Properties

Base field 4.4.9248.1
Weight [2, 2, 2, 2]
Level norm 26
Level $[26, 26, -w^{3} + w^{2} + 3w]$
Label 4.4.9248.1-26.1-c
Dimension 6
CM no
Base change no

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Base field 4.4.9248.1

Generator \(w\), with minimal polynomial \(x^{4} - 5x^{2} + 2\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[26, 26, -w^{3} + w^{2} + 3w]$
Label 4.4.9248.1-26.1-c
Dimension 6
Is CM no
Is base change no
Parent newspace dimension 14

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} \) \(\mathstrut -\mathstrut x^{5} \) \(\mathstrut -\mathstrut 9x^{4} \) \(\mathstrut +\mathstrut 5x^{3} \) \(\mathstrut +\mathstrut 20x^{2} \) \(\mathstrut -\mathstrut 2x \) \(\mathstrut -\mathstrut 6\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $-1$
2 $[2, 2, w + 1]$ $\phantom{-}e$
13 $[13, 13, -w^{2} + w + 3]$ $-1$
13 $[13, 13, w^{2} + w - 3]$ $\phantom{-}\frac{1}{2}e^{5} - \frac{9}{2}e^{3} - e^{2} + 8e + 3$
19 $[19, 19, -w^{3} + 3w + 1]$ $-\frac{1}{2}e^{5} + e^{4} + \frac{7}{2}e^{3} - 5e^{2} - 4e + 1$
19 $[19, 19, -w^{3} + 3w - 1]$ $\phantom{-}\frac{1}{2}e^{5} - e^{4} - \frac{5}{2}e^{3} + 4e^{2} - 1$
43 $[43, 43, -w^{2} + w - 1]$ $-e^{5} + e^{4} + 8e^{3} - 5e^{2} - 13e + 6$
43 $[43, 43, w^{2} + w + 1]$ $\phantom{-}e^{5} - e^{4} - 7e^{3} + 5e^{2} + 8e - 2$
49 $[49, 7, w^{3} + w^{2} - 6w - 3]$ $-\frac{1}{2}e^{5} + e^{4} + \frac{9}{2}e^{3} - 7e^{2} - 7e + 7$
49 $[49, 7, w^{3} - w^{2} - 6w + 3]$ $\phantom{-}e^{5} - 2e^{4} - 9e^{3} + 12e^{2} + 18e - 6$
53 $[53, 53, 2w^{3} - w^{2} - 9w + 3]$ $\phantom{-}e^{5} - 8e^{3} - 2e^{2} + 11e + 4$
53 $[53, 53, 2w^{3} + w^{2} - 9w - 3]$ $-\frac{3}{2}e^{5} + 2e^{4} + \frac{21}{2}e^{3} - 8e^{2} - 14e + 1$
59 $[59, 59, w^{3} - w^{2} - 4w + 1]$ $-e^{3} - 2e^{2} + 7e + 8$
59 $[59, 59, -w^{3} - w^{2} + 4w + 1]$ $-2e^{5} + 3e^{4} + 16e^{3} - 15e^{2} - 28e + 6$
67 $[67, 67, 3w^{3} - 13w + 1]$ $-\frac{1}{2}e^{5} + 2e^{4} + \frac{3}{2}e^{3} - 10e^{2} + 3$
67 $[67, 67, -w^{3} + w^{2} + 6w - 5]$ $-e^{3} - 2e^{2} + 7e + 8$
81 $[81, 3, -3]$ $\phantom{-}e^{5} - 2e^{4} - 9e^{3} + 12e^{2} + 18e - 2$
83 $[83, 83, -2w^{3} - w^{2} + 9w + 7]$ $-\frac{1}{2}e^{5} + e^{4} + \frac{5}{2}e^{3} - 8e^{2} + 2e + 11$
83 $[83, 83, 4w^{3} - 18w - 1]$ $\phantom{-}\frac{3}{2}e^{5} - 3e^{4} - \frac{21}{2}e^{3} + 19e^{2} + 12e - 15$
89 $[89, 89, -2w^{3} + 10w + 1]$ $-\frac{1}{2}e^{5} + 2e^{4} + \frac{1}{2}e^{3} - 11e^{2} + 10e + 9$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2,2,w]$ $1$
13 $[13,13,-w^{2}+w+3]$ $1$