Properties

Base field 4.4.15952.1
Weight [2, 2, 2, 2]
Level norm 17
Level $[17, 17, -w^{3} + w^{2} + 6w - 1]$
Label 4.4.15952.1-17.1-b
Dimension 21
CM no
Base change no

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Base field 4.4.15952.1

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

Form

Weight [2, 2, 2, 2]
Level $[17, 17, -w^{3} + w^{2} + 6w - 1]$
Label 4.4.15952.1-17.1-b
Dimension 21
Is CM no
Is base change no
Parent newspace dimension 42

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{21} \) \(\mathstrut +\mathstrut 5x^{20} \) \(\mathstrut -\mathstrut 19x^{19} \) \(\mathstrut -\mathstrut 125x^{18} \) \(\mathstrut +\mathstrut 110x^{17} \) \(\mathstrut +\mathstrut 1294x^{16} \) \(\mathstrut +\mathstrut 81x^{15} \) \(\mathstrut -\mathstrut 7211x^{14} \) \(\mathstrut -\mathstrut 3631x^{13} \) \(\mathstrut +\mathstrut 23611x^{12} \) \(\mathstrut +\mathstrut 17397x^{11} \) \(\mathstrut -\mathstrut 46651x^{10} \) \(\mathstrut -\mathstrut 40136x^{9} \) \(\mathstrut +\mathstrut 54932x^{8} \) \(\mathstrut +\mathstrut 50361x^{7} \) \(\mathstrut -\mathstrut 36489x^{6} \) \(\mathstrut -\mathstrut 33877x^{5} \) \(\mathstrut +\mathstrut 12175x^{4} \) \(\mathstrut +\mathstrut 10879x^{3} \) \(\mathstrut -\mathstrut 1695x^{2} \) \(\mathstrut -\mathstrut 1160x \) \(\mathstrut +\mathstrut 132\)

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Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}e$
3 $[3, 3, -w^{3} + w^{2} + 5w - 2]$ $...$
11 $[11, 11, -w^{3} + 5w + 1]$ $...$
11 $[11, 11, -w + 2]$ $...$
13 $[13, 13, -w^{3} + w^{2} + 4w + 1]$ $...$
17 $[17, 17, -w^{3} + w^{2} + 6w - 1]$ $\phantom{-}1$
17 $[17, 17, -w^{2} - w + 3]$ $...$
23 $[23, 23, w^{3} - 6w]$ $...$
27 $[27, 3, w^{3} + w^{2} - 5w - 4]$ $...$
41 $[41, 41, -w^{3} + w^{2} + 5w]$ $...$
41 $[41, 41, 2w^{3} - 11w - 4]$ $...$
53 $[53, 53, 2w^{3} - 2w^{2} - 11w + 6]$ $...$
59 $[59, 59, 2w^{3} - 11w - 2]$ $...$
67 $[67, 67, w^{3} - 7w - 1]$ $...$
71 $[71, 71, 3w^{3} - 2w^{2} - 15w + 1]$ $...$
79 $[79, 79, -3w^{3} + w^{2} + 16w + 3]$ $...$
89 $[89, 89, -4w^{3} + 2w^{2} + 22w - 3]$ $...$
101 $[101, 101, -2w^{3} + 13w + 6]$ $...$
101 $[101, 101, w^{3} + w^{2} - 6w - 3]$ $...$
101 $[101, 101, -3w^{3} + 2w^{2} + 17w - 3]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
17 $[17, 17, -w^{3} + w^{2} + 6w - 1]$ $-1$