Properties

Label 2.2.389.1-4.1-a
Base field \(\Q(\sqrt{389}) \)
Weight $[2, 2]$
Level norm $4$
Level $[4, 2, 2]$
Dimension $6$
CM no
Base change no

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Base field \(\Q(\sqrt{389}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 97\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2]$
Level: $[4, 2, 2]$
Dimension: $6$
CM: no
Base change: no
Newspace dimension: $36$

Hecke eigenvalues ($q$-expansion)

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

\(x^{6} - 3x^{5} - 18x^{4} + 41x^{3} + 90x^{2} - 111x - 163\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, 2]$ $-1$
5 $[5, 5, -3w - 28]$ $-e + 1$
5 $[5, 5, -3w + 31]$ $\phantom{-}e$
7 $[7, 7, -w - 9]$ $-\frac{1}{6}e^{5} + \frac{1}{2}e^{4} + \frac{7}{3}e^{3} - \frac{11}{2}e^{2} - \frac{29}{6}e + \frac{26}{3}$
7 $[7, 7, -w + 10]$ $\phantom{-}\frac{1}{6}e^{5} - \frac{1}{3}e^{4} - \frac{8}{3}e^{3} + \frac{17}{6}e^{2} + \frac{23}{3}e + 1$
9 $[9, 3, 3]$ $-\frac{1}{12}e^{4} + \frac{1}{6}e^{3} + \frac{19}{12}e^{2} - \frac{5}{3}e - \frac{103}{12}$
11 $[11, 11, -2w - 19]$ $-\frac{1}{12}e^{5} + \frac{1}{6}e^{4} + \frac{19}{12}e^{3} - \frac{5}{3}e^{2} - \frac{79}{12}e + 2$
11 $[11, 11, 2w - 21]$ $\phantom{-}\frac{1}{12}e^{5} - \frac{1}{4}e^{4} - \frac{17}{12}e^{3} + \frac{13}{4}e^{2} + \frac{59}{12}e - \frac{55}{12}$
13 $[13, 13, w - 11]$ $-\frac{1}{12}e^{5} + \frac{23}{12}e^{3} + e^{2} - \frac{113}{12}e - \frac{20}{3}$
13 $[13, 13, -w - 10]$ $\phantom{-}\frac{1}{12}e^{5} - \frac{5}{12}e^{4} - \frac{13}{12}e^{3} + \frac{71}{12}e^{2} + \frac{25}{12}e - \frac{53}{4}$
17 $[17, 17, -8w - 75]$ $\phantom{-}\frac{1}{12}e^{5} - \frac{5}{12}e^{4} - \frac{13}{12}e^{3} + \frac{71}{12}e^{2} + \frac{25}{12}e - \frac{49}{4}$
17 $[17, 17, -8w + 83]$ $-\frac{1}{12}e^{5} + \frac{23}{12}e^{3} + e^{2} - \frac{113}{12}e - \frac{17}{3}$
19 $[19, 19, -5w + 52]$ $\phantom{-}\frac{1}{4}e^{4} - \frac{1}{2}e^{3} - \frac{17}{4}e^{2} + \frac{11}{2}e + \frac{57}{4}$
19 $[19, 19, 5w + 47]$ $\phantom{-}\frac{1}{4}e^{4} - \frac{1}{2}e^{3} - \frac{17}{4}e^{2} + \frac{7}{2}e + \frac{61}{4}$
41 $[41, 41, -w - 7]$ $\phantom{-}\frac{1}{4}e^{5} - \frac{1}{2}e^{4} - \frac{15}{4}e^{3} + 4e^{2} + \frac{35}{4}e + 4$
41 $[41, 41, w - 8]$ $-\frac{1}{4}e^{5} + \frac{3}{4}e^{4} + \frac{13}{4}e^{3} - \frac{31}{4}e^{2} - \frac{19}{4}e + \frac{51}{4}$
59 $[59, 59, -w - 12]$ $-\frac{1}{6}e^{5} + \frac{23}{6}e^{3} + \frac{5}{2}e^{2} - \frac{55}{3}e - \frac{95}{6}$
59 $[59, 59, w - 13]$ $\phantom{-}\frac{1}{6}e^{5} - \frac{5}{6}e^{4} - \frac{13}{6}e^{3} + \frac{37}{3}e^{2} + \frac{8}{3}e - 28$
67 $[67, 67, -w - 5]$ $\phantom{-}\frac{1}{6}e^{5} + \frac{1}{6}e^{4} - \frac{25}{6}e^{3} - \frac{25}{6}e^{2} + \frac{121}{6}e + \frac{33}{2}$
67 $[67, 67, w - 6]$ $-\frac{1}{6}e^{5} + e^{4} + \frac{11}{6}e^{3} - 14e^{2} - \frac{5}{6}e + \frac{86}{3}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, 2]$ $1$