Properties

Label 6.6.592661.1-49.1-d
Base field 6.6.592661.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $49$
Level $[49, 7, -w^{4} + 4w^{2} + w - 3]$
Dimension $5$
CM no
Base change no

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Base field 6.6.592661.1

Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 5x^{4} + 4x^{3} + 5x^{2} - 2x - 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[49, 7, -w^{4} + 4w^{2} + w - 3]$
Dimension: $5$
CM: no
Base change: no
Newspace dimension: $13$

Hecke eigenvalues ($q$-expansion)

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

\(x^{5} + 3x^{4} - 60x^{3} - 112x^{2} + 720x - 336\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
7 $[7, 7, w^{5} - 5w^{3} + 4w]$ $\phantom{-}2$
13 $[13, 13, -w^{3} + 3w]$ $\phantom{-}e$
25 $[25, 5, w^{4} - w^{3} - 4w^{2} + 2w + 2]$ $-\frac{1}{48}e^{4} - \frac{1}{48}e^{3} + \frac{19}{24}e^{2} + \frac{1}{4}e + \frac{3}{2}$
31 $[31, 31, -w^{5} + 5w^{3} - 5w + 1]$ $\phantom{-}\frac{5}{144}e^{4} + \frac{17}{144}e^{3} - \frac{125}{72}e^{2} - \frac{49}{12}e + \frac{67}{6}$
31 $[31, 31, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ $-\frac{1}{48}e^{4} + \frac{1}{16}e^{3} + \frac{29}{24}e^{2} - \frac{9}{4}e - \frac{17}{2}$
37 $[37, 37, w^{4} - 5w^{2} + w + 3]$ $\phantom{-}\frac{1}{144}e^{4} + \frac{1}{144}e^{3} - \frac{31}{72}e^{2} + \frac{13}{12}e + \frac{35}{6}$
43 $[43, 43, -2w^{5} + w^{4} + 9w^{3} - 3w^{2} - 6w]$ $-\frac{1}{12}e^{3} + \frac{1}{12}e^{2} + 3e - 1$
47 $[47, 47, w^{5} - w^{4} - 4w^{3} + 4w^{2} - 2]$ $-\frac{1}{48}e^{4} - \frac{1}{48}e^{3} + \frac{31}{24}e^{2} + \frac{3}{4}e - \frac{23}{2}$
49 $[49, 7, -w^{4} + 4w^{2} + w - 3]$ $-1$
53 $[53, 53, -w^{4} + w^{3} + 4w^{2} - 3w - 4]$ $\phantom{-}\frac{1}{144}e^{4} - \frac{11}{144}e^{3} - \frac{25}{72}e^{2} + \frac{49}{12}e + \frac{17}{6}$
59 $[59, 59, w^{4} - 5w^{2} - w + 5]$ $-\frac{5}{144}e^{4} - \frac{5}{144}e^{3} + \frac{119}{72}e^{2} + \frac{13}{12}e - \frac{73}{6}$
61 $[61, 61, w^{3} - w^{2} - 3w]$ $\phantom{-}\frac{1}{16}e^{4} + \frac{7}{48}e^{3} - \frac{71}{24}e^{2} - \frac{21}{4}e + \frac{31}{2}$
64 $[64, 2, -2]$ $-\frac{1}{12}e^{3} + \frac{1}{12}e^{2} + 3e - 2$
67 $[67, 67, -2w^{5} + w^{4} + 9w^{3} - 3w^{2} - 7w]$ $-\frac{1}{36}e^{4} - \frac{7}{36}e^{3} + \frac{17}{9}e^{2} + \frac{26}{3}e - \frac{58}{3}$
67 $[67, 67, 2w^{5} - w^{4} - 10w^{3} + 4w^{2} + 9w - 1]$ $\phantom{-}\frac{5}{144}e^{4} + \frac{17}{144}e^{3} - \frac{125}{72}e^{2} - \frac{61}{12}e + \frac{43}{6}$
73 $[73, 73, w^{5} - w^{4} - 4w^{3} + 5w^{2} + w - 3]$ $-e + 4$
73 $[73, 73, 3w^{5} - 3w^{4} - 13w^{3} + 11w^{2} + 7w - 3]$ $-\frac{1}{144}e^{4} - \frac{13}{144}e^{3} + \frac{1}{72}e^{2} + \frac{29}{12}e + \frac{25}{6}$
83 $[83, 83, -2w^{5} + 3w^{4} + 9w^{3} - 11w^{2} - 6w + 2]$ $-\frac{1}{24}e^{4} - \frac{1}{24}e^{3} + \frac{19}{12}e^{2} + \frac{1}{2}e + 1$
97 $[97, 97, -2w^{4} + w^{3} + 9w^{2} - 3w - 4]$ $-\frac{1}{48}e^{4} - \frac{3}{16}e^{3} + \frac{35}{24}e^{2} + \frac{35}{4}e - \frac{39}{2}$
101 $[101, 101, -2w^{5} + 3w^{4} + 9w^{3} - 11w^{2} - 6w + 4]$ $\phantom{-}\frac{1}{72}e^{4} + \frac{7}{72}e^{3} - \frac{17}{18}e^{2} - \frac{23}{6}e + \frac{44}{3}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$49$ $[49, 7, -w^{4} + 4w^{2} + w - 3]$ $1$