Properties

Base field 4.4.18625.1
Weight [2, 2, 2, 2]
Level norm 16
Level $[16, 2, 2]$
Label 4.4.18625.1-16.1-c
Dimension 11
CM no
Base change yes

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Base field 4.4.18625.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 14x^{2} + 9x + 41\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[16, 2, 2]$
Label 4.4.18625.1-16.1-c
Dimension 11
Is CM no
Is base change yes
Parent newspace dimension 30

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{11} \) \(\mathstrut -\mathstrut x^{10} \) \(\mathstrut -\mathstrut 53x^{9} \) \(\mathstrut +\mathstrut 46x^{8} \) \(\mathstrut +\mathstrut 1006x^{7} \) \(\mathstrut -\mathstrut 720x^{6} \) \(\mathstrut -\mathstrut 8252x^{5} \) \(\mathstrut +\mathstrut 4144x^{4} \) \(\mathstrut +\mathstrut 28752x^{3} \) \(\mathstrut -\mathstrut 3520x^{2} \) \(\mathstrut -\mathstrut 35840x \) \(\mathstrut -\mathstrut 15360\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, \frac{1}{6}w^{3} - \frac{7}{3}w - \frac{17}{6}]$ $\phantom{-}1$
4 $[4, 2, w - 3]$ $\phantom{-}1$
5 $[5, 5, -\frac{1}{6}w^{3} + w^{2} + \frac{1}{3}w - \frac{25}{6}]$ $\phantom{-}e$
9 $[9, 3, \frac{1}{6}w^{3} - \frac{7}{3}w + \frac{13}{6}]$ $...$
9 $[9, 3, -w - 2]$ $...$
11 $[11, 11, -\frac{1}{6}w^{3} + \frac{7}{3}w + \frac{11}{6}]$ $...$
11 $[11, 11, -w + 2]$ $...$
41 $[41, 41, -w]$ $...$
41 $[41, 41, \frac{1}{6}w^{3} - \frac{7}{3}w + \frac{1}{6}]$ $...$
59 $[59, 59, -\frac{1}{6}w^{3} + \frac{1}{3}w + \frac{23}{6}]$ $...$
59 $[59, 59, -\frac{1}{3}w^{3} + \frac{11}{3}w + \frac{11}{3}]$ $...$
61 $[61, 61, -\frac{5}{3}w^{3} - 3w^{2} + \frac{46}{3}w + \frac{79}{3}]$ $...$
61 $[61, 61, \frac{5}{6}w^{3} + w^{2} - \frac{23}{3}w - \frac{55}{6}]$ $...$
61 $[61, 61, w^{3} + 2w^{2} - 9w - 17]$ $...$
61 $[61, 61, -\frac{1}{6}w^{3} + \frac{10}{3}w + \frac{35}{6}]$ $...$
71 $[71, 71, -\frac{1}{2}w^{3} + 2w^{2} + 4w - \frac{33}{2}]$ $...$
71 $[71, 71, \frac{1}{6}w^{3} - w^{2} - \frac{4}{3}w + \frac{67}{6}]$ $...$
79 $[79, 79, \frac{1}{2}w^{3} - 3w + \frac{1}{2}]$ $...$
79 $[79, 79, -\frac{2}{3}w^{3} + \frac{19}{3}w - \frac{2}{3}]$ $...$
89 $[89, 89, \frac{1}{2}w^{3} + w^{2} - 5w - \frac{15}{2}]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, \frac{1}{6}w^{3} - \frac{7}{3}w - \frac{17}{6}]$ $-1$
4 $[4, 2, w - 3]$ $-1$