Properties

Label 4.4.11197.1-13.1-a
Base field 4.4.11197.1
Weight $[2, 2, 2, 2]$
Level norm $13$
Level $[13, 13, -w^{2} + 2w + 2]$
Dimension $7$
CM no
Base change no

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Base field 4.4.11197.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[13, 13, -w^{2} + 2w + 2]$
Dimension: $7$
CM: no
Base change: no
Newspace dimension: $14$

Hecke eigenvalues ($q$-expansion)

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

\(x^{7} - 4x^{6} - 9x^{5} + 45x^{4} + 5x^{3} - 101x^{2} + 10x + 16\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}e$
7 $[7, 7, w^{3} - 2w^{2} - 3w + 1]$ $-\frac{7}{2}e^{6} + 4e^{5} + \frac{85}{2}e^{4} - \frac{71}{2}e^{3} - \frac{229}{2}e^{2} + \frac{45}{2}e + 22$
11 $[11, 11, -w - 2]$ $-e^{6} + e^{5} + 12e^{4} - 9e^{3} - 32e^{2} + 7e + 8$
11 $[11, 11, -w^{3} + 2w^{2} + 3w - 2]$ $-e + 2$
13 $[13, 13, -w^{2} + 2w + 2]$ $-1$
16 $[16, 2, 2]$ $\phantom{-}2e^{6} - 2e^{5} - 25e^{4} + 17e^{3} + 71e^{2} - 5e - 13$
19 $[19, 19, -w^{3} + 2w^{2} + 4w - 1]$ $\phantom{-}7e^{6} - 8e^{5} - 85e^{4} + 71e^{3} + 228e^{2} - 45e - 34$
23 $[23, 23, -w^{2} + w + 3]$ $-3e^{6} + 3e^{5} + 37e^{4} - 26e^{3} - 103e^{2} + 12e + 22$
23 $[23, 23, -w^{2} + 3]$ $-2e^{6} + 2e^{5} + 25e^{4} - 16e^{3} - 72e^{2} - e + 16$
27 $[27, 3, w^{3} - 3w^{2} - w + 4]$ $-\frac{3}{2}e^{6} + e^{5} + \frac{37}{2}e^{4} - \frac{13}{2}e^{3} - \frac{103}{2}e^{2} - \frac{25}{2}e + 8$
29 $[29, 29, -w^{3} + 3w^{2} + 3w - 5]$ $\phantom{-}4e^{6} - 4e^{5} - 49e^{4} + 34e^{3} + 134e^{2} - 10e - 18$
29 $[29, 29, w^{3} - 2w^{2} - 4w]$ $-\frac{3}{2}e^{6} + 2e^{5} + \frac{35}{2}e^{4} - \frac{37}{2}e^{3} - \frac{83}{2}e^{2} + \frac{33}{2}e$
47 $[47, 47, -w^{3} + 2w^{2} + 3w - 5]$ $-\frac{5}{2}e^{6} + 2e^{5} + \frac{63}{2}e^{4} - \frac{33}{2}e^{3} - \frac{183}{2}e^{2} + \frac{1}{2}e + 20$
47 $[47, 47, w^{2} - 3w - 2]$ $\phantom{-}\frac{9}{2}e^{6} - 4e^{5} - \frac{111}{2}e^{4} + \frac{65}{2}e^{3} + \frac{309}{2}e^{2} + \frac{1}{2}e - 28$
61 $[61, 61, -w^{3} + 2w^{2} + 5w - 3]$ $\phantom{-}\frac{3}{2}e^{6} - e^{5} - \frac{37}{2}e^{4} + \frac{17}{2}e^{3} + \frac{101}{2}e^{2} - \frac{1}{2}e - 6$
67 $[67, 67, -w^{3} + w^{2} + 5w - 1]$ $\phantom{-}\frac{9}{2}e^{6} - 5e^{5} - \frac{111}{2}e^{4} + \frac{91}{2}e^{3} + \frac{309}{2}e^{2} - \frac{71}{2}e - 36$
67 $[67, 67, -2w^{3} + 3w^{2} + 11w - 7]$ $-\frac{7}{2}e^{6} + 4e^{5} + \frac{85}{2}e^{4} - \frac{73}{2}e^{3} - \frac{229}{2}e^{2} + \frac{61}{2}e + 16$
83 $[83, 83, -2w + 3]$ $\phantom{-}\frac{5}{2}e^{6} - 2e^{5} - \frac{61}{2}e^{4} + \frac{33}{2}e^{3} + \frac{167}{2}e^{2} - \frac{1}{2}e - 16$
89 $[89, 89, 3w^{3} - 7w^{2} - 9w + 9]$ $-2e^{6} + 3e^{5} + 24e^{4} - 29e^{3} - 63e^{2} + 38e + 14$
97 $[97, 97, w^{3} - w^{2} - 4w - 3]$ $-6e^{6} + 7e^{5} + 73e^{4} - 63e^{3} - 197e^{2} + 43e + 34$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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