Properties

Label 3.3.1957.1-11.1-e
Base field 3.3.1957.1
Weight $[2, 2, 2]$
Level norm $11$
Level $[11, 11, 10w + 4]$
Dimension $23$
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: $[11, 11, 10w + 4]$
Dimension: $23$
CM: no
Base change: no
Newspace dimension: $96$

Hecke eigenvalues ($q$-expansion)

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

\(x^{23} + 5x^{22} - 25x^{21} - 154x^{20} + 220x^{19} + 1974x^{18} - 581x^{17} - 13738x^{16} - 2875x^{15} + 57073x^{14} + 24849x^{13} - 147450x^{12} - 73137x^{11} + 239696x^{10} + 105872x^{9} - 239245x^{8} - 75281x^{7} + 134150x^{6} + 23440x^{5} - 34254x^{4} - 3842x^{3} + 3190x^{2} + 219x - 87\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w^{2}]$ $\phantom{-}e$
4 $[4, 2, w^{2} + w + 1]$ $...$
5 $[5, 5, w]$ $...$
11 $[11, 11, 10w + 4]$ $-1$
13 $[13, 13, 12w^{2} + w + 7]$ $...$
17 $[17, 17, w + 1]$ $...$
17 $[17, 17, 16w^{2} + 16]$ $...$
17 $[17, 17, 16w^{2} + 16w + 8]$ $...$
19 $[19, 19, 18w^{2} + 18w + 1]$ $...$
19 $[19, 19, -w^{2} + 7]$ $...$
25 $[25, 5, 4w^{2} + w + 4]$ $...$
27 $[27, 3, -3]$ $...$
29 $[29, 29, w + 7]$ $...$
41 $[41, 41, 40w^{2} + 18]$ $...$
43 $[43, 43, w^{2} - 11]$ $...$
47 $[47, 47, 2w^{2} + 2w - 13]$ $...$
59 $[59, 59, w^{2} - 3]$ $...$
73 $[73, 73, w^{2} + 2w - 1]$ $...$
79 $[79, 79, w^{2} + 37]$ $...$
97 $[97, 97, w^{2} + 2w - 7]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$11$ $[11, 11, 10w + 4]$ $1$