Properties

Label 4.4.8789.1-29.1-a
Base field 4.4.8789.1
Weight $[2, 2, 2, 2]$
Level norm $29$
Level $[29, 29, w^{3} - 2w^{2} - 5w]$
Dimension $7$
CM no
Base change no

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Base field 4.4.8789.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} - 2x + 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[29, 29, w^{3} - 2w^{2} - 5w]$
Dimension: $7$
CM: no
Base change: no
Newspace dimension: $20$

Hecke eigenvalues ($q$-expansion)

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

\(x^{7} + 6x^{6} - 50x^{4} - 43x^{3} + 119x^{2} + 81x - 115\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -w^{3} + 2w^{2} + 3w]$ $\phantom{-}e$
7 $[7, 7, w - 1]$ $-e^{6} - 5e^{5} + 2e^{4} + 34e^{3} + 20e^{2} - 40e - 17$
11 $[11, 11, -w^{3} + 2w^{2} + 4w]$ $-2e^{6} - 8e^{5} + 14e^{4} + 63e^{3} - 32e^{2} - 110e + 70$
13 $[13, 13, -2w^{3} + 3w^{2} + 10w - 2]$ $-e^{6} - 3e^{5} + 13e^{4} + 31e^{3} - 61e^{2} - 80e + 104$
16 $[16, 2, 2]$ $-e^{5} - 4e^{4} + 5e^{3} + 26e^{2} - 29$
17 $[17, 17, -w^{3} + 2w^{2} + 5w - 3]$ $\phantom{-}e^{6} + 4e^{5} - 7e^{4} - 31e^{3} + 17e^{2} + 51e - 38$
17 $[17, 17, -w^{3} + w^{2} + 5w]$ $\phantom{-}e^{6} + 5e^{5} - 2e^{4} - 34e^{3} - 20e^{2} + 40e + 15$
17 $[17, 17, -w^{2} + 2w + 1]$ $\phantom{-}e^{6} + 4e^{5} - 7e^{4} - 32e^{3} + 16e^{2} + 59e - 37$
19 $[19, 19, w^{2} - w - 2]$ $-2e^{6} - 6e^{5} + 24e^{4} + 57e^{3} - 105e^{2} - 133e + 175$
29 $[29, 29, w^{3} - 2w^{2} - 5w]$ $\phantom{-}1$
29 $[29, 29, w^{2} - w - 3]$ $\phantom{-}4e^{6} + 17e^{5} - 24e^{4} - 131e^{3} + 37e^{2} + 218e - 110$
31 $[31, 31, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}3e^{6} + 12e^{5} - 23e^{4} - 99e^{3} + 66e^{2} + 186e - 147$
43 $[43, 43, 2w^{3} - 3w^{2} - 11w]$ $\phantom{-}e^{6} + 4e^{5} - 9e^{4} - 36e^{3} + 36e^{2} + 80e - 83$
47 $[47, 47, w^{3} - 7w - 4]$ $-2e^{6} - 7e^{5} + 19e^{4} + 60e^{3} - 67e^{2} - 118e + 118$
53 $[53, 53, -2w^{3} + 3w^{2} + 9w - 1]$ $\phantom{-}e^{6} + 3e^{5} - 12e^{4} - 28e^{3} + 50e^{2} + 61e - 72$
61 $[61, 61, -w - 3]$ $-7e^{6} - 25e^{5} + 65e^{4} + 214e^{3} - 227e^{2} - 430e + 408$
73 $[73, 73, -w^{3} + 2w^{2} + 3w - 3]$ $\phantom{-}2e^{6} + 6e^{5} - 23e^{4} - 54e^{3} + 97e^{2} + 119e - 163$
73 $[73, 73, w^{3} - w^{2} - 7w - 1]$ $\phantom{-}2e^{6} + 7e^{5} - 18e^{4} - 57e^{3} + 60e^{2} + 105e - 105$
81 $[81, 3, -3]$ $-e^{6} - 3e^{5} + 13e^{4} + 31e^{3} - 63e^{2} - 82e + 109$
83 $[83, 83, -2w^{3} + 3w^{2} + 9w + 1]$ $\phantom{-}4e^{6} + 10e^{5} - 59e^{4} - 111e^{3} + 287e^{2} + 301e - 457$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$29$ $[29, 29, w^{3} - 2w^{2} - 5w]$ $-1$