Properties

Label 4.4.16609.1-16.1-e
Base field 4.4.16609.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 2, 2]$
Dimension $7$
CM no
Base change no

Related objects

Downloads

Learn more about

Base field 4.4.16609.1

Generator \(w\), with minimal polynomial \(x^{4} - 7x^{2} - x + 9\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[16, 2, 2]$
Dimension: $7$
CM: no
Base change: no
Newspace dimension: $23$

Hecke eigenvalues ($q$-expansion)

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

\(x^{7} + x^{6} - 18x^{5} - 17x^{4} + 78x^{3} + 72x^{2} - 20x - 16\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w^{2} + w + 4]$ $-1$
3 $[3, 3, -w^{2} + w + 3]$ $\phantom{-}e$
5 $[5, 5, w^{2} - 4]$ $\phantom{-}\frac{1}{60}e^{6} - \frac{7}{60}e^{5} - \frac{11}{30}e^{4} + \frac{33}{20}e^{3} + \frac{21}{10}e^{2} - \frac{23}{5}e - \frac{23}{15}$
8 $[8, 2, w^{3} - w^{2} - 4w + 5]$ $-1$
17 $[17, 17, -w^{2} + w + 5]$ $-\frac{17}{60}e^{6} - \frac{1}{60}e^{5} + \frac{157}{30}e^{4} - \frac{1}{20}e^{3} - \frac{237}{10}e^{2} + \frac{1}{5}e + \frac{151}{15}$
27 $[27, 3, -w^{3} + 4w - 2]$ $-\frac{4}{15}e^{6} - \frac{2}{15}e^{5} + \frac{73}{15}e^{4} + \frac{13}{5}e^{3} - \frac{108}{5}e^{2} - \frac{62}{5}e + \frac{68}{15}$
29 $[29, 29, -w^{2} + w + 1]$ $\phantom{-}\frac{1}{4}e^{6} + \frac{1}{4}e^{5} - \frac{9}{2}e^{4} - \frac{17}{4}e^{3} + \frac{39}{2}e^{2} + 18e - 3$
29 $[29, 29, -w^{3} + 4w + 2]$ $\phantom{-}\frac{1}{4}e^{6} + \frac{1}{4}e^{5} - \frac{9}{2}e^{4} - \frac{17}{4}e^{3} + \frac{39}{2}e^{2} + 16e - 7$
37 $[37, 37, -2w^{3} + 3w^{2} + 9w - 13]$ $\phantom{-}\frac{17}{60}e^{6} + \frac{1}{60}e^{5} - \frac{157}{30}e^{4} - \frac{19}{20}e^{3} + \frac{237}{10}e^{2} + \frac{44}{5}e - \frac{151}{15}$
41 $[41, 41, w^{3} - w^{2} - 5w + 2]$ $\phantom{-}\frac{3}{20}e^{6} - \frac{1}{20}e^{5} - \frac{23}{10}e^{4} + \frac{17}{20}e^{3} + \frac{69}{10}e^{2} - \frac{17}{5}e + \frac{11}{5}$
43 $[43, 43, -w^{3} + w^{2} + 3w - 4]$ $-\frac{4}{15}e^{6} - \frac{2}{15}e^{5} + \frac{73}{15}e^{4} + \frac{8}{5}e^{3} - \frac{108}{5}e^{2} - \frac{12}{5}e + \frac{128}{15}$
61 $[61, 61, w^{2} - 2w - 2]$ $-\frac{1}{4}e^{6} - \frac{1}{4}e^{5} + \frac{9}{2}e^{4} + \frac{17}{4}e^{3} - \frac{39}{2}e^{2} - 16e + 3$
61 $[61, 61, 2w^{2} - w - 8]$ $\phantom{-}\frac{23}{60}e^{6} + \frac{19}{60}e^{5} - \frac{193}{30}e^{4} - \frac{101}{20}e^{3} + \frac{253}{10}e^{2} + \frac{96}{5}e - \frac{109}{15}$
67 $[67, 67, -4w^{3} + 5w^{2} + 18w - 22]$ $\phantom{-}\frac{4}{15}e^{6} + \frac{2}{15}e^{5} - \frac{73}{15}e^{4} - \frac{13}{5}e^{3} + \frac{103}{5}e^{2} + \frac{77}{5}e - \frac{8}{15}$
73 $[73, 73, -w^{2} - 2w + 2]$ $\phantom{-}\frac{1}{4}e^{6} + \frac{1}{4}e^{5} - \frac{9}{2}e^{4} - \frac{17}{4}e^{3} + \frac{37}{2}e^{2} + 16e + 5$
79 $[79, 79, w^{2} - 2w - 4]$ $\phantom{-}\frac{2}{3}e^{6} + \frac{1}{3}e^{5} - \frac{38}{3}e^{4} - 5e^{3} + 59e^{2} + 19e - \frac{52}{3}$
89 $[89, 89, w^{2} + w - 5]$ $-\frac{1}{60}e^{6} + \frac{7}{60}e^{5} + \frac{11}{30}e^{4} - \frac{33}{20}e^{3} - \frac{31}{10}e^{2} + \frac{33}{5}e + \frac{143}{15}$
89 $[89, 89, 2w^{3} - 2w^{2} - 9w + 8]$ $-\frac{11}{20}e^{6} - \frac{3}{20}e^{5} + \frac{101}{10}e^{4} + \frac{51}{20}e^{3} - \frac{453}{10}e^{2} - \frac{56}{5}e + \frac{93}{5}$
89 $[89, 89, w^{3} - 5w - 5]$ $-\frac{11}{12}e^{6} - \frac{7}{12}e^{5} + \frac{97}{6}e^{4} + \frac{33}{4}e^{3} - \frac{135}{2}e^{2} - 28e + \frac{49}{3}$
89 $[89, 89, -w^{3} + 2w^{2} + 4w - 4]$ $-\frac{13}{20}e^{6} - \frac{9}{20}e^{5} + \frac{113}{10}e^{4} + \frac{133}{20}e^{3} - \frac{449}{10}e^{2} - \frac{118}{5}e + \frac{19}{5}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w^{2} + w + 4]$ $1$
$8$ $[8, 2, w^{3} - w^{2} - 4w + 5]$ $1$