Properties

Base field 4.4.15952.1
Weight [2, 2, 2, 2]
Level norm 1
Level $[1, 1, 1]$
Label 4.4.15952.1-1.1-a
Dimension 6
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 $[1, 1, 1]$
Label 4.4.15952.1-1.1-a
Dimension 6
Is CM no
Is base change no
Parent newspace dimension 6

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} \) \(\mathstrut -\mathstrut 10x^{4} \) \(\mathstrut +\mathstrut 23x^{2} \) \(\mathstrut -\mathstrut 2\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}e$
3 $[3, 3, -w^{3} + w^{2} + 5w - 2]$ $-\frac{1}{2}e^{5} + \frac{9}{2}e^{3} - 9e$
11 $[11, 11, -w^{3} + 5w + 1]$ $\phantom{-}\frac{1}{2}e^{5} - \frac{11}{2}e^{3} + 13e$
11 $[11, 11, -w + 2]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{7}{2}e^{2} + 3$
13 $[13, 13, -w^{3} + w^{2} + 4w + 1]$ $-e^{5} + 9e^{3} - 16e$
17 $[17, 17, -w^{3} + w^{2} + 6w - 1]$ $\phantom{-}\frac{1}{2}e^{5} - \frac{11}{2}e^{3} + 15e$
17 $[17, 17, -w^{2} - w + 3]$ $-\frac{1}{2}e^{4} + \frac{5}{2}e^{2} + 5$
23 $[23, 23, w^{3} - 6w]$ $\phantom{-}e^{4} - 7e^{2} + 6$
27 $[27, 3, w^{3} + w^{2} - 5w - 4]$ $-\frac{1}{2}e^{5} + \frac{13}{2}e^{3} - 19e$
41 $[41, 41, -w^{3} + w^{2} + 5w]$ $\phantom{-}e^{5} - 11e^{3} + 32e$
41 $[41, 41, 2w^{3} - 11w - 4]$ $-\frac{1}{2}e^{5} + \frac{5}{2}e^{3} + e$
53 $[53, 53, 2w^{3} - 2w^{2} - 11w + 6]$ $\phantom{-}e^{5} - 9e^{3} + 18e$
59 $[59, 59, 2w^{3} - 11w - 2]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{1}{2}e^{2} - 7$
67 $[67, 67, w^{3} - 7w - 1]$ $-\frac{3}{2}e^{4} + \frac{23}{2}e^{2} - 7$
71 $[71, 71, 3w^{3} - 2w^{2} - 15w + 1]$ $\phantom{-}2e^{5} - 20e^{3} + 42e$
79 $[79, 79, -3w^{3} + w^{2} + 16w + 3]$ $\phantom{-}e^{5} - 11e^{3} + 24e$
89 $[89, 89, -4w^{3} + 2w^{2} + 22w - 3]$ $\phantom{-}\frac{3}{2}e^{5} - \frac{25}{2}e^{3} + 21e$
101 $[101, 101, -2w^{3} + 13w + 6]$ $-4e^{2} + 14$
101 $[101, 101, w^{3} + w^{2} - 6w - 3]$ $-e^{4} + 7e^{2} - 4$
101 $[101, 101, -3w^{3} + 2w^{2} + 17w - 3]$ $-2e^{5} + 20e^{3} - 46e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

This form has no Atkin-Lehner eigenvalues since the level is \((1)\).