Properties

Label 4.4.17600.1-11.1-d
Base field 4.4.17600.1
Weight $[2, 2, 2, 2]$
Level norm $11$
Level $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 4w + 11]$
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: $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 4w + 11]$
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:

\(x^{8} - 41x^{6} + 591x^{4} - 3440x^{2} + 6400\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -\frac{1}{2}w^{3} + w^{2} + 4w - 8]$ $-\frac{7}{320}e^{7} + \frac{207}{320}e^{5} - \frac{1817}{320}e^{3} + \frac{27}{2}e$
11 $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 4w + 11]$ $-1$
11 $[11, 11, -\frac{1}{2}w^{2} - w + 2]$ $\phantom{-}e$
11 $[11, 11, -\frac{1}{2}w^{2} + w + 2]$ $\phantom{-}\frac{1}{80}e^{7} - \frac{21}{80}e^{5} + \frac{91}{80}e^{3} + \frac{3}{4}e$
19 $[19, 19, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 4w + 5]$ $\phantom{-}\frac{9}{320}e^{7} - \frac{209}{320}e^{5} + \frac{1319}{320}e^{3} - \frac{29}{4}e$
19 $[19, 19, \frac{1}{2}w^{3} + w^{2} - 4w - 9]$ $-e^{2} + 10$
19 $[19, 19, \frac{1}{2}w^{3} - w^{2} - 4w + 9]$ $\phantom{-}\frac{1}{16}e^{6} - \frac{25}{16}e^{4} + \frac{191}{16}e^{2} - 30$
19 $[19, 19, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 4w - 5]$ $-\frac{3}{80}e^{7} + \frac{83}{80}e^{5} - \frac{693}{80}e^{3} + \frac{45}{2}e$
25 $[25, 5, \frac{1}{2}w^{2} - 1]$ $\phantom{-}\frac{1}{16}e^{6} - \frac{25}{16}e^{4} + \frac{175}{16}e^{2} - 19$
29 $[29, 29, \frac{1}{2}w^{3} - 4w - 1]$ $-\frac{7}{160}e^{7} + \frac{207}{160}e^{5} - \frac{1817}{160}e^{3} + 26e$
29 $[29, 29, -\frac{1}{2}w^{3} + 4w - 1]$ $-\frac{9}{160}e^{7} + \frac{249}{160}e^{5} - \frac{1999}{160}e^{3} + \frac{105}{4}e$
31 $[31, 31, -w - 1]$ $-\frac{13}{160}e^{7} + \frac{373}{160}e^{5} - \frac{3203}{160}e^{3} + \frac{95}{2}e$
31 $[31, 31, w - 1]$ $-\frac{13}{320}e^{7} + \frac{373}{320}e^{5} - \frac{3043}{320}e^{3} + \frac{73}{4}e$
41 $[41, 41, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 4w - 2]$ $\phantom{-}\frac{1}{320}e^{7} - \frac{41}{320}e^{5} + \frac{591}{320}e^{3} - \frac{31}{4}e$
41 $[41, 41, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 2]$ $-\frac{1}{40}e^{7} + \frac{31}{40}e^{5} - \frac{301}{40}e^{3} + \frac{85}{4}e$
49 $[49, 7, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 5w - 7]$ $\phantom{-}\frac{1}{32}e^{7} - \frac{25}{32}e^{5} + \frac{191}{32}e^{3} - 16e$
49 $[49, 7, \frac{3}{2}w^{3} - \frac{7}{2}w^{2} - 13w + 29]$ $-\frac{3}{40}e^{7} + \frac{83}{40}e^{5} - \frac{693}{40}e^{3} + 43e$
59 $[59, 59, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + 3w + 10]$ $\phantom{-}\frac{1}{8}e^{6} - \frac{25}{8}e^{4} + \frac{167}{8}e^{2} - 30$
59 $[59, 59, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 3w + 10]$ $\phantom{-}\frac{3}{16}e^{6} - \frac{75}{16}e^{4} + \frac{541}{16}e^{2} - 70$
61 $[61, 61, \frac{1}{2}w^{2} + w - 6]$ $\phantom{-}\frac{5}{16}e^{6} - \frac{141}{16}e^{4} + \frac{1195}{16}e^{2} - 177$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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