Properties

Label 2.2.281.1-9.1-b
Base field \(\Q(\sqrt{281}) \)
Weight $[2, 2]$
Level norm $9$
Level $[9, 3, 3]$
Dimension $30$
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: $[9, 3, 3]$
Dimension: $30$
CM: no
Base change: no
Newspace dimension: $100$

Hecke eigenvalues ($q$-expansion)

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

\(x^{30} - 3x^{29} - 42x^{28} + 131x^{27} + 767x^{26} - 2523x^{25} - 7955x^{24} + 28219x^{23} + 51106x^{22} - 202994x^{21} - 205513x^{20} + 981779x^{19} + 475961x^{18} - 3237610x^{17} - 361044x^{16} + 7215057x^{15} - 1196333x^{14} - 10507920x^{13} + 3991896x^{12} + 9336804x^{11} - 5149526x^{10} - 4439546x^{9} + 3101669x^{8} + 889388x^{7} - 755535x^{6} - 80815x^{5} + 70140x^{4} + 6198x^{3} - 1685x^{2} - 229x - 7\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w + 8]$ $...$
2 $[2, 2, -w + 9]$ $\phantom{-}e$
5 $[5, 5, -76w + 675]$ $...$
5 $[5, 5, 76w + 599]$ $...$
7 $[7, 7, -8w - 63]$ $...$
7 $[7, 7, -8w + 71]$ $...$
9 $[9, 3, 3]$ $-1$
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
$9$ $[9, 3, 3]$ $1$