Properties

Label 3.3.1957.1-8.1-b
Base field 3.3.1957.1
Weight $[2, 2, 2]$
Level norm $8$
Level $[8, 2, 2]$
Dimension $6$
CM no
Base change no

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Base field 3.3.1957.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x + 10\); narrow class number \(4\) and class number \(2\).

Form

Weight: $[2, 2, 2]$
Level: $[8, 2, 2]$
Dimension: $6$
CM: no
Base change: no
Newspace dimension: $24$

Hecke eigenvalues ($q$-expansion)

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

\(x^{6} + x^{5} - 25x^{4} - 32x^{3} + 110x^{2} + 204x + 72\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w^{2}]$ $-1$
4 $[4, 2, w^{2} + w + 1]$ $\phantom{-}1$
5 $[5, 5, w]$ $\phantom{-}e$
11 $[11, 11, 10w + 4]$ $\phantom{-}\frac{13}{36}e^{5} - \frac{11}{36}e^{4} - \frac{313}{36}e^{3} + \frac{37}{9}e^{2} + \frac{649}{18}e + \frac{37}{3}$
13 $[13, 13, 12w^{2} + w + 7]$ $\phantom{-}\frac{4}{9}e^{5} - \frac{2}{9}e^{4} - \frac{97}{9}e^{3} + \frac{13}{9}e^{2} + \frac{416}{9}e + \frac{82}{3}$
17 $[17, 17, w + 1]$ $-\frac{13}{36}e^{5} + \frac{11}{36}e^{4} + \frac{313}{36}e^{3} - \frac{37}{9}e^{2} - \frac{667}{18}e - \frac{37}{3}$
17 $[17, 17, 16w^{2} + 16]$ $\phantom{-}\frac{7}{36}e^{5} + \frac{1}{36}e^{4} - \frac{181}{36}e^{3} - \frac{37}{18}e^{2} + \frac{445}{18}e + \frac{58}{3}$
17 $[17, 17, 16w^{2} + 16w + 8]$ $-\frac{1}{4}e^{5} + \frac{1}{4}e^{4} + \frac{23}{4}e^{3} - \frac{7}{2}e^{2} - \frac{41}{2}e - 6$
19 $[19, 19, 18w^{2} + 18w + 1]$ $\phantom{-}\frac{13}{36}e^{5} - \frac{11}{36}e^{4} - \frac{313}{36}e^{3} + \frac{37}{9}e^{2} + \frac{649}{18}e + \frac{43}{3}$
19 $[19, 19, -w^{2} + 7]$ $\phantom{-}\frac{25}{36}e^{5} - \frac{17}{36}e^{4} - \frac{595}{36}e^{3} + \frac{107}{18}e^{2} + \frac{1183}{18}e + \frac{82}{3}$
25 $[25, 5, 4w^{2} + w + 4]$ $-\frac{1}{4}e^{5} + \frac{1}{4}e^{4} + \frac{23}{4}e^{3} - \frac{7}{2}e^{2} - \frac{41}{2}e - 4$
27 $[27, 3, -3]$ $\phantom{-}\frac{4}{9}e^{5} - \frac{2}{9}e^{4} - \frac{97}{9}e^{3} + \frac{13}{9}e^{2} + \frac{416}{9}e + \frac{88}{3}$
29 $[29, 29, w + 7]$ $-\frac{4}{9}e^{5} + \frac{2}{9}e^{4} + \frac{97}{9}e^{3} - \frac{22}{9}e^{2} - \frac{407}{9}e - \frac{58}{3}$
41 $[41, 41, 40w^{2} + 18]$ $-\frac{25}{36}e^{5} + \frac{17}{36}e^{4} + \frac{595}{36}e^{3} - \frac{89}{18}e^{2} - \frac{1219}{18}e - \frac{112}{3}$
43 $[43, 43, w^{2} - 11]$ $\phantom{-}\frac{19}{36}e^{5} - \frac{5}{36}e^{4} - \frac{463}{36}e^{3} - \frac{2}{9}e^{2} + \frac{979}{18}e + \frac{103}{3}$
47 $[47, 47, 2w^{2} + 2w - 13]$ $\phantom{-}2e$
59 $[59, 59, w^{2} - 3]$ $\phantom{-}\frac{19}{36}e^{5} - \frac{5}{36}e^{4} - \frac{463}{36}e^{3} - \frac{2}{9}e^{2} + \frac{1015}{18}e + \frac{97}{3}$
73 $[73, 73, w^{2} + 2w - 1]$ $\phantom{-}\frac{5}{12}e^{5} - \frac{1}{12}e^{4} - \frac{119}{12}e^{3} + \frac{1}{6}e^{2} + \frac{233}{6}e + 22$
79 $[79, 79, w^{2} + 37]$ $\phantom{-}\frac{2}{3}e^{5} - \frac{1}{3}e^{4} - \frac{47}{3}e^{3} + \frac{8}{3}e^{2} + \frac{184}{3}e + 34$
97 $[97, 97, w^{2} + 2w - 7]$ $\phantom{-}\frac{25}{36}e^{5} - \frac{17}{36}e^{4} - \frac{595}{36}e^{3} + \frac{89}{18}e^{2} + \frac{1237}{18}e + \frac{118}{3}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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