Properties

Label 3.3.1345.1-31.1-a
Base field 3.3.1345.1
Weight $[2, 2, 2]$
Level norm $31$
Level $[31, 31, w^{2} - w - 8]$
Dimension $25$
CM no
Base change no

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Base field 3.3.1345.1

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

Form

Weight: $[2, 2, 2]$
Level: $[31, 31, w^{2} - w - 8]$
Dimension: $25$
CM: no
Base change: no
Newspace dimension: $59$

Hecke eigenvalues ($q$-expansion)

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

\(x^{25} - x^{24} - 71x^{23} + 84x^{22} + 2135x^{21} - 2893x^{20} - 35579x^{19} + 54260x^{18} + 359657x^{17} - 613930x^{16} - 2255633x^{15} + 4348134x^{14} + 8512119x^{13} - 19208563x^{12} - 17074590x^{11} + 50641475x^{10} + 9795370x^{9} - 71486921x^{8} + 19540613x^{7} + 41242839x^{6} - 25750511x^{5} - 1822618x^{4} + 5139140x^{3} - 1526080x^{2} + 178864x - 7456\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -w - 1]$ $\phantom{-}e$
5 $[5, 5, w + 2]$ $...$
7 $[7, 7, w + 3]$ $...$
7 $[7, 7, -w + 2]$ $...$
7 $[7, 7, -w + 1]$ $...$
8 $[8, 2, 2]$ $...$
13 $[13, 13, -w^{2} + w + 4]$ $...$
19 $[19, 19, -w^{2} + 5]$ $...$
23 $[23, 23, -w^{2} - w + 3]$ $...$
27 $[27, 3, 3]$ $...$
29 $[29, 29, w^{2} - w - 3]$ $...$
31 $[31, 31, w^{2} - w - 8]$ $-1$
37 $[37, 37, -w - 4]$ $...$
43 $[43, 43, 2w^{2} - 4w - 3]$ $...$
47 $[47, 47, w^{2} - 3]$ $...$
53 $[53, 53, 2w^{2} - w - 11]$ $...$
59 $[59, 59, w^{2} - 2w - 4]$ $...$
67 $[67, 67, w^{2} + w - 8]$ $...$
71 $[71, 71, w^{2} + w - 11]$ $...$
73 $[73, 73, -w^{2} + 4w - 2]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$31$ $[31, 31, w^{2} - w - 8]$ $1$