Properties

Label 2.2.229.1-11.2-d
Base field \(\Q(\sqrt{229}) \)
Weight $[2, 2]$
Level norm $11$
Level $[11,11,-w + 2]$
Dimension $35$
CM no
Base change no

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Base field \(\Q(\sqrt{229}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 57\); narrow class number \(3\) and class number \(3\).

Form

Weight: $[2, 2]$
Level: $[11,11,-w + 2]$
Dimension: $35$
CM: no
Base change: no
Newspace dimension: $186$

Hecke eigenvalues ($q$-expansion)

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

\(x^{35} - 10x^{34} - 19x^{33} + 490x^{32} - 553x^{31} - 10391x^{30} + 25391x^{29} + 123363x^{28} - 441031x^{27} - 867039x^{26} + 4530403x^{25} + 3197287x^{24} - 30860046x^{23} + 450259x^{22} + 145792455x^{21} - 73272536x^{20} - 484403785x^{19} + 430418719x^{18} + 1121320228x^{17} - 1410842338x^{16} - 1736560733x^{15} + 2995725440x^{14} + 1600576284x^{13} - 4225897995x^{12} - 483137204x^{11} + 3875321675x^{10} - 644093461x^{9} - 2165838756x^{8} + 803276922x^{7} + 641819817x^{6} - 351235625x^{5} - 69661322x^{4} + 57993125x^{3} - 1565705x^{2} - 2064580x + 181300\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $...$
3 $[3, 3, w + 2]$ $\phantom{-}e$
4 $[4, 2, 2]$ $...$
5 $[5, 5, w + 1]$ $...$
5 $[5, 5, w + 3]$ $...$
11 $[11, 11, w + 1]$ $...$
11 $[11, 11, w + 9]$ $-1$
17 $[17, 17, w + 2]$ $...$
17 $[17, 17, w + 14]$ $...$
19 $[19, 19, w]$ $...$
19 $[19, 19, w + 18]$ $...$
37 $[37, 37, -w - 4]$ $...$
37 $[37, 37, w - 5]$ $...$
43 $[43, 43, w + 16]$ $...$
43 $[43, 43, w + 26]$ $...$
49 $[49, 7, -7]$ $...$
53 $[53, 53, -w - 10]$ $...$
53 $[53, 53, w - 11]$ $...$
61 $[61, 61, w + 15]$ $...$
61 $[61, 61, w + 45]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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