Properties

Label 3.3.1929.1-13.1-a
Base field 3.3.1929.1
Weight $[2, 2, 2]$
Level norm $13$
Level $[13, 13, -w]$
Dimension $22$
CM no
Base change no

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Base field 3.3.1929.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 10x + 13\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[13, 13, -w]$
Dimension: $22$
CM: no
Base change: no
Newspace dimension: $44$

Hecke eigenvalues ($q$-expansion)

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

\(x^{22} + 4x^{21} - 32x^{20} - 142x^{19} + 400x^{18} + 2096x^{17} - 2383x^{16} - 16836x^{15} + 5530x^{14} + 80630x^{13} + 10902x^{12} - 235904x^{11} - 101418x^{10} + 411310x^{9} + 260130x^{8} - 388892x^{7} - 305939x^{6} + 149634x^{5} + 141979x^{4} + 3172x^{3} - 3849x^{2} + 170x + 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w - 2]$ $\phantom{-}e$
3 $[3, 3, w - 1]$ $...$
7 $[7, 7, w^{2} + w - 7]$ $...$
7 $[7, 7, -w^{2} + 11]$ $...$
7 $[7, 7, -w^{2} + 9]$ $...$
8 $[8, 2, 2]$ $...$
13 $[13, 13, -w]$ $\phantom{-}1$
19 $[19, 19, -w^{2} - w + 4]$ $...$
23 $[23, 23, w^{2} + w - 10]$ $...$
29 $[29, 29, 2w^{2} - 21]$ $...$
37 $[37, 37, 2w^{2} + w - 17]$ $...$
43 $[43, 43, 3w^{2} + 3w - 22]$ $...$
47 $[47, 47, w^{2} - 6]$ $...$
47 $[47, 47, w^{2} - 3]$ $...$
47 $[47, 47, -w^{2} + 12]$ $...$
53 $[53, 53, w^{2} - w - 4]$ $...$
61 $[61, 61, w^{2} - 5]$ $...$
67 $[67, 67, w^{2} - w - 7]$ $...$
73 $[73, 73, 7w^{2} + 3w - 66]$ $...$
79 $[79, 79, 2w^{2} - 19]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13, 13, -w]$ $-1$