Properties

Label 4.4.19525.1-9.2-c
Base field 4.4.19525.1
Weight $[2, 2, 2, 2]$
Level norm $9$
Level $[9,3,w + 2]$
Dimension $8$
CM no
Base change no

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Base field 4.4.19525.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 14x^{2} + 15x + 45\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[9,3,w + 2]$
Dimension: $8$
CM: no
Base change: no
Newspace dimension: $14$

Hecke eigenvalues ($q$-expansion)

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

\(x^{8} - 30x^{6} + 236x^{4} - 584x^{2} + 256\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, \frac{2}{3}w^{2} + \frac{1}{3}w - 5]$ $-\frac{9}{352}e^{7} + \frac{125}{176}e^{5} - \frac{397}{88}e^{3} + \frac{277}{44}e$
5 $[5, 5, \frac{2}{3}w^{2} - \frac{5}{3}w - 4]$ $\phantom{-}e$
9 $[9, 3, -w + 3]$ $\phantom{-}\frac{9}{176}e^{6} - \frac{57}{44}e^{4} + \frac{265}{44}e^{2} - \frac{34}{11}$
9 $[9, 3, w + 2]$ $-1$
11 $[11, 11, \frac{2}{3}w^{2} + \frac{1}{3}w - 4]$ $\phantom{-}e$
16 $[16, 2, 2]$ $\phantom{-}\frac{9}{176}e^{6} - \frac{57}{44}e^{4} + \frac{265}{44}e^{2} - \frac{23}{11}$
19 $[19, 19, \frac{1}{3}w^{3} - \frac{10}{3}w - 3]$ $\phantom{-}\frac{9}{352}e^{7} - \frac{125}{176}e^{5} + \frac{419}{88}e^{3} - \frac{475}{44}e$
19 $[19, 19, \frac{1}{3}w^{3} - w^{2} - \frac{7}{3}w + 6]$ $-\frac{1}{44}e^{7} + \frac{29}{44}e^{5} - \frac{207}{44}e^{3} + \frac{205}{22}e$
29 $[29, 29, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{8}{3}w - 2]$ $-\frac{5}{352}e^{7} + \frac{89}{176}e^{5} - \frac{443}{88}e^{3} + \frac{567}{44}e$
29 $[29, 29, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ $-\frac{1}{88}e^{7} + \frac{29}{88}e^{5} - \frac{109}{44}e^{3} + \frac{54}{11}e$
31 $[31, 31, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w + 1]$ $-\frac{7}{352}e^{7} + \frac{85}{176}e^{5} - \frac{189}{88}e^{3} + \frac{103}{44}e$
31 $[31, 31, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{8}{3}w - 4]$ $-\frac{13}{176}e^{7} + \frac{183}{88}e^{5} - \frac{151}{11}e^{3} + \frac{230}{11}e$
49 $[49, 7, \frac{1}{3}w^{3} - \frac{10}{3}w - 1]$ $\phantom{-}\frac{7}{176}e^{7} - \frac{12}{11}e^{5} + \frac{299}{44}e^{3} - \frac{123}{11}e$
49 $[49, 7, -\frac{1}{3}w^{3} + w^{2} + \frac{7}{3}w - 4]$ $\phantom{-}\frac{3}{176}e^{7} - \frac{19}{44}e^{5} + \frac{81}{44}e^{3} + \frac{40}{11}e$
59 $[59, 59, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{5}{3}w - 11]$ $-\frac{1}{88}e^{6} + \frac{9}{44}e^{4} + \frac{14}{11}e^{2} - \frac{100}{11}$
59 $[59, 59, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 5w - 13]$ $-\frac{5}{88}e^{6} + \frac{14}{11}e^{4} - \frac{91}{22}e^{2} + \frac{6}{11}$
61 $[61, 61, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{2}{3}w - 9]$ $-\frac{3}{88}e^{6} + \frac{49}{44}e^{4} - \frac{101}{11}e^{2} + \frac{140}{11}$
61 $[61, 61, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 4w + 2]$ $-\frac{1}{44}e^{7} + \frac{9}{22}e^{5} + \frac{17}{11}e^{3} - \frac{200}{11}e$
61 $[61, 61, \frac{2}{3}w^{2} - \frac{5}{3}w - 1]$ $\phantom{-}\frac{7}{176}e^{7} - \frac{85}{88}e^{5} + \frac{167}{44}e^{3} + \frac{73}{22}e$
61 $[61, 61, -\frac{1}{3}w^{2} + \frac{4}{3}w + 6]$ $-\frac{1}{44}e^{6} + \frac{29}{44}e^{4} - \frac{109}{22}e^{2} + \frac{174}{11}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$9$ $[9,3,w + 2]$ $1$