Properties

Label 4.4.17069.1-9.2-c
Base field 4.4.17069.1
Weight $[2, 2, 2, 2]$
Level norm $9$
Level $[9, 3, w^{3} - 2w^{2} - 5w + 1]$
Dimension $9$
CM no
Base change yes

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Base field 4.4.17069.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 8x^{2} - 4x + 3\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[9, 3, w^{3} - 2w^{2} - 5w + 1]$
Dimension: $9$
CM: no
Base change: yes
Newspace dimension: $19$

Hecke eigenvalues ($q$-expansion)

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

\(x^{9} - 18x^{7} - 2x^{6} + 94x^{5} + 26x^{4} - 140x^{3} - 72x^{2} + 20x + 10\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
3 $[3, 3, w^{3} - 2w^{2} - 6w + 1]$ $\phantom{-}e$
9 $[9, 3, w^{3} - 2w^{2} - 5w + 1]$ $-1$
16 $[16, 2, 2]$ $-\frac{425}{747}e^{8} + \frac{268}{747}e^{7} + \frac{7423}{747}e^{6} - \frac{3634}{747}e^{5} - \frac{12155}{249}e^{4} + \frac{9554}{747}e^{3} + \frac{15614}{249}e^{2} + \frac{1964}{249}e - \frac{3211}{747}$
17 $[17, 17, w^{3} - w^{2} - 8w - 5]$ $-\frac{256}{747}e^{8} + \frac{5}{747}e^{7} + \frac{4640}{747}e^{6} + \frac{328}{747}e^{5} - \frac{8218}{249}e^{4} - \frac{4733}{747}e^{3} + \frac{12706}{249}e^{2} + \frac{4147}{249}e - \frac{5576}{747}$
17 $[17, 17, -2w^{3} + 4w^{2} + 11w - 2]$ $\phantom{-}\frac{136}{747}e^{8} - \frac{26}{747}e^{7} - \frac{2465}{747}e^{6} + \frac{386}{747}e^{5} + \frac{4288}{249}e^{4} - \frac{1384}{747}e^{3} - \frac{6112}{249}e^{2} + \frac{248}{249}e + \frac{2402}{747}$
17 $[17, 17, -w^{3} + 3w^{2} + 2w - 2]$ $-\frac{256}{747}e^{8} + \frac{5}{747}e^{7} + \frac{4640}{747}e^{6} + \frac{328}{747}e^{5} - \frac{8218}{249}e^{4} - \frac{4733}{747}e^{3} + \frac{12706}{249}e^{2} + \frac{4147}{249}e - \frac{5576}{747}$
17 $[17, 17, w^{3} - 2w^{2} - 4w + 1]$ $\phantom{-}\frac{136}{747}e^{8} - \frac{26}{747}e^{7} - \frac{2465}{747}e^{6} + \frac{386}{747}e^{5} + \frac{4288}{249}e^{4} - \frac{1384}{747}e^{3} - \frac{6112}{249}e^{2} + \frac{248}{249}e + \frac{2402}{747}$
25 $[25, 5, w^{3} - 3w^{2} - 3w + 1]$ $-\frac{196}{249}e^{8} + \frac{140}{249}e^{7} + \frac{3428}{249}e^{6} - \frac{2021}{249}e^{5} - \frac{5672}{83}e^{4} + \frac{6418}{249}e^{3} + \frac{7666}{83}e^{2} + \frac{82}{83}e - \frac{3242}{249}$
25 $[25, 5, w^{2} - 2w - 7]$ $-\frac{196}{249}e^{8} + \frac{140}{249}e^{7} + \frac{3428}{249}e^{6} - \frac{2021}{249}e^{5} - \frac{5672}{83}e^{4} + \frac{6418}{249}e^{3} + \frac{7666}{83}e^{2} + \frac{82}{83}e - \frac{3242}{249}$
29 $[29, 29, w^{3} - 2w^{2} - 6w - 1]$ $\phantom{-}\frac{65}{249}e^{8} - \frac{82}{249}e^{7} - \frac{1147}{249}e^{6} + \frac{1294}{249}e^{5} + \frac{1942}{83}e^{4} - \frac{5246}{249}e^{3} - \frac{2804}{83}e^{2} + \frac{1344}{83}e + \frac{1906}{249}$
29 $[29, 29, w - 2]$ $\phantom{-}\frac{65}{249}e^{8} - \frac{82}{249}e^{7} - \frac{1147}{249}e^{6} + \frac{1294}{249}e^{5} + \frac{1942}{83}e^{4} - \frac{5246}{249}e^{3} - \frac{2804}{83}e^{2} + \frac{1344}{83}e + \frac{1906}{249}$
53 $[53, 53, w^{3} - 3w^{2} - 4w + 4]$ $\phantom{-}\frac{146}{747}e^{8} + \frac{38}{747}e^{7} - \frac{2833}{747}e^{6} - \frac{794}{747}e^{5} + \frac{5570}{249}e^{4} + \frac{4666}{747}e^{3} - \frac{10355}{249}e^{2} - \frac{1550}{249}e + \frac{10510}{747}$
53 $[53, 53, -w^{3} + 3w^{2} + 4w - 5]$ $\phantom{-}\frac{146}{747}e^{8} + \frac{38}{747}e^{7} - \frac{2833}{747}e^{6} - \frac{794}{747}e^{5} + \frac{5570}{249}e^{4} + \frac{4666}{747}e^{3} - \frac{10355}{249}e^{2} - \frac{1550}{249}e + \frac{10510}{747}$
61 $[61, 61, -w^{3} + 2w^{2} + 7w - 4]$ $-\frac{278}{249}e^{8} + \frac{163}{249}e^{7} + \frac{4852}{249}e^{6} - \frac{2305}{249}e^{5} - \frac{7984}{83}e^{4} + \frac{7106}{249}e^{3} + \frac{10736}{83}e^{2} - \frac{48}{83}e - \frac{6382}{249}$
61 $[61, 61, -4w^{3} + 11w^{2} + 14w - 8]$ $-\frac{278}{249}e^{8} + \frac{163}{249}e^{7} + \frac{4852}{249}e^{6} - \frac{2305}{249}e^{5} - \frac{7984}{83}e^{4} + \frac{7106}{249}e^{3} + \frac{10736}{83}e^{2} - \frac{48}{83}e - \frac{6382}{249}$
101 $[101, 101, -w^{3} + 2w^{2} + 7w - 1]$ $-\frac{1100}{747}e^{8} + \frac{430}{747}e^{7} + \frac{19564}{747}e^{6} - \frac{6154}{747}e^{5} - \frac{33452}{249}e^{4} + \frac{20246}{747}e^{3} + \frac{48908}{249}e^{2} - \frac{1420}{249}e - \frac{31336}{747}$
103 $[103, 103, -w^{3} + 3w^{2} + 2w - 5]$ $\phantom{-}\frac{70}{249}e^{8} - \frac{50}{249}e^{7} - \frac{1331}{249}e^{6} + \frac{704}{249}e^{5} + \frac{2500}{83}e^{4} - \frac{1972}{249}e^{3} - \frac{4137}{83}e^{2} - \frac{468}{83}e + \frac{1976}{249}$
103 $[103, 103, -w^{3} + w^{2} + 8w + 2]$ $\phantom{-}\frac{70}{249}e^{8} - \frac{50}{249}e^{7} - \frac{1331}{249}e^{6} + \frac{704}{249}e^{5} + \frac{2500}{83}e^{4} - \frac{1972}{249}e^{3} - \frac{4137}{83}e^{2} - \frac{468}{83}e + \frac{1976}{249}$
113 $[113, 113, w^{3} - 3w^{2} - 3w + 7]$ $\phantom{-}\frac{754}{747}e^{8} - \frac{254}{747}e^{7} - \frac{13106}{747}e^{6} + \frac{2909}{747}e^{5} + \frac{21166}{249}e^{4} - \frac{2488}{747}e^{3} - \frac{25654}{249}e^{2} - \frac{8131}{249}e + \frac{5078}{747}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$9$ $[9, 3, w^{3} - 2w^{2} - 5w + 1]$ $1$