Properties

Label 4.4.12197.1-11.1-b
Base field 4.4.12197.1
Weight $[2, 2, 2, 2]$
Level norm $11$
Level $[11, 11, w^{3} - w^{2} - 4w + 2]$
Dimension $5$
CM no
Base change no

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Base field 4.4.12197.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 3x + 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[11, 11, w^{3} - w^{2} - 4w + 2]$
Dimension: $5$
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:

\(x^{5} + x^{4} - 17x^{3} - 12x^{2} + 62x + 53\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, w + 1]$ $\phantom{-}\frac{2}{31}e^{4} - \frac{3}{31}e^{3} - \frac{42}{31}e^{2} + \frac{50}{31}e + \frac{185}{31}$
5 $[5, 5, -w + 2]$ $\phantom{-}e$
11 $[11, 11, w^{3} - w^{2} - 4w + 2]$ $-1$
13 $[13, 13, w^{3} - w^{2} - 4w]$ $\phantom{-}0$
16 $[16, 2, 2]$ $\phantom{-}\frac{5}{62}e^{4} + \frac{4}{31}e^{3} - \frac{43}{62}e^{2} - \frac{61}{62}e + \frac{13}{62}$
17 $[17, 17, -w^{2} + w + 3]$ $-\frac{9}{31}e^{4} - \frac{2}{31}e^{3} + \frac{127}{31}e^{2} - \frac{8}{31}e - \frac{228}{31}$
19 $[19, 19, w^{3} - 5w]$ $-\frac{4}{31}e^{4} + \frac{6}{31}e^{3} + \frac{53}{31}e^{2} - \frac{69}{31}e - \frac{60}{31}$
19 $[19, 19, -w + 3]$ $\phantom{-}\frac{8}{31}e^{4} - \frac{12}{31}e^{3} - \frac{137}{31}e^{2} + \frac{169}{31}e + \frac{430}{31}$
23 $[23, 23, 2w^{3} - 2w^{2} - 9w + 4]$ $-\frac{1}{31}e^{4} + \frac{17}{31}e^{3} + \frac{52}{31}e^{2} - \frac{180}{31}e - \frac{232}{31}$
23 $[23, 23, w^{2} - 2]$ $\phantom{-}\frac{13}{31}e^{4} + \frac{27}{31}e^{3} - \frac{149}{31}e^{2} - \frac{171}{31}e + \frac{226}{31}$
25 $[25, 5, w^{2} - 3]$ $-\frac{7}{31}e^{4} - \frac{5}{31}e^{3} + \frac{85}{31}e^{2} + \frac{42}{31}e - \frac{105}{31}$
37 $[37, 37, -w^{3} + 2w^{2} + 4w - 6]$ $-\frac{3}{31}e^{4} - \frac{11}{31}e^{3} + \frac{32}{31}e^{2} + \frac{49}{31}e + \frac{79}{31}$
37 $[37, 37, -w^{3} + w^{2} + 6w - 4]$ $-\frac{27}{62}e^{4} - \frac{34}{31}e^{3} + \frac{319}{62}e^{2} + \frac{503}{62}e - \frac{405}{62}$
41 $[41, 41, w^{2} - w - 5]$ $-\frac{10}{31}e^{4} - \frac{16}{31}e^{3} + \frac{117}{31}e^{2} + \frac{60}{31}e + \frac{5}{31}$
47 $[47, 47, w^{3} - 6w + 1]$ $\phantom{-}\frac{16}{31}e^{4} + \frac{38}{31}e^{3} - \frac{150}{31}e^{2} - \frac{251}{31}e - \frac{70}{31}$
61 $[61, 61, -w^{3} + w^{2} + 6w - 2]$ $\phantom{-}\frac{12}{31}e^{4} + \frac{13}{31}e^{3} - \frac{159}{31}e^{2} - \frac{134}{31}e + \frac{304}{31}$
67 $[67, 67, 2w^{3} - w^{2} - 9w + 2]$ $\phantom{-}\frac{1}{31}e^{4} + \frac{45}{31}e^{3} + \frac{72}{31}e^{2} - \frac{409}{31}e - \frac{481}{31}$
67 $[67, 67, w^{3} - 7w + 3]$ $-\frac{13}{62}e^{4} - \frac{29}{31}e^{3} + \frac{25}{62}e^{2} + \frac{605}{62}e + \frac{487}{62}$
73 $[73, 73, 2w^{3} - w^{2} - 9w]$ $\phantom{-}\frac{24}{31}e^{4} + \frac{26}{31}e^{3} - \frac{287}{31}e^{2} - \frac{144}{31}e + \frac{484}{31}$
81 $[81, 3, -3]$ $\phantom{-}\frac{2}{31}e^{4} - \frac{34}{31}e^{3} - \frac{135}{31}e^{2} + \frac{329}{31}e + \frac{650}{31}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$11$ $[11, 11, w^{3} - w^{2} - 4w + 2]$ $1$