Properties

Label 4.4.7600.1-25.1-c
Base field 4.4.7600.1
Weight $[2, 2, 2, 2]$
Level norm $25$
Level $[25, 5, 2w^{2} - 9]$
Dimension $10$
CM no
Base change yes

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Base field 4.4.7600.1

Generator \(w\), with minimal polynomial \(x^{4} - 9x^{2} + 19\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[25, 5, 2w^{2} - 9]$
Dimension: $10$
CM: no
Base change: yes
Newspace dimension: $16$

Hecke eigenvalues ($q$-expansion)

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

\(x^{10} - 38x^{8} + 469x^{6} - 2056x^{4} + 3008x^{2} - 512\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -w^{3} + w^{2} + 5w - 6]$ $\phantom{-}e$
9 $[9, 3, -w^{2} - w + 4]$ $-\frac{9}{832}e^{9} + \frac{11}{32}e^{7} - \frac{2765}{832}e^{5} + \frac{503}{52}e^{3} - \frac{181}{26}e$
9 $[9, 3, w^{2} - w - 4]$ $-\frac{9}{832}e^{9} + \frac{11}{32}e^{7} - \frac{2765}{832}e^{5} + \frac{503}{52}e^{3} - \frac{181}{26}e$
11 $[11, 11, w + 1]$ $-\frac{1}{208}e^{9} + \frac{3}{16}e^{7} - \frac{443}{208}e^{5} + \frac{1277}{208}e^{3} - \frac{105}{26}e$
11 $[11, 11, w - 1]$ $-\frac{1}{208}e^{9} + \frac{3}{16}e^{7} - \frac{443}{208}e^{5} + \frac{1277}{208}e^{3} - \frac{105}{26}e$
19 $[19, 19, -w]$ $\phantom{-}\frac{1}{832}e^{9} + \frac{1}{32}e^{7} - \frac{1195}{832}e^{5} + \frac{1207}{104}e^{3} - \frac{281}{13}e$
19 $[19, 19, -w^{2} - w + 6]$ $-\frac{3}{416}e^{8} + \frac{5}{16}e^{6} - \frac{1615}{416}e^{4} + \frac{643}{52}e^{2} - \frac{56}{13}$
19 $[19, 19, -w^{2} + w + 6]$ $-\frac{3}{416}e^{8} + \frac{5}{16}e^{6} - \frac{1615}{416}e^{4} + \frac{643}{52}e^{2} - \frac{56}{13}$
25 $[25, 5, 2w^{2} - 9]$ $-1$
29 $[29, 29, -w^{3} + 4w + 2]$ $\phantom{-}\frac{7}{416}e^{8} - \frac{5}{16}e^{6} + \frac{371}{416}e^{4} - \frac{23}{13}e^{2} + \frac{70}{13}$
29 $[29, 29, -w^{3} + 4w - 2]$ $\phantom{-}\frac{7}{416}e^{8} - \frac{5}{16}e^{6} + \frac{371}{416}e^{4} - \frac{23}{13}e^{2} + \frac{70}{13}$
41 $[41, 41, 2w^{2} - w - 7]$ $\phantom{-}\frac{7}{832}e^{9} - \frac{11}{32}e^{7} + \frac{3595}{832}e^{5} - \frac{3551}{208}e^{3} + \frac{269}{13}e$
41 $[41, 41, w^{3} - w^{2} - 6w + 4]$ $\phantom{-}\frac{7}{832}e^{9} - \frac{11}{32}e^{7} + \frac{3595}{832}e^{5} - \frac{3551}{208}e^{3} + \frac{269}{13}e$
61 $[61, 61, -w^{3} + 3w^{2} + 6w - 14]$ $-\frac{3}{416}e^{9} + \frac{1}{4}e^{7} - \frac{1043}{416}e^{5} + \frac{1155}{208}e^{3} - \frac{17}{13}e$
61 $[61, 61, w^{3} + 2w^{2} - 5w - 8]$ $\phantom{-}\frac{1}{52}e^{9} - \frac{11}{16}e^{7} + \frac{795}{104}e^{5} - \frac{5459}{208}e^{3} + \frac{275}{13}e$
61 $[61, 61, -w^{3} + 2w^{2} + 5w - 8]$ $\phantom{-}\frac{1}{52}e^{9} - \frac{11}{16}e^{7} + \frac{795}{104}e^{5} - \frac{5459}{208}e^{3} + \frac{275}{13}e$
61 $[61, 61, w^{3} + 3w^{2} - 6w - 14]$ $-\frac{3}{416}e^{9} + \frac{1}{4}e^{7} - \frac{1043}{416}e^{5} + \frac{1155}{208}e^{3} - \frac{17}{13}e$
89 $[89, 89, -w^{3} + w^{2} + 6w - 9]$ $-\frac{7}{416}e^{8} + \frac{5}{16}e^{6} - \frac{163}{416}e^{4} - \frac{175}{26}e^{2} + \frac{190}{13}$
89 $[89, 89, 2w^{3} - w^{2} - 10w + 10]$ $-\frac{7}{416}e^{8} + \frac{5}{16}e^{6} - \frac{163}{416}e^{4} - \frac{175}{26}e^{2} + \frac{190}{13}$
109 $[109, 109, -w^{3} + 5w^{2} + 7w - 23]$ $\phantom{-}\frac{1}{208}e^{9} - \frac{1}{4}e^{7} + \frac{625}{208}e^{5} - \frac{359}{104}e^{3} - \frac{415}{26}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$25$ $[25, 5, 2w^{2} - 9]$ $1$