Properties

Label 3.3.1489.1-31.2-c
Base field 3.3.1489.1
Weight $[2, 2, 2]$
Level norm $31$
Level $[31, 31, w^{2} - w - 8]$
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: $[31, 31, w^{2} - w - 8]$
Dimension: $29$
CM: no
Base change: no
Newspace dimension: $60$

Hecke eigenvalues ($q$-expansion)

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

\(x^{29} - 13x^{28} - 41x^{27} + 1176x^{26} - 1410x^{25} - 43681x^{24} + 129162x^{23} + 853373x^{22} - 3721389x^{21} - 9099500x^{20} + 58157417x^{19} + 43469597x^{18} - 551917810x^{17} + 95705466x^{16} + 3269354956x^{15} - 2522693022x^{14} - 11830875913x^{13} + 14782839900x^{12} + 23905814972x^{11} - 43260004856x^{10} - 19285602566x^{9} + 65119965466x^{8} - 10831708085x^{7} - 42632315829x^{6} + 24200847527x^{5} + 5028592134x^{4} - 7239388255x^{3} + 1715006532x^{2} - 23165509x - 21751336\)

  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 $[29, 29, w^{2} - 2w - 5]$ $...$
31 $[31, 31, w^{2} - 3w - 6]$ $...$
31 $[31, 31, w^{2} - w - 8]$ $\phantom{-}1$
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
$31$ $[31, 31, w^{2} - w - 8]$ $-1$