Properties

Base field 3.3.1129.1
Weight [2, 2, 2]
Level norm 17
Level $[17, 17, -w^{2} + w + 4]$
Label 3.3.1129.1-17.1-e
Dimension 14
CM no
Base change no

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Base field 3.3.1129.1

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

Form

Weight [2, 2, 2]
Level $[17, 17, -w^{2} + w + 4]$
Label 3.3.1129.1-17.1-e
Dimension 14
Is CM no
Is base change no
Parent newspace dimension 34

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{14} \) \(\mathstrut -\mathstrut 30x^{12} \) \(\mathstrut +\mathstrut 8x^{11} \) \(\mathstrut +\mathstrut 329x^{10} \) \(\mathstrut -\mathstrut 175x^{9} \) \(\mathstrut -\mathstrut 1602x^{8} \) \(\mathstrut +\mathstrut 1255x^{7} \) \(\mathstrut +\mathstrut 3262x^{6} \) \(\mathstrut -\mathstrut 3415x^{5} \) \(\mathstrut -\mathstrut 1605x^{4} \) \(\mathstrut +\mathstrut 2650x^{3} \) \(\mathstrut -\mathstrut 744x^{2} \) \(\mathstrut -\mathstrut 8x \) \(\mathstrut +\mathstrut 16\)

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Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
3 $[3, 3, w + 1]$ $...$
3 $[3, 3, w + 2]$ $...$
8 $[8, 2, 2]$ $...$
11 $[11, 11, -w^{2} + 5]$ $...$
13 $[13, 13, w^{2} - w - 7]$ $...$
17 $[17, 17, -w^{2} + w + 4]$ $\phantom{-}1$
19 $[19, 19, -w^{2} - w + 4]$ $...$
29 $[29, 29, 2w^{2} - 2w - 11]$ $...$
31 $[31, 31, w^{2} - 2w - 4]$ $...$
37 $[37, 37, -2w^{2} + 3w + 7]$ $...$
41 $[41, 41, w^{2} - 2]$ $...$
59 $[59, 59, 2w^{2} - 13]$ $...$
61 $[61, 61, w^{2} + w - 10]$ $...$
67 $[67, 67, 2w^{2} - w - 11]$ $...$
73 $[73, 73, -w^{2} - 1]$ $...$
83 $[83, 83, w^{2} - w - 10]$ $...$
89 $[89, 89, -w^{2} + 4w - 2]$ $...$
97 $[97, 97, w^{2} - 2w - 7]$ $...$
97 $[97, 97, -w^{2} - 4w - 5]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
17 $[17, 17, -w^{2} + w + 4]$ $-1$