Properties

Label 3.3.1304.1-11.1-d
Base field 3.3.1304.1
Weight $[2, 2, 2]$
Level norm $11$
Level $[11, 11, 2w^{2} - 21]$
Dimension $21$
CM no
Base change no

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Base field 3.3.1304.1

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

Form

Weight: $[2, 2, 2]$
Level: $[11, 11, 2w^{2} - 21]$
Dimension: $21$
CM: no
Base change: no
Newspace dimension: $35$

Hecke eigenvalues ($q$-expansion)

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

\(x^{21} - 4x^{20} - 26x^{19} + 117x^{18} + 262x^{17} - 1424x^{16} - 1207x^{15} + 9346x^{14} + 1647x^{13} - 35805x^{12} + 7253x^{11} + 80968x^{10} - 34722x^{9} - 104417x^{8} + 58458x^{7} + 70925x^{6} - 44286x^{5} - 21774x^{4} + 14244x^{3} + 1676x^{2} - 1344x + 128\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w]$ $\phantom{-}e$
2 $[2, 2, -\frac{1}{2}w^{2} + \frac{3}{2}w]$ $...$
3 $[3, 3, -w^{2} + 3w + 1]$ $...$
9 $[9, 3, w^{2} + w - 7]$ $...$
11 $[11, 11, 2w^{2} - 21]$ $\phantom{-}1$
17 $[17, 17, -\frac{1}{2}w^{2} + \frac{5}{2}w]$ $...$
19 $[19, 19, -\frac{1}{2}w^{2} + \frac{1}{2}w + 2]$ $...$
37 $[37, 37, w^{2} - w - 13]$ $...$
37 $[37, 37, -\frac{1}{2}w^{2} + \frac{1}{2}w + 8]$ $...$
37 $[37, 37, \frac{5}{2}w^{2} - \frac{17}{2}w - 2]$ $...$
47 $[47, 47, -\frac{3}{2}w^{2} + \frac{11}{2}w]$ $...$
53 $[53, 53, w^{2} - w - 7]$ $...$
59 $[59, 59, 2w - 1]$ $...$
61 $[61, 61, -\frac{3}{2}w^{2} + \frac{3}{2}w + 20]$ $...$
67 $[67, 67, w^{2} - 3w - 3]$ $...$
71 $[71, 71, w^{2} - w - 1]$ $...$
73 $[73, 73, 3w^{2} - w - 33]$ $...$
79 $[79, 79, w^{2} - w - 11]$ $...$
79 $[79, 79, w^{2} - 3w + 1]$ $...$
79 $[79, 79, -2w - 5]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$11$ $[11, 11, 2w^{2} - 21]$ $-1$