Properties

Label 4.4.19225.1-16.1-g
Base field 4.4.19225.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 2, 2]$
Dimension $7$
CM no
Base change yes

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Base field 4.4.19225.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 15x^{2} + 2x + 44\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[16, 2, 2]$
Dimension: $7$
CM: no
Base change: yes
Newspace dimension: $29$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{7} - 5x^{6} - 39x^{5} + 171x^{4} + 315x^{3} - 663x^{2} - 1105x - 250\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, w + 2]$ $-1$
4 $[4, 2, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{9}{2}w - 10]$ $-1$
9 $[9, 3, \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - \frac{5}{2}w + 17]$ $\phantom{-}e$
9 $[9, 3, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 28]$ $\phantom{-}e$
11 $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 11]$ $\phantom{-}\frac{1}{135}e^{6} - \frac{1}{9}e^{5} - \frac{8}{45}e^{4} + \frac{167}{45}e^{3} - \frac{7}{9}e^{2} - \frac{172}{15}e - \frac{122}{27}$
11 $[11, 11, -w - 3]$ $\phantom{-}\frac{1}{135}e^{6} - \frac{1}{9}e^{5} - \frac{8}{45}e^{4} + \frac{167}{45}e^{3} - \frac{7}{9}e^{2} - \frac{172}{15}e - \frac{122}{27}$
25 $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ $-\frac{2}{135}e^{6} + \frac{1}{45}e^{5} + \frac{22}{45}e^{4} - \frac{22}{45}e^{3} - \frac{47}{45}e^{2} - 4e - \frac{8}{27}$
29 $[29, 29, w + 1]$ $\phantom{-}\frac{4}{135}e^{6} - \frac{7}{45}e^{5} - \frac{13}{15}e^{4} + \frac{26}{5}e^{3} - \frac{7}{15}e^{2} - \frac{154}{9}e - \frac{80}{27}$
29 $[29, 29, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 9]$ $\phantom{-}\frac{4}{135}e^{6} - \frac{7}{45}e^{5} - \frac{13}{15}e^{4} + \frac{26}{5}e^{3} - \frac{7}{15}e^{2} - \frac{154}{9}e - \frac{80}{27}$
31 $[31, 31, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 16]$ $-\frac{2}{135}e^{6} + \frac{1}{5}e^{5} + \frac{4}{9}e^{4} - \frac{311}{45}e^{3} - \frac{43}{45}e^{2} + \frac{1199}{45}e + \frac{358}{27}$
31 $[31, 31, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 5]$ $\phantom{-}\frac{4}{135}e^{6} - \frac{4}{45}e^{5} - \frac{17}{15}e^{4} + 3e^{3} + \frac{116}{15}e^{2} - \frac{521}{45}e - \frac{332}{27}$
31 $[31, 31, -w + 3]$ $\phantom{-}\frac{4}{135}e^{6} - \frac{4}{45}e^{5} - \frac{17}{15}e^{4} + 3e^{3} + \frac{116}{15}e^{2} - \frac{521}{45}e - \frac{332}{27}$
31 $[31, 31, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 29]$ $-\frac{2}{135}e^{6} + \frac{1}{5}e^{5} + \frac{4}{9}e^{4} - \frac{311}{45}e^{3} - \frac{43}{45}e^{2} + \frac{1199}{45}e + \frac{358}{27}$
59 $[59, 59, 2w^{2} - w - 13]$ $\phantom{-}\frac{1}{135}e^{6} - \frac{1}{15}e^{5} - \frac{16}{45}e^{4} + \frac{106}{45}e^{3} + \frac{206}{45}e^{2} - \frac{95}{9}e - \frac{440}{27}$
59 $[59, 59, \frac{9}{2}w^{3} - \frac{31}{2}w^{2} - \frac{61}{2}w + 85]$ $\phantom{-}\frac{1}{135}e^{6} - \frac{1}{15}e^{5} - \frac{16}{45}e^{4} + \frac{106}{45}e^{3} + \frac{206}{45}e^{2} - \frac{95}{9}e - \frac{440}{27}$
61 $[61, 61, 2w^{3} - 6w^{2} - 15w + 31]$ $-\frac{8}{135}e^{6} + \frac{4}{15}e^{5} + \frac{86}{45}e^{4} - \frac{392}{45}e^{3} - \frac{214}{45}e^{2} + \frac{1214}{45}e + \frac{298}{27}$
61 $[61, 61, -\frac{3}{2}w^{3} + \frac{11}{2}w^{2} + \frac{21}{2}w - 34]$ $-\frac{8}{135}e^{6} + \frac{4}{15}e^{5} + \frac{86}{45}e^{4} - \frac{392}{45}e^{3} - \frac{214}{45}e^{2} + \frac{1214}{45}e + \frac{298}{27}$
71 $[71, 71, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 32]$ $\phantom{-}\frac{1}{135}e^{6} + \frac{1}{9}e^{5} - \frac{2}{5}e^{4} - \frac{61}{15}e^{3} + \frac{14}{3}e^{2} + \frac{904}{45}e + \frac{88}{27}$
71 $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 13]$ $\phantom{-}\frac{1}{135}e^{6} + \frac{1}{9}e^{5} - \frac{2}{5}e^{4} - \frac{61}{15}e^{3} + \frac{14}{3}e^{2} + \frac{904}{45}e + \frac{88}{27}$
79 $[79, 79, -3w^{3} + 10w^{2} + 19w - 51]$ $\phantom{-}\frac{1}{45}e^{6} - \frac{4}{45}e^{5} - \frac{38}{45}e^{4} + \frac{128}{45}e^{3} + \frac{253}{45}e^{2} - \frac{59}{9}e - 10$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, w + 2]$ $1$
$4$ $[4, 2, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{9}{2}w - 10]$ $1$