Properties

Label 6.6.1279733.1-29.4-g
Base field 6.6.1279733.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $29$
Level $[29,29,w^{2} - w - 1]$
Dimension $7$
CM no
Base change no

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Base field 6.6.1279733.1

Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 6x^{4} + 10x^{3} + 10x^{2} - 11x - 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[29,29,w^{2} - w - 1]$
Dimension: $7$
CM: no
Base change: no
Newspace dimension: $22$

Hecke eigenvalues ($q$-expansion)

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

\(x^{7} + 7x^{6} - 6x^{5} - 120x^{4} - 214x^{3} - 100x^{2} + 7x + 9\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
7 $[7, 7, w^{4} - 2w^{3} - 3w^{2} + 6w - 1]$ $\phantom{-}e$
7 $[7, 7, -w^{4} + w^{3} + 4w^{2} - w - 1]$ $\phantom{-}\frac{5}{4}e^{6} + \frac{49}{6}e^{5} - \frac{34}{3}e^{4} - \frac{434}{3}e^{3} - \frac{399}{2}e^{2} - \frac{199}{6}e + \frac{81}{4}$
13 $[13, 13, w^{5} - 2w^{4} - 4w^{3} + 7w^{2} + 3w - 3]$ $\phantom{-}\frac{1}{3}e^{6} + 2e^{5} - 4e^{4} - \frac{109}{3}e^{3} - \frac{107}{3}e^{2} + 8e + 4$
29 $[29, 29, -w^{4} + w^{3} + 4w^{2} - 3w - 2]$ $\phantom{-}\frac{35}{6}e^{6} + \frac{227}{6}e^{5} - \frac{109}{2}e^{4} - \frac{4031}{6}e^{3} - \frac{1803}{2}e^{2} - \frac{733}{6}e + 96$
29 $[29, 29, w^{4} - 5w^{2} - 2w + 4]$ $-\frac{9}{4}e^{6} - \frac{29}{2}e^{5} + \frac{65}{3}e^{4} + \frac{775}{3}e^{3} + \frac{2017}{6}e^{2} + \frac{187}{6}e - \frac{165}{4}$
29 $[29, 29, -w^{4} + w^{3} + 3w^{2} - w + 2]$ $-\frac{39}{4}e^{6} - 63e^{5} + \frac{185}{2}e^{4} + \frac{2241}{2}e^{3} + 1482e^{2} + 172e - \frac{669}{4}$
29 $[29, 29, -w^{2} + w + 1]$ $\phantom{-}1$
41 $[41, 41, -w^{5} + w^{4} + 4w^{3} - w^{2} - 3w - 1]$ $\phantom{-}e^{6} + \frac{19}{3}e^{5} - \frac{31}{3}e^{4} - \frac{341}{3}e^{3} - \frac{410}{3}e^{2} + 2e + 18$
43 $[43, 43, 2w^{3} - 2w^{2} - 7w + 3]$ $\phantom{-}\frac{7}{3}e^{6} + \frac{46}{3}e^{5} - \frac{62}{3}e^{4} - \frac{815}{3}e^{3} - \frac{1145}{3}e^{2} - \frac{184}{3}e + 45$
43 $[43, 43, w^{3} - w^{2} - 2w + 1]$ $\phantom{-}\frac{43}{12}e^{6} + \frac{137}{6}e^{5} - \frac{107}{3}e^{4} - \frac{1223}{3}e^{3} - \frac{3091}{6}e^{2} - \frac{203}{6}e + \frac{249}{4}$
64 $[64, 2, -2]$ $-\frac{25}{6}e^{6} - 27e^{5} + \frac{116}{3}e^{4} + 479e^{3} + 649e^{2} + \frac{278}{3}e - \frac{145}{2}$
71 $[71, 71, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 8w - 3]$ $-\frac{29}{2}e^{6} - \frac{563}{6}e^{5} + \frac{821}{6}e^{4} + \frac{10009}{6}e^{3} + \frac{13303}{6}e^{2} + \frac{539}{2}e - 246$
71 $[71, 71, w^{5} - 2w^{4} - 2w^{3} + 5w^{2} - 3w - 1]$ $\phantom{-}\frac{40}{3}e^{6} + \frac{517}{6}e^{5} - \frac{253}{2}e^{4} - \frac{9197}{6}e^{3} - \frac{12161}{6}e^{2} - \frac{1385}{6}e + \frac{459}{2}$
83 $[83, 83, -2w^{4} + 3w^{3} + 6w^{2} - 7w + 2]$ $-\frac{16}{3}e^{6} - \frac{104}{3}e^{5} + \frac{148}{3}e^{4} + 615e^{3} + \frac{2498}{3}e^{2} + \frac{371}{3}e - 84$
83 $[83, 83, w^{4} - w^{3} - 5w^{2} + 2w + 3]$ $\phantom{-}\frac{9}{2}e^{6} + 29e^{5} - \frac{130}{3}e^{4} - \frac{1550}{3}e^{3} - \frac{2017}{3}e^{2} - \frac{193}{3}e + \frac{141}{2}$
83 $[83, 83, -w^{5} + 3w^{4} + w^{3} - 9w^{2} + 5w + 3]$ $-\frac{29}{2}e^{6} - \frac{281}{3}e^{5} + \frac{412}{3}e^{4} + \frac{4994}{3}e^{3} + 2208e^{2} + \frac{830}{3}e - \frac{489}{2}$
83 $[83, 83, w^{5} - 7w^{3} + 10w - 1]$ $\phantom{-}\frac{13}{3}e^{6} + \frac{167}{6}e^{5} - \frac{251}{6}e^{4} - \frac{989}{2}e^{3} - \frac{3869}{6}e^{2} - \frac{169}{2}e + \frac{117}{2}$
97 $[97, 97, w^{5} - 2w^{4} - 3w^{3} + 5w^{2} - w - 1]$ $-\frac{3}{4}e^{6} - \frac{14}{3}e^{5} + \frac{15}{2}e^{4} + \frac{165}{2}e^{3} + \frac{320}{3}e^{2} + \frac{55}{3}e - \frac{9}{4}$
97 $[97, 97, w^{5} - 5w^{3} - w^{2} + 3w - 3]$ $\phantom{-}\frac{3}{2}e^{6} + \frac{59}{6}e^{5} - \frac{79}{6}e^{4} - \frac{1043}{6}e^{3} - \frac{493}{2}e^{2} - \frac{269}{6}e + 15$
113 $[113, 113, w^{4} - w^{3} - 4w^{2} + w + 4]$ $\phantom{-}\frac{29}{12}e^{6} + \frac{47}{3}e^{5} - \frac{133}{6}e^{4} - \frac{555}{2}e^{3} - \frac{1142}{3}e^{2} - 61e + \frac{117}{4}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$29$ $[29,29,w^{2} - w - 1]$ $-1$