Properties

Label 4.4.17600.1-11.2-a
Base field 4.4.17600.1
Weight $[2, 2, 2, 2]$
Level norm $11$
Level $[11, 11, -\frac{1}{2}w^{2} - w + 2]$
Dimension $8$
CM no
Base change no

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Base field 4.4.17600.1

Generator \(w\), with minimal polynomial \(x^{4} - 14x^{2} + 44\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[11, 11, -\frac{1}{2}w^{2} - w + 2]$
Dimension: $8$
CM: no
Base change: no
Newspace dimension: $16$

Hecke eigenvalues ($q$-expansion)

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

\(x^{8} - 5x^{7} - 4x^{6} + 49x^{5} - 46x^{4} - 58x^{3} + 65x^{2} + 18x - 17\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -\frac{1}{2}w^{3} + w^{2} + 4w - 8]$ $\phantom{-}e$
11 $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 4w + 11]$ $\phantom{-}\frac{116}{617}e^{7} - \frac{465}{617}e^{6} - \frac{675}{617}e^{5} + \frac{4084}{617}e^{4} - \frac{2968}{617}e^{3} - \frac{1309}{617}e^{2} + \frac{2152}{617}e - \frac{1289}{617}$
11 $[11, 11, -\frac{1}{2}w^{2} - w + 2]$ $-1$
11 $[11, 11, -\frac{1}{2}w^{2} + w + 2]$ $\phantom{-}\frac{10}{617}e^{7} - \frac{72}{617}e^{6} - \frac{5}{617}e^{5} + \frac{501}{617}e^{4} - \frac{575}{617}e^{3} + \frac{1302}{617}e^{2} - \frac{857}{617}e - \frac{526}{617}$
19 $[19, 19, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 4w + 5]$ $-\frac{23}{617}e^{7} + \frac{289}{617}e^{6} - \frac{297}{617}e^{5} - \frac{3065}{617}e^{4} + \frac{4716}{617}e^{3} + \frac{4903}{617}e^{2} - \frac{5001}{617}e - \frac{1505}{617}$
19 $[19, 19, \frac{1}{2}w^{3} + w^{2} - 4w - 9]$ $\phantom{-}\frac{168}{617}e^{7} - \frac{716}{617}e^{6} - \frac{1318}{617}e^{5} + \frac{7553}{617}e^{4} - \frac{1022}{617}e^{3} - \frac{13172}{617}e^{2} + \frac{1521}{617}e + \frac{5601}{617}$
19 $[19, 19, \frac{1}{2}w^{3} - w^{2} - 4w + 9]$ $-\frac{247}{617}e^{7} + \frac{1038}{617}e^{6} + \frac{1666}{617}e^{5} - \frac{10462}{617}e^{4} + \frac{4639}{617}e^{3} + \frac{14856}{617}e^{2} - \frac{7029}{617}e - \frac{4037}{617}$
19 $[19, 19, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 4w - 5]$ $\phantom{-}\frac{97}{617}e^{7} - \frac{575}{617}e^{6} - \frac{357}{617}e^{5} + \frac{6032}{617}e^{4} - \frac{4035}{617}e^{3} - \frac{10323}{617}e^{2} + \frac{1374}{617}e + \frac{6991}{617}$
25 $[25, 5, \frac{1}{2}w^{2} - 1]$ $\phantom{-}\frac{257}{617}e^{7} - \frac{1110}{617}e^{6} - \frac{1671}{617}e^{5} + \frac{10963}{617}e^{4} - \frac{5214}{617}e^{3} - \frac{14171}{617}e^{2} + \frac{6789}{617}e + \frac{4128}{617}$
29 $[29, 29, \frac{1}{2}w^{3} - 4w - 1]$ $-\frac{486}{617}e^{7} + \frac{1895}{617}e^{6} + \frac{3945}{617}e^{5} - \frac{19536}{617}e^{4} + \frac{2648}{617}e^{3} + \frac{30877}{617}e^{2} - \frac{6229}{617}e - \frac{10099}{617}$
29 $[29, 29, -\frac{1}{2}w^{3} + 4w - 1]$ $\phantom{-}\frac{438}{617}e^{7} - \frac{2043}{617}e^{6} - \frac{2070}{617}e^{5} + \frac{19229}{617}e^{4} - \frac{15930}{617}e^{3} - \frac{16272}{617}e^{2} + \frac{14168}{617}e + \frac{3122}{617}$
31 $[31, 31, -w - 1]$ $-\frac{161}{617}e^{7} + \frac{789}{617}e^{6} + \frac{389}{617}e^{5} - \frac{6647}{617}e^{4} + \frac{8949}{617}e^{3} - \frac{231}{617}e^{2} - \frac{4157}{617}e + \frac{3039}{617}$
31 $[31, 31, w - 1]$ $\phantom{-}\frac{10}{617}e^{7} - \frac{72}{617}e^{6} - \frac{5}{617}e^{5} + \frac{1118}{617}e^{4} - \frac{1192}{617}e^{3} - \frac{4868}{617}e^{2} + \frac{2845}{617}e + \frac{4410}{617}$
41 $[41, 41, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 4w - 2]$ $\phantom{-}\frac{374}{617}e^{7} - \frac{1212}{617}e^{6} - \frac{3889}{617}e^{5} + \frac{13061}{617}e^{4} + \frac{6260}{617}e^{3} - \frac{25592}{617}e^{2} - \frac{4040}{617}e + \frac{10067}{617}$
41 $[41, 41, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 2]$ $\phantom{-}\frac{340}{617}e^{7} - \frac{1831}{617}e^{6} - \frac{787}{617}e^{5} + \frac{17034}{617}e^{4} - \frac{20167}{617}e^{3} - \frac{12496}{617}e^{2} + \frac{18371}{617}e + \frac{3094}{617}$
49 $[49, 7, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 5w - 7]$ $\phantom{-}\frac{143}{617}e^{7} - \frac{536}{617}e^{6} - \frac{997}{617}e^{5} + \frac{4758}{617}e^{4} - \frac{2361}{617}e^{3} - \frac{1619}{617}e^{2} + \frac{3355}{617}e - \frac{488}{617}$
49 $[49, 7, \frac{3}{2}w^{3} - \frac{7}{2}w^{2} - 13w + 29]$ $-\frac{366}{617}e^{7} + \frac{1648}{617}e^{6} + \frac{2034}{617}e^{5} - \frac{15992}{617}e^{4} + \frac{10556}{617}e^{3} + \frac{17502}{617}e^{2} - \frac{8492}{617}e - \frac{4071}{617}$
59 $[59, 59, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + 3w + 10]$ $\phantom{-}\frac{263}{617}e^{7} - \frac{783}{617}e^{6} - \frac{2908}{617}e^{5} + \frac{8302}{617}e^{4} + \frac{6164}{617}e^{3} - \frac{15611}{617}e^{2} - \frac{5078}{617}e + \frac{4923}{617}$
59 $[59, 59, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 3w + 10]$ $-\frac{37}{617}e^{7} + \frac{143}{617}e^{6} + \frac{327}{617}e^{5} - \frac{1175}{617}e^{4} - \frac{649}{617}e^{3} - \frac{992}{617}e^{2} + \frac{3356}{617}e + \frac{4661}{617}$
61 $[61, 61, \frac{1}{2}w^{2} + w - 6]$ $\phantom{-}\frac{55}{617}e^{7} - \frac{396}{617}e^{6} + \frac{281}{617}e^{5} + \frac{3064}{617}e^{4} - \frac{6556}{617}e^{3} + \frac{2842}{617}e^{2} + \frac{2382}{617}e - \frac{1659}{617}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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