Properties

Label 2.2.181.1-16.1-b
Base field \(\Q(\sqrt{181}) \)
Weight $[2, 2]$
Level norm $16$
Level $[16, 4, 4]$
Dimension $16$
CM no
Base change no

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Base field \(\Q(\sqrt{181}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 45\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2]$
Level: $[16, 4, 4]$
Dimension: $16$
CM: no
Base change: no
Newspace dimension: $49$

Hecke eigenvalues ($q$-expansion)

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

\(x^{16} - 4x^{15} - 26x^{14} + 112x^{13} + 237x^{12} - 1137x^{11} - 991x^{10} + 5368x^{9} + 2340x^{8} - 12625x^{7} - 4029x^{6} + 14204x^{5} + 5006x^{4} - 6420x^{3} - 2723x^{2} + 643x + 287\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w - 6]$ $\phantom{-}e$
3 $[3, 3, -w + 7]$ $...$
4 $[4, 2, 2]$ $\phantom{-}0$
5 $[5, 5, 4w + 25]$ $...$
5 $[5, 5, -4w + 29]$ $...$
11 $[11, 11, w - 8]$ $...$
11 $[11, 11, -w - 7]$ $...$
13 $[13, 13, 3w + 19]$ $...$
13 $[13, 13, 3w - 22]$ $...$
29 $[29, 29, 6w + 37]$ $...$
29 $[29, 29, 6w - 43]$ $...$
37 $[37, 37, 2w - 13]$ $...$
37 $[37, 37, 2w + 11]$ $...$
43 $[43, 43, -w - 1]$ $...$
43 $[43, 43, w - 2]$ $...$
49 $[49, 7, -7]$ $...$
59 $[59, 59, 5w - 37]$ $...$
59 $[59, 59, 5w + 32]$ $...$
67 $[67, 67, 21w + 131]$ $...$
67 $[67, 67, 21w - 152]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, 2]$ $1$