Properties

Label 2.2.281.1-14.1-c
Base field \(\Q(\sqrt{281}) \)
Weight $[2, 2]$
Level norm $14$
Level $[14, 14, -135w - 1064]$
Dimension $16$
CM no
Base change no

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Base field \(\Q(\sqrt{281}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 70\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2]$
Level: $[14, 14, -135w - 1064]$
Dimension: $16$
CM: no
Base change: no
Newspace dimension: $79$

Hecke eigenvalues ($q$-expansion)

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

\(x^{16} - 3x^{15} - 21x^{14} + 71x^{13} + 156x^{12} - 657x^{11} - 406x^{10} + 2970x^{9} - 468x^{8} - 6608x^{7} + 4123x^{6} + 6109x^{5} - 6094x^{4} - 881x^{3} + 2118x^{2} - 359x - 68\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w + 8]$ $\phantom{-}1$
2 $[2, 2, -w + 9]$ $\phantom{-}e$
5 $[5, 5, -76w + 675]$ $...$
5 $[5, 5, 76w + 599]$ $...$
7 $[7, 7, -8w - 63]$ $-1$
7 $[7, 7, -8w + 71]$ $...$
9 $[9, 3, 3]$ $...$
17 $[17, 17, 42w + 331]$ $...$
17 $[17, 17, 42w - 373]$ $...$
29 $[29, 29, -6w - 47]$ $...$
29 $[29, 29, 6w - 53]$ $...$
31 $[31, 31, 10w + 79]$ $...$
31 $[31, 31, -10w + 89]$ $...$
43 $[43, 43, 2w - 19]$ $...$
43 $[43, 43, -2w - 17]$ $...$
53 $[53, 53, 194w + 1529]$ $...$
53 $[53, 53, -194w + 1723]$ $...$
59 $[59, 59, -110w - 867]$ $...$
59 $[59, 59, 110w - 977]$ $...$
79 $[79, 79, 650w - 5773]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w + 8]$ $-1$
$7$ $[7, 7, -8w - 63]$ $1$