Properties

Label 3.3.1257.1-13.1-a
Base field 3.3.1257.1
Weight $[2, 2, 2]$
Level norm $13$
Level $[13, 13, w + 2]$
Dimension $10$
CM no
Base change no

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Base field 3.3.1257.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x + 9\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[13, 13, w + 2]$
Dimension: $10$
CM: no
Base change: no
Newspace dimension: $24$

Hecke eigenvalues ($q$-expansion)

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

\(x^{10} - 19x^{8} + 112x^{6} - 264x^{4} + 243x^{2} - 72\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w + 3]$ $-\frac{5}{51}e^{8} + \frac{91}{51}e^{6} - \frac{159}{17}e^{4} + 16e^{2} - \frac{116}{17}$
3 $[3, 3, w - 2]$ $\phantom{-}e$
5 $[5, 5, w^{2} + w - 5]$ $-\frac{2}{17}e^{9} + \frac{116}{51}e^{7} - \frac{688}{51}e^{5} + 29e^{3} - \frac{299}{17}e$
8 $[8, 2, 2]$ $\phantom{-}\frac{1}{17}e^{8} - \frac{58}{51}e^{6} + \frac{344}{51}e^{4} - 15e^{2} + \frac{141}{17}$
13 $[13, 13, w + 2]$ $-1$
13 $[13, 13, -2w + 5]$ $\phantom{-}\frac{8}{51}e^{9} - \frac{149}{51}e^{7} + \frac{821}{51}e^{5} - 30e^{3} + \frac{206}{17}e$
13 $[13, 13, -w^{2} - w + 4]$ $-\frac{8}{51}e^{9} + \frac{149}{51}e^{7} - \frac{821}{51}e^{5} + 30e^{3} - \frac{206}{17}e$
19 $[19, 19, -w^{2} + w + 4]$ $\phantom{-}\frac{22}{51}e^{9} - \frac{397}{51}e^{7} + \frac{2092}{51}e^{5} - 77e^{3} + \frac{660}{17}e$
23 $[23, 23, -w^{2} - w + 7]$ $\phantom{-}\frac{2}{51}e^{9} - \frac{11}{17}e^{7} + \frac{133}{51}e^{5} - e^{3} - \frac{76}{17}e$
25 $[25, 5, w^{2} - 2w - 1]$ $-\frac{13}{51}e^{9} + \frac{223}{51}e^{7} - \frac{1060}{51}e^{5} + 33e^{3} - \frac{186}{17}e$
29 $[29, 29, w^{2} - 5]$ $\phantom{-}\frac{16}{51}e^{9} - \frac{281}{51}e^{7} + \frac{468}{17}e^{5} - 48e^{3} + \frac{378}{17}e$
31 $[31, 31, w^{2} + w - 8]$ $\phantom{-}\frac{3}{17}e^{9} - \frac{58}{17}e^{7} + \frac{344}{17}e^{5} - 44e^{3} + \frac{491}{17}e$
41 $[41, 41, w^{2} + w - 11]$ $\phantom{-}\frac{1}{51}e^{8} + \frac{3}{17}e^{6} - \frac{316}{51}e^{4} + 24e^{2} - \frac{378}{17}$
47 $[47, 47, w^{2} + 2w - 1]$ $-\frac{43}{51}e^{8} + \frac{752}{51}e^{6} - \frac{1245}{17}e^{4} + 127e^{2} - \frac{984}{17}$
59 $[59, 59, w^{2} + w - 1]$ $\phantom{-}\frac{19}{51}e^{8} - \frac{113}{17}e^{6} + \frac{1748}{51}e^{4} - 63e^{2} + \frac{468}{17}$
61 $[61, 61, -w^{2} + 5w - 7]$ $\phantom{-}\frac{15}{17}e^{8} - \frac{256}{17}e^{6} + \frac{1210}{17}e^{4} - 115e^{2} + \frac{874}{17}$
67 $[67, 67, 2w^{2} - 13]$ $\phantom{-}\frac{15}{17}e^{9} - \frac{273}{17}e^{7} + \frac{1465}{17}e^{5} - 166e^{3} + \frac{1418}{17}e$
89 $[89, 89, -2w^{2} + w + 20]$ $-\frac{11}{51}e^{8} + \frac{69}{17}e^{6} - \frac{1216}{51}e^{4} + 58e^{2} - \frac{738}{17}$
89 $[89, 89, 5w^{2} + 8w - 19]$ $-\frac{7}{51}e^{9} + \frac{124}{51}e^{7} - \frac{610}{51}e^{5} + 17e^{3} + \frac{11}{17}e$
89 $[89, 89, w^{2} + 2w - 7]$ $-\frac{22}{51}e^{9} + \frac{397}{51}e^{7} - \frac{2092}{51}e^{5} + 76e^{3} - \frac{592}{17}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13, 13, w + 2]$ $1$