^{4} - \frac{53}{4}e^{3} + \frac{45}{4}e^{2} + \frac{67}{4}e - 12$
7 $[7, 7, -w^{3} + 6w - 2]$ $-1$
8 $[8, 2, w^{3} - 7w + 3]$ $\phantom{-}\frac{1}{4}e^{7} - \frac{3}{4}e^{6} - \frac{9}{4}e^{5} + \frac{13}{2}e^{4} + \frac{23}{4}e^{3} - \frac{57}{4}e^{2} - \frac{17}{4}e + 9$
11 $[11, 11, -w^{3} + 6w - 4]$ $\phantom{-}\frac{3}{4}e^{7} - \frac{5}{4}e^{6} - \frac{31}{4}e^{5} + \frac{21}{2}e^{4} + \frac{93}{4}e^{3} - \frac{91}{4}e^{2} - \frac{83}{4}e + 13$
17 $[17, 17, w^{3} + w^{2} - 6w - 1]$ $\phantom{-}\frac{5}{4}e^{7} - \frac{9}{4}e^{6} - \frac{53}{4}e^{5} + 19e^{4} + \frac{173}{4}e^{3} - \frac{165}{4}e^{2} - \frac{175}{4}e + 22$
17 $[17, 17, -w^{2} - w + 3]$ $-e^{7} + \frac{3}{2}e^{6} + 11e^{5} - \frac{27}{2}e^{4} - \frac{73}{2}e^{3} + 35e^{2} + \frac{73}{2}e - 27$
31 $[31, 31, 2w^{3} + w^{2} - 13w + 3]$ $-\frac{3}{2}e^{7} + \frac{5}{2}e^{6} + \frac{35}{2}e^{5} - 24e^{4} - \frac{125}{2}e^{3} + \frac{131}{2}e^{2} + \frac{131}{2}e - 49$
37 $[37, 37, -3w^{3} - w^{2} + 18w - 3]$ $\phantom{-}\frac{1}{2}e^{7} - e^{6} - \frac{9}{2}e^{5} + \frac{15}{2}e^{4} + 11e^{3} - \frac{21}{2}e^{2} - 8e + 1$
41 $[41, 41, w^{2} + 2w - 4]$ $-\frac{1}{4}e^{7} + \frac{1}{4}e^{6} + \frac{9}{4}e^{5} - 2e^{4} - \frac{21}{4}e^{3} + \frac{17}{4}e^{2} + \frac{19}{4}e + 1$
47 $[47, 47, 2w^{3} + 2w^{2} - 11w - 2]$ $\phantom{-}e^{5} - e^{4} - 8e^{3} + 7e^{2} + 11e - 10$
47 $[47, 47, -3w^{3} - w^{2} + 19w - 6]$ $\phantom{-}\frac{3}{2}e^{7} - \frac{3}{2}e^{6} - \frac{37}{2}e^{5} + 14e^{4} + \frac{139}{2}e^{3} - \frac{75}{2}e^{2} - \frac{155}{2}e + 32$
59 $[59, 59, -2w^{3} + 13w - 6]$ $\phantom{-}\frac{1}{2}e^{7} - \frac{1}{2}e^{6} - \frac{11}{2}e^{5} + 4e^{4} + \frac{33}{2}e^{3} - \frac{15}{2}e^{2} - \frac{17}{2}e + 3$
59 $[59, 59, -w^{3} - w^{2} + 5w + 2]$ $-\frac{5}{4}e^{7} + \frac{3}{4}e^{6} + \frac{61}{4}e^{5} - \frac{11}{2}e^{4} - \frac{227}{4}e^{3} + \frac{49}{4}e^{2} + \frac{249}{4}e - 16$
59 $[59, 59, w^{2} + w - 1]$ $-\frac{3}{4}e^{7} + \frac{5}{4}e^{6} + \frac{31}{4}e^{5} - \frac{19}{2}e^{4} - \frac{93}{4}e^{3} + \frac{59}{4}e^{2} + \frac{83}{4}e + 2$
59 $[59, 59, w^{2} + 2w - 6]$ $\phantom{-}\frac{1}{4}e^{7} + \frac{5}{4}e^{6} - \frac{21}{4}e^{5} - \frac{23}{2}e^{4} + \frac{107}{4}e^{3} + \frac{99}{4}e^{2} - \frac{133}{4}e - 6$
61 $[61, 61, -w^{3} + w^{2} + 8w - 7]$ $\phantom{-}\frac{1}{4}e^{7} - \frac{1}{4}e^{6} - \frac{17}{4}e^{5} + 4e^{4} + \frac{81}{4}e^{3} - \frac{69}{4}e^{2} - \frac{103}{4}e + 18$
67 $[67, 67, w^{3} + 2w^{2} - 4w - 4]$ $\phantom{-}\frac{1}{2}e^{7} - \frac{1}{2}e^{6} - \frac{15}{2}e^{5} + 6e^{4} + \frac{69}{2}e^{3} - \frac{39}{2}e^{2} - \frac{93}{2}e + 15$
73 $[73, 73, -2w^{3} - w^{2} + 12w - 4]$ $\phantom{-}\frac{1}{4}e^{7} + \frac{1}{4}e^{6} - \frac{13}{4}e^{5} - \frac{5}{2}e^{4} + \frac{47}{4}e^{3} + \frac{11}{4}e^{2} - \frac{49}{4}e + 14$
81 $[81, 3, -3]$ $-\frac{1}{2}e^{7} + 2e^{6} + \frac{7}{2}e^{5} - \frac{33}{2}e^{4} - 4e^{3} + \frac{57}{2}e^{2} - 3e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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