Properties

Label 2.2.328.1-4.1-l
Base field \(\Q(\sqrt{82}) \)
Weight $[2, 2]$
Level norm $4$
Level $[4, 2, 2]$
Dimension $4$
CM no
Base change no

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Base field \(\Q(\sqrt{82}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 82\); narrow class number \(4\) and class number \(4\).

Form

Weight: $[2, 2]$
Level: $[4, 2, 2]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $60$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} + 2x^{3} + 2x^{2} - 12x + 36\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}0$
3 $[3, 3, w + 1]$ $\phantom{-}e$
3 $[3, 3, w + 2]$ $\phantom{-}\frac{1}{6}e^{3} + \frac{1}{3}e^{2} + \frac{1}{3}e - 2$
11 $[11, 11, w + 4]$ $\phantom{-}\frac{1}{42}e^{3} + \frac{4}{21}e^{2} - \frac{17}{21}e + \frac{6}{7}$
11 $[11, 11, w + 7]$ $-\frac{4}{21}e^{3} - \frac{11}{21}e^{2} - \frac{11}{21}e + \frac{22}{7}$
13 $[13, 13, w + 2]$ $\phantom{-}\frac{1}{42}e^{3} + \frac{4}{21}e^{2} + \frac{4}{21}e - \frac{8}{7}$
13 $[13, 13, w + 11]$ $-\frac{1}{42}e^{3} - \frac{4}{21}e^{2} - \frac{4}{21}e - \frac{6}{7}$
19 $[19, 19, w + 5]$ $\phantom{-}\frac{1}{14}e^{3} + \frac{4}{7}e^{2} - \frac{3}{7}e + \frac{18}{7}$
19 $[19, 19, w + 14]$ $-\frac{5}{21}e^{3} - \frac{19}{21}e^{2} - \frac{19}{21}e + \frac{38}{7}$
23 $[23, 23, w + 6]$ $\phantom{-}\frac{1}{21}e^{3} - \frac{13}{21}e^{2} + \frac{8}{21}e - \frac{2}{7}$
23 $[23, 23, w + 17]$ $\phantom{-}\frac{2}{7}e^{3} + \frac{9}{7}e^{2} + \frac{16}{7}e - \frac{12}{7}$
25 $[25, 5, -5]$ $-4$
29 $[29, 29, w + 13]$ $-\frac{5}{21}e^{3} + \frac{2}{21}e^{2} + \frac{2}{21}e - \frac{4}{7}$
29 $[29, 29, w + 16]$ $-\frac{2}{21}e^{3} - \frac{16}{21}e^{2} - \frac{58}{21}e - \frac{24}{7}$
31 $[31, 31, w + 12]$ $\phantom{-}\frac{1}{7}e^{3} + \frac{1}{7}e^{2} + \frac{8}{7}e - \frac{6}{7}$
31 $[31, 31, w + 19]$ $\phantom{-}\frac{4}{21}e^{3} + \frac{11}{21}e^{2} + \frac{32}{21}e - \frac{8}{7}$
41 $[41, 41, w]$ $-\frac{1}{3}e^{3} - \frac{2}{3}e^{2} - \frac{8}{3}e + 2$
49 $[49, 7, -7]$ $-4$
53 $[53, 53, w + 20]$ $\phantom{-}\frac{1}{3}e^{3} + \frac{2}{3}e^{2} + \frac{2}{3}e - 4$
53 $[53, 53, w + 33]$ $\phantom{-}2e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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