Properties

Label 2.2.281.1-10.1-i
Base field \(\Q(\sqrt{281}) \)
Weight $[2, 2]$
Level norm $10$
Level $[10, 10, -9w + 80]$
Dimension $17$
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: $[10, 10, -9w + 80]$
Dimension: $17$
CM: no
Base change: no
Newspace dimension: $53$

Hecke eigenvalues ($q$-expansion)

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

\(x^{17} - x^{16} - 27x^{15} + 22x^{14} + 298x^{13} - 180x^{12} - 1733x^{11} + 651x^{10} + 5668x^{9} - 805x^{8} - 10164x^{7} - 823x^{6} + 8699x^{5} + 2350x^{4} - 2228x^{3} - 780x^{2} + 22x + 6\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w + 8]$ $\phantom{-}1$
2 $[2, 2, -w + 9]$ $\phantom{-}e$
5 $[5, 5, -76w + 675]$ $\phantom{-}1$
5 $[5, 5, 76w + 599]$ $...$
7 $[7, 7, -8w - 63]$ $...$
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
$2$ $[2, 2, w + 8]$ $-1$
$5$ $[5, 5, -76w + 675]$ $-1$