Properties

Label 2.2.21.1-768.1-w
Base field Q(21)\Q(\sqrt{21})
Weight [2,2][2, 2]
Level norm 768768
Level [768,48,16w+16][768, 48, 16 w + 16]
Dimension 11
CM no
Base change no

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Base field Q(21)\Q(\sqrt{21})

Generator ww, with minimal polynomial x2x5x^{2} - x - 5; narrow class number 22 and class number 11.

Form

Weight: [2,2][2, 2]
Level: [768,48,16w+16][768, 48, 16 w + 16]
Dimension: 11
CM: no
Base change: no
Newspace dimension: 6262

Hecke eigenvalues (qq-expansion)

The Hecke eigenvalue field is Q\Q.
Norm Prime Eigenvalue
3 [3,3,w+1][3, 3, w + 1] 1-1
4 [4,2,2][4, 2, 2] 0\phantom{-}0
5 [5,5,w][5, 5, w] 2\phantom{-}2
5 [5,5,w1][5, 5, w - 1] 4\phantom{-}4
7 [7,7,w3][7, 7, -w - 3] 2-2
17 [17,17,2w+3][17, 17, -2 w + 3] 0\phantom{-}0
17 [17,17,2w1][17, 17, -2 w - 1] 2\phantom{-}2
37 [37,37,w+6][37, 37, w + 6] 2-2
37 [37,37,w+7][37, 37, -w + 7] 6\phantom{-}6
41 [41,41,3w+1][41, 41, 3 w + 1] 12-12
41 [41,41,3w+4][41, 41, -3 w + 4] 2-2
43 [43,43,3w+8][43, 43, 3 w + 8] 10\phantom{-}10
43 [43,43,3w11][43, 43, 3 w - 11] 10\phantom{-}10
47 [47,47,3w2][47, 47, 3 w - 2] 4\phantom{-}4
47 [47,47,3w1][47, 47, 3 w - 1] 0\phantom{-}0
59 [59,59,5w6][59, 59, -5 w - 6] 12-12
59 [59,59,4w3][59, 59, -4 w - 3] 12\phantom{-}12
67 [67,67,w8][67, 67, -w - 8] 4\phantom{-}4
67 [67,67,w9][67, 67, w - 9] 8-8
79 [79,79,2w11][79, 79, 2 w - 11] 8\phantom{-}8
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
33 [3,3,w+1][3, 3, w + 1] 11
44 [4,2,2][4, 2, 2] 11