↑

Properties

Label 4.4.2225.1-19.2-a
Base field 4.4.2225.1
Weight [2,2,2,2][2, 2, 2, 2]
Level norm 1919
Level [19,19,12w3+12w2−52w−1][19,19,\frac{1}{2} w^3 + \frac{1}{2} w^2 - \frac{5}{2} w - 1]
Dimension 11
CM no
Base change no

Related objects

Downloads

Learn more

Base field 4.4.2225.1

Generator ww, with minimal polynomial x4−x3−5x2+2x+4x^4 - x^3 - 5 x^2 + 2 x + 4; narrow class number 11 and class number 11.

Form

Weight: [2,2,2,2][2, 2, 2, 2]
Level: [19,19,12w3+12w2−52w−1][19,19,\frac{1}{2} w^3 + \frac{1}{2} w^2 - \frac{5}{2} w - 1]
Dimension: 11
CM: no
Base change: no
Newspace dimension: 11

Hecke eigenvalues (qq-expansion)

The Hecke eigenvalue field is Q\Q.
Norm Prime Eigenvalue
4 [4,2,−w][4, 2, -w] −1-1
4 [4,2,12w3−12w2−52w+1][4, 2, \frac{1}{2} w^3 - \frac{1}{2} w^2 - \frac{5}{2} w + 1] −3\phantom{-}3
19 [19,19,12w3−32w2−12w+4][19, 19, \frac{1}{2} w^3 - \frac{3}{2} w^2 - \frac{1}{2} w + 4] −4\phantom{-}4
19 [19,19,12w3+12w2−52w−1][19, 19, \frac{1}{2} w^3 + \frac{1}{2} w^2 - \frac{5}{2} w - 1] −1-1
25 [25,5,w3−w2−3w+1][25, 5, w^3 - w^2 - 3 w + 1] −2\phantom{-}2
29 [29,29,−12w3+32w2+32w−1][29, 29, -\frac{1}{2} w^3 + \frac{3}{2} w^2 + \frac{3}{2} w - 1] −10\phantom{-}10
29 [29,29,−w2+5][29, 29, -w^2 + 5] −6-6
31 [31,31,−w3+2w2+3w−3][31, 31, -w^3 + 2 w^2 + 3 w - 3] −8-8
31 [31,31,−12w3−12w2+32w+3][31, 31, -\frac{1}{2} w^3 - \frac{1}{2} w^2 + \frac{3}{2} w + 3] −8-8
41 [41,41,−12w3−12w2+52w][41, 41, -\frac{1}{2} w^3 - \frac{1}{2} w^2 + \frac{5}{2} w] −2-2
41 [41,41,−12w3+32w2+12w−5][41, 41, -\frac{1}{2} w^3 + \frac{3}{2} w^2 + \frac{1}{2} w - 5] −6\phantom{-}6
59 [59,59,w3−w2−5w+1][59, 59, w^3 - w^2 - 5 w + 1] −4\phantom{-}4
59 [59,59,32w3−12w2−112w−1][59, 59, \frac{3}{2} w^3 - \frac{1}{2} w^2 - \frac{11}{2} w - 1] −4-4
61 [61,61,32w3−12w2−112w−2][61, 61, \frac{3}{2} w^3 - \frac{1}{2} w^2 - \frac{11}{2} w - 2] −2\phantom{-}2
61 [61,61,−2w2+w+7][61, 61, -2 w^2 + w + 7] −2\phantom{-}2
71 [71,71,12w3−32w2−52w+6][71, 71, \frac{1}{2} w^3 - \frac{3}{2} w^2 - \frac{5}{2} w + 6] −0\phantom{-}0
71 [71,71,−12w3+52w2−12w−5][71, 71, -\frac{1}{2} w^3 + \frac{5}{2} w^2 - \frac{1}{2} w - 5] −8\phantom{-}8
71 [71,71,12w3+32w2−72w−5][71, 71, \frac{1}{2} w^3 + \frac{3}{2} w^2 - \frac{7}{2} w - 5] −0\phantom{-}0
71 [71,71,−w3+3w2+2w−7][71, 71, -w^3 + 3 w^2 + 2 w - 7] −8-8
81 [81,3,−3][81, 3, -3] −2\phantom{-}2
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
1919 [19,19,12w3+12w2−52w−1][19,19,\frac{1}{2} w^3 + \frac{1}{2} w^2 - \frac{5}{2} w - 1] 11