Properties

Label 3.3.1556.1-11.1-e
Base field 3.3.1556.1
Weight $[2, 2, 2]$
Level norm $11$
Level $[11, 11, w]$
Dimension $6$
CM no
Base change no

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Base field 3.3.1556.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x + 11\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[11, 11, w]$
Dimension: $6$
CM: no
Base change: no
Newspace dimension: $34$

Hecke eigenvalues ($q$-expansion)

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

\(x^{6} + 6x^{5} + x^{4} - 40x^{3} - 53x^{2} - 14x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w - 1]$ $\phantom{-}\frac{6}{5}e^{5} + \frac{69}{10}e^{4} - \frac{2}{5}e^{3} - \frac{237}{5}e^{2} - 52e - \frac{73}{10}$
3 $[3, 3, w - 2]$ $-\frac{6}{5}e^{5} - \frac{69}{10}e^{4} + \frac{2}{5}e^{3} + \frac{237}{5}e^{2} + 53e + \frac{73}{10}$
9 $[9, 3, w^{2} + w - 7]$ $-\frac{1}{10}e^{5} - \frac{7}{10}e^{4} - \frac{4}{5}e^{3} + \frac{21}{5}e^{2} + \frac{21}{2}e + \frac{29}{10}$
11 $[11, 11, w]$ $-1$
11 $[11, 11, -2w + 3]$ $\phantom{-}\frac{8}{5}e^{5} + \frac{46}{5}e^{4} - \frac{7}{10}e^{3} - \frac{637}{10}e^{2} - \frac{139}{2}e - \frac{79}{10}$
11 $[11, 11, -w^{2} + 3w - 1]$ $\phantom{-}\frac{21}{10}e^{5} + \frac{61}{5}e^{4} + \frac{3}{10}e^{3} - \frac{827}{10}e^{2} - 100e - \frac{169}{10}$
17 $[17, 17, w + 2]$ $\phantom{-}\frac{9}{5}e^{5} + \frac{53}{5}e^{4} + \frac{2}{5}e^{3} - \frac{363}{5}e^{2} - 85e - \frac{56}{5}$
17 $[17, 17, -2w + 5]$ $\phantom{-}\frac{1}{5}e^{5} + \frac{7}{5}e^{4} + \frac{11}{10}e^{3} - \frac{99}{10}e^{2} - \frac{35}{2}e - \frac{3}{10}$
17 $[17, 17, -w^{2} - w + 5]$ $-\frac{13}{10}e^{5} - \frac{38}{5}e^{4} + \frac{1}{10}e^{3} + \frac{531}{10}e^{2} + 60e + \frac{47}{10}$
23 $[23, 23, w - 4]$ $-3e^{5} - 18e^{4} - 2e^{3} + 123e^{2} + 151e + 25$
29 $[29, 29, w^{2} - 6]$ $\phantom{-}\frac{1}{10}e^{5} + \frac{7}{10}e^{4} + \frac{3}{10}e^{3} - \frac{57}{10}e^{2} - 7e + \frac{13}{5}$
31 $[31, 31, w^{2} - w - 1]$ $-\frac{7}{5}e^{5} - \frac{83}{10}e^{4} - \frac{1}{5}e^{3} + \frac{294}{5}e^{2} + 67e + \frac{21}{10}$
37 $[37, 37, -w^{2} - 2w + 6]$ $-\frac{43}{10}e^{5} - \frac{123}{5}e^{4} + \frac{8}{5}e^{3} + \frac{838}{5}e^{2} + \frac{377}{2}e + \frac{156}{5}$
43 $[43, 43, w^{2} - 3w + 3]$ $-\frac{18}{5}e^{5} - \frac{217}{10}e^{4} - \frac{14}{5}e^{3} + \frac{741}{5}e^{2} + 184e + \frac{259}{10}$
47 $[47, 47, 3w^{2} - 28]$ $-\frac{3}{5}e^{5} - \frac{27}{10}e^{4} + \frac{16}{5}e^{3} + \frac{96}{5}e^{2} + 5e - \frac{81}{10}$
53 $[53, 53, w^{2} - w - 3]$ $\phantom{-}\frac{16}{5}e^{5} + \frac{92}{5}e^{4} - \frac{9}{10}e^{3} - \frac{1259}{10}e^{2} - \frac{285}{2}e - \frac{213}{10}$
61 $[61, 61, -5w + 6]$ $\phantom{-}\frac{9}{5}e^{5} + \frac{111}{10}e^{4} + \frac{12}{5}e^{3} - \frac{378}{5}e^{2} - 99e - \frac{147}{10}$
71 $[71, 71, w^{2} - w - 7]$ $\phantom{-}\frac{6}{5}e^{5} + \frac{69}{10}e^{4} - \frac{2}{5}e^{3} - \frac{237}{5}e^{2} - 52e - \frac{143}{10}$
83 $[83, 83, -2w^{2} - w + 14]$ $-6e^{5} - 35e^{4} - \frac{1}{2}e^{3} + \frac{481}{2}e^{2} + \frac{567}{2}e + \frac{73}{2}$
89 $[89, 89, w^{2} + 3w - 3]$ $\phantom{-}\frac{3}{5}e^{5} + \frac{47}{10}e^{4} + \frac{24}{5}e^{3} - \frac{156}{5}e^{2} - 61e - \frac{239}{10}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$11$ $[11, 11, w]$ $1$