Properties

Label 4.4.11197.1-16.1-c
Base field 4.4.11197.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 2, 2]$
Dimension $10$
CM no
Base change no

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Base field 4.4.11197.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[16, 2, 2]$
Dimension: $10$
CM: no
Base change: no
Newspace dimension: $18$

Hecke eigenvalues ($q$-expansion)

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

\(x^{10} - 23x^{8} + 169x^{6} - 469x^{4} + 410x^{2} - 16\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}e$
7 $[7, 7, w^{3} - 2w^{2} - 3w + 1]$ $-\frac{1}{48}e^{9} + \frac{5}{12}e^{7} - \frac{39}{16}e^{5} + \frac{131}{24}e^{3} - \frac{20}{3}e$
11 $[11, 11, -w - 2]$ $\phantom{-}\frac{1}{16}e^{8} - \frac{4}{3}e^{6} + \frac{137}{16}e^{4} - \frac{147}{8}e^{2} + \frac{19}{3}$
11 $[11, 11, -w^{3} + 2w^{2} + 3w - 2]$ $-\frac{1}{24}e^{9} + e^{7} - \frac{63}{8}e^{5} + \frac{293}{12}e^{3} - 26e$
13 $[13, 13, -w^{2} + 2w + 2]$ $\phantom{-}\frac{1}{12}e^{7} - \frac{7}{4}e^{5} + \frac{21}{2}e^{3} - \frac{46}{3}e$
16 $[16, 2, 2]$ $-1$
19 $[19, 19, -w^{3} + 2w^{2} + 4w - 1]$ $-\frac{1}{12}e^{7} + \frac{3}{2}e^{5} - \frac{25}{4}e^{3} + \frac{17}{6}e$
23 $[23, 23, -w^{2} + w + 3]$ $\phantom{-}\frac{1}{12}e^{9} - \frac{11}{6}e^{7} + \frac{25}{2}e^{5} - \frac{373}{12}e^{3} + \frac{137}{6}e$
23 $[23, 23, -w^{2} + 3]$ $-e^{2} + 6$
27 $[27, 3, w^{3} - 3w^{2} - w + 4]$ $\phantom{-}\frac{5}{48}e^{9} - \frac{29}{12}e^{7} + \frac{287}{16}e^{5} - \frac{1201}{24}e^{3} + \frac{265}{6}e$
29 $[29, 29, -w^{3} + 3w^{2} + 3w - 5]$ $\phantom{-}\frac{1}{12}e^{9} - \frac{7}{4}e^{7} + \frac{43}{4}e^{5} - \frac{247}{12}e^{3} + \frac{11}{2}e$
29 $[29, 29, w^{3} - 2w^{2} - 4w]$ $\phantom{-}\frac{1}{12}e^{9} - \frac{7}{4}e^{7} + \frac{43}{4}e^{5} - \frac{247}{12}e^{3} + \frac{11}{2}e$
47 $[47, 47, -w^{3} + 2w^{2} + 3w - 5]$ $-\frac{1}{48}e^{8} + \frac{1}{2}e^{6} - \frac{59}{16}e^{4} + \frac{179}{24}e^{2} + 3$
47 $[47, 47, w^{2} - 3w - 2]$ $-\frac{1}{8}e^{9} + \frac{11}{4}e^{7} - \frac{149}{8}e^{5} + 44e^{3} - \frac{49}{2}e$
61 $[61, 61, -w^{3} + 2w^{2} + 5w - 3]$ $\phantom{-}\frac{5}{48}e^{8} - \frac{9}{4}e^{6} + \frac{227}{16}e^{4} - \frac{643}{24}e^{2} + 13$
67 $[67, 67, -w^{3} + w^{2} + 5w - 1]$ $\phantom{-}\frac{1}{24}e^{8} - \frac{11}{12}e^{6} + \frac{53}{8}e^{4} - \frac{233}{12}e^{2} + \frac{38}{3}$
67 $[67, 67, -2w^{3} + 3w^{2} + 11w - 7]$ $\phantom{-}0$
83 $[83, 83, -2w + 3]$ $-\frac{1}{6}e^{8} + \frac{10}{3}e^{6} - \frac{37}{2}e^{4} + \frac{86}{3}e^{2} - \frac{4}{3}$
89 $[89, 89, 3w^{3} - 7w^{2} - 9w + 9]$ $\phantom{-}\frac{1}{4}e^{9} - \frac{17}{3}e^{7} + \frac{161}{4}e^{5} - \frac{207}{2}e^{3} + \frac{239}{3}e$
97 $[97, 97, w^{3} - w^{2} - 4w - 3]$ $\phantom{-}\frac{5}{24}e^{8} - \frac{13}{3}e^{6} + \frac{207}{8}e^{4} - \frac{523}{12}e^{2} + \frac{4}{3}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$16$ $[16, 2, 2]$ $1$