Properties

Label 2.2.344.1-10.1-g
Base field \(\Q(\sqrt{86}) \)
Weight $[2, 2]$
Level norm $10$
Level $[10, 10, 3w - 28]$
Dimension $16$
CM no
Base change no

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Base field \(\Q(\sqrt{86}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 86\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2]$
Level: $[10, 10, 3w - 28]$
Dimension: $16$
CM: no
Base change: no
Newspace dimension: $56$

Hecke eigenvalues ($q$-expansion)

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

\(x^{16} - 53x^{14} - 7x^{13} + 1088x^{12} + 240x^{11} - 11161x^{10} - 2572x^{9} + 61898x^{8} + 9997x^{7} - 185824x^{6} - 4660x^{5} + 277360x^{4} - 43720x^{3} - 151305x^{2} + 53514x - 4212\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -11w + 102]$ $-1$
5 $[5, 5, w - 9]$ $\phantom{-}e$
5 $[5, 5, w + 9]$ $-1$
7 $[7, 7, 4w - 37]$ $...$
7 $[7, 7, 4w + 37]$ $...$
9 $[9, 3, 3]$ $...$
11 $[11, 11, 7w + 65]$ $...$
11 $[11, 11, -7w + 65]$ $...$
17 $[17, 17, -2w - 19]$ $...$
17 $[17, 17, 2w - 19]$ $...$
29 $[29, 29, -15w + 139]$ $...$
29 $[29, 29, -15w - 139]$ $...$
37 $[37, 37, -w - 7]$ $...$
37 $[37, 37, w - 7]$ $...$
41 $[41, 41, -40w + 371]$ $...$
41 $[41, 41, 62w - 575]$ $...$
43 $[43, 43, -51w + 473]$ $...$
59 $[59, 59, -5w + 47]$ $...$
59 $[59, 59, 5w + 47]$ $...$
61 $[61, 61, -w - 5]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -11w + 102]$ $1$
$5$ $[5, 5, w + 9]$ $1$