Properties

Label 4.4.19429.1-21.1-e
Base field 4.4.19429.1
Weight $[2, 2, 2, 2]$
Level norm $21$
Level $[21, 21, w^{2} - w - 6]$
Dimension $6$
CM no
Base change no

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Base field 4.4.19429.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} - x + 5\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[21, 21, w^{2} - w - 6]$
Dimension: $6$
CM: no
Base change: no
Newspace dimension: $37$

Hecke eigenvalues ($q$-expansion)

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

\(x^{6} - 3x^{5} - 11x^{4} + 33x^{3} - 8x^{2} - 8x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ $-1$
5 $[5, 5, w]$ $\phantom{-}e$
7 $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$ $\phantom{-}1$
13 $[13, 13, -w^{2} + w + 4]$ $\phantom{-}15e^{5} - 48e^{4} - 155e^{3} + 526e^{2} - 230e - 75$
13 $[13, 13, -w^{3} + 2w^{2} + 5w - 2]$ $-12e^{5} + 38e^{4} + 125e^{3} - 416e^{2} + 173e + 58$
16 $[16, 2, 2]$ $-e^{5} + 3e^{4} + 11e^{3} - 33e^{2} + 7e + 6$
17 $[17, 17, -w + 2]$ $\phantom{-}10e^{5} - 32e^{4} - 104e^{3} + 351e^{2} - 146e - 52$
19 $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ $-3e^{5} + 10e^{4} + 30e^{3} - 110e^{2} + 57e + 15$
27 $[27, 3, w^{3} - 3w^{2} - 4w + 7]$ $\phantom{-}41e^{5} - 132e^{4} - 423e^{3} + 1447e^{2} - 634e - 199$
31 $[31, 31, w^{3} - 3w^{2} - 3w + 7]$ $\phantom{-}34e^{5} - 109e^{4} - 351e^{3} + 1194e^{2} - 523e - 165$
31 $[31, 31, -w^{3} + w^{2} + 6w + 1]$ $-4e^{5} + 12e^{4} + 43e^{3} - 131e^{2} + 45e + 20$
41 $[41, 41, w^{2} - w - 1]$ $-14e^{5} + 45e^{4} + 145e^{3} - 493e^{2} + 209e + 70$
43 $[43, 43, 2w^{3} - 5w^{2} - 6w + 4]$ $-11e^{5} + 36e^{4} + 112e^{3} - 395e^{2} + 186e + 52$
47 $[47, 47, -w^{3} + 2w^{2} + 5w - 1]$ $-47e^{5} + 152e^{4} + 483e^{3} - 1667e^{2} + 746e + 229$
53 $[53, 53, -w - 3]$ $-20e^{5} + 65e^{4} + 205e^{3} - 714e^{2} + 322e + 99$
53 $[53, 53, -w^{3} + 3w^{2} + 3w - 6]$ $-9e^{5} + 29e^{4} + 92e^{3} - 317e^{2} + 148e + 36$
59 $[59, 59, 2w^{2} - 3w - 6]$ $-3e^{5} + 9e^{4} + 33e^{3} - 99e^{2} + 25e + 17$
59 $[59, 59, w^{3} - w^{2} - 7w - 3]$ $\phantom{-}7e^{5} - 22e^{4} - 73e^{3} + 240e^{2} - 103e - 28$
79 $[79, 79, 2w^{3} - 4w^{2} - 8w + 3]$ $\phantom{-}e^{3} - e^{2} - 11e + 6$
79 $[79, 79, w^{2} - 2w - 1]$ $-18e^{5} + 57e^{4} + 188e^{3} - 625e^{2} + 256e + 91$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ $1$
$7$ $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$ $-1$