Properties

Label 2.2.13.1-675.2-g
Base field Q(13)\Q(\sqrt{13})
Weight [2,2][2, 2]
Level norm 675675
Level [675,45,15w15][675,45,15 w - 15]
Dimension 11
CM no
Base change no

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Base field Q(13)\Q(\sqrt{13})

Generator ww, with minimal polynomial x2x3x^2 - x - 3; narrow class number 11 and class number 11.

Form

Weight: [2,2][2, 2]
Level: [675,45,15w15][675,45,15 w - 15]
Dimension: 11
CM: no
Base change: no
Newspace dimension: 2020

Hecke eigenvalues (qq-expansion)

The Hecke eigenvalue field is Q\Q.
Norm Prime Eigenvalue
3 [3,3,w][3, 3, -w] 1\phantom{-}1
3 [3,3,w+1][3, 3, -w + 1] 0\phantom{-}0
4 [4,2,2][4, 2, 2] 1-1
13 [13,13,2w+1][13, 13, -2 w + 1] 4-4
17 [17,17,w+4][17, 17, w + 4] 0\phantom{-}0
17 [17,17,w+5][17, 17, -w + 5] 0\phantom{-}0
23 [23,23,3w+1][23, 23, 3 w + 1] 0\phantom{-}0
23 [23,23,3w+4][23, 23, -3 w + 4] 6-6
25 [25,5,5][25, 5, 5] 1\phantom{-}1
29 [29,29,3w2][29, 29, 3 w - 2] 6-6
29 [29,29,3w+1][29, 29, -3 w + 1] 6-6
43 [43,43,4w1][43, 43, -4 w - 1] 2\phantom{-}2
43 [43,43,4w5][43, 43, 4 w - 5] 8\phantom{-}8
49 [49,7,7][49, 7, -7] 10-10
53 [53,53,w7][53, 53, -w - 7] 6-6
53 [53,53,w8][53, 53, w - 8] 6-6
61 [61,61,3w8][61, 61, -3 w - 8] 2\phantom{-}2
61 [61,61,3w11][61, 61, 3 w - 11] 10-10
79 [79,79,5w4][79, 79, 5 w - 4] 8\phantom{-}8
79 [79,79,5w1][79, 79, 5 w - 1] 4-4
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
33 [3,3,w1][3,3,w - 1] 1-1
33 [3,3,w][3,3,w] 1-1
2525 [25,5,5][25,5,5] 1-1