Properties

Label 3.3.1489.1-29.1-b
Base field 3.3.1489.1
Weight $[2, 2, 2]$
Level norm $29$
Level $[29, 29, w^{2} - 2w - 5]$
Dimension $29$
CM no
Base change no

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Base field 3.3.1489.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 10x - 7\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[29, 29, w^{2} - 2w - 5]$
Dimension: $29$
CM: no
Base change: no
Newspace dimension: $58$

Hecke eigenvalues ($q$-expansion)

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

\(x^{29} + 18x^{28} + 40x^{27} - 1144x^{26} - 7483x^{25} + 17630x^{24} + 285639x^{23} + 339946x^{22} - 4802113x^{21} - 15535294x^{20} + 33814947x^{19} + 227547988x^{18} + 52881747x^{17} - 1638440244x^{16} - 2542894266x^{15} + 5360453206x^{14} + 17309247252x^{13} - 122125718x^{12} - 50920051656x^{11} - 49160503488x^{10} + 52898731876x^{9} + 120035190778x^{8} + 33311108292x^{7} - 83030399610x^{6} - 78767927441x^{5} - 11161181264x^{4} + 16478627548x^{3} + 8777157968x^{2} + 1500335424x + 76912384\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
7 $[7, 7, w]$ $\phantom{-}e$
8 $[8, 2, 2]$ $...$
13 $[13, 13, w^{2} - 3w - 5]$ $...$
17 $[17, 17, w - 1]$ $...$
19 $[19, 19, -w^{2} + 2w + 6]$ $...$
19 $[19, 19, -w^{2} + 2w + 10]$ $...$
19 $[19, 19, -w + 3]$ $...$
23 $[23, 23, w - 2]$ $...$
27 $[27, 3, 3]$ $...$
29 $[29, 29, w^{2} - 2w - 5]$ $-1$
31 $[31, 31, w^{2} - 3w - 6]$ $...$
31 $[31, 31, w^{2} - w - 8]$ $...$
31 $[31, 31, w^{2} - 2w - 4]$ $...$
41 $[41, 41, w^{2} - w - 5]$ $...$
43 $[43, 43, w^{2} - 3w - 10]$ $...$
47 $[47, 47, -w - 4]$ $...$
47 $[47, 47, w^{2} - w - 9]$ $...$
47 $[47, 47, -2w^{2} + 3w + 17]$ $...$
49 $[49, 7, w^{2} - w - 10]$ $...$
53 $[53, 53, w^{2} - w - 4]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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