Properties

Label 4.4.10304.1-23.1-e
Base field 4.4.10304.1
Weight $[2, 2, 2, 2]$
Level norm $23$
Level $[23, 23, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 3w - 3]$
Dimension $10$
CM no
Base change no

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Base field 4.4.10304.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 7x^{2} + 8x + 8\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[23, 23, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 3w - 3]$
Dimension: $10$
CM: no
Base change: no
Newspace dimension: $30$

Hecke eigenvalues ($q$-expansion)

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

\(x^{10} - 17x^{8} + 101x^{6} - 251x^{4} + 230x^{2} - 32\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, \frac{1}{2}w^{2} + \frac{1}{2}w - 2]$ $\phantom{-}e$
2 $[2, 2, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w + 1]$ $-\frac{1}{8}e^{9} + \frac{15}{8}e^{7} - \frac{73}{8}e^{5} + \frac{133}{8}e^{3} - \frac{37}{4}e$
7 $[7, 7, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + w - 3]$ $-\frac{1}{4}e^{7} + 3e^{5} - \frac{37}{4}e^{3} + \frac{11}{2}e$
23 $[23, 23, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 3w - 3]$ $-1$
25 $[25, 5, -\frac{1}{2}w^{3} + \frac{9}{2}w + 1]$ $\phantom{-}e^{3} - 7e$
25 $[25, 5, -\frac{1}{2}w^{3} + \frac{5}{2}w - 1]$ $-\frac{1}{2}e^{9} + \frac{15}{2}e^{7} - \frac{73}{2}e^{5} + \frac{131}{2}e^{3} - 32e$
31 $[31, 31, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 2w - 1]$ $-\frac{1}{4}e^{9} + \frac{15}{4}e^{7} - \frac{73}{4}e^{5} + \frac{133}{4}e^{3} - \frac{37}{2}e$
31 $[31, 31, \frac{1}{2}w^{3} - w^{2} - \frac{3}{2}w + 1]$ $\phantom{-}\frac{1}{4}e^{9} - \frac{15}{4}e^{7} + \frac{69}{4}e^{5} - \frac{93}{4}e^{3} - \frac{3}{2}e$
41 $[41, 41, \frac{3}{2}w^{3} - w^{2} - \frac{21}{2}w - 5]$ $\phantom{-}\frac{1}{2}e^{7} - 7e^{5} + \frac{57}{2}e^{3} - 30e$
41 $[41, 41, \frac{1}{2}w^{3} - 2w^{2} - \frac{5}{2}w + 7]$ $\phantom{-}\frac{1}{4}e^{9} - \frac{15}{4}e^{7} + \frac{73}{4}e^{5} - \frac{133}{4}e^{3} + \frac{43}{2}e$
47 $[47, 47, -w^{2} - w + 5]$ $\phantom{-}\frac{1}{2}e^{8} - 7e^{6} + \frac{59}{2}e^{4} - 35e^{2} - 8$
47 $[47, 47, -w^{3} + \frac{1}{2}w^{2} + \frac{13}{2}w + 5]$ $-\frac{1}{2}e^{8} + 7e^{6} - \frac{61}{2}e^{4} + 45e^{2} - 8$
49 $[49, 7, \frac{1}{2}w^{2} - \frac{1}{2}w - 5]$ $-\frac{1}{4}e^{8} + 3e^{6} - \frac{37}{4}e^{4} + \frac{3}{2}e^{2} + 12$
73 $[73, 73, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 3]$ $\phantom{-}e^{5} - 10e^{3} + 21e$
73 $[73, 73, \frac{1}{2}w^{3} - w^{2} - \frac{7}{2}w + 1]$ $\phantom{-}\frac{1}{4}e^{9} - \frac{15}{4}e^{7} + \frac{73}{4}e^{5} - \frac{121}{4}e^{3} + \frac{7}{2}e$
79 $[79, 79, w^{2} - 3w + 1]$ $-\frac{1}{4}e^{9} + \frac{13}{4}e^{7} - \frac{49}{4}e^{5} + \frac{51}{4}e^{3} + \frac{1}{2}e$
79 $[79, 79, w^{2} + w - 1]$ $-\frac{1}{4}e^{9} + \frac{13}{4}e^{7} - \frac{49}{4}e^{5} + \frac{55}{4}e^{3} - \frac{11}{2}e$
81 $[81, 3, -3]$ $\phantom{-}\frac{1}{2}e^{8} - 7e^{6} + \frac{59}{2}e^{4} - 35e^{2} - 10$
89 $[89, 89, -\frac{1}{2}w^{3} + 3w^{2} + \frac{7}{2}w - 11]$ $-\frac{1}{4}e^{9} + \frac{5}{2}e^{7} - \frac{13}{4}e^{5} - 16e^{3} + 20e$
89 $[89, 89, \frac{1}{2}w^{3} - \frac{5}{2}w - 3]$ $\phantom{-}\frac{3}{4}e^{8} - 10e^{6} + \frac{159}{4}e^{4} - \frac{99}{2}e^{2} + 14$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$23$ $[23, 23, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 3w - 3]$ $1$