Properties

Base field 3.3.1129.1
Weight [2, 2, 2]
Level norm 19
Level $[19, 19, -w^{2} - w + 4]$
Label 3.3.1129.1-19.1-d
Dimension 10
CM no
Base change no

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Base field 3.3.1129.1

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

Form

Weight [2, 2, 2]
Level $[19, 19, -w^{2} - w + 4]$
Label 3.3.1129.1-19.1-d
Dimension 10
Is CM no
Is base change no
Parent newspace dimension 36

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{10} \) \(\mathstrut -\mathstrut 24x^{8} \) \(\mathstrut +\mathstrut 202x^{6} \) \(\mathstrut -\mathstrut 704x^{4} \) \(\mathstrut +\mathstrut 864x^{2} \) \(\mathstrut -\mathstrut 128\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}\frac{1}{32}e^{8} - \frac{5}{8}e^{6} + \frac{61}{16}e^{4} - \frac{27}{4}e^{2}$
3 $[3, 3, w + 1]$ $\phantom{-}e$
3 $[3, 3, w + 2]$ $\phantom{-}\frac{1}{64}e^{9} - \frac{5}{16}e^{7} + \frac{61}{32}e^{5} - \frac{27}{8}e^{3} - e$
8 $[8, 2, 2]$ $-\frac{1}{8}e^{8} + \frac{9}{4}e^{6} - \frac{47}{4}e^{4} + \frac{33}{2}e^{2} + 2$
11 $[11, 11, -w^{2} + 5]$ $-\frac{1}{64}e^{9} + \frac{5}{16}e^{7} - \frac{69}{32}e^{5} + \frac{51}{8}e^{3} - \frac{13}{2}e$
13 $[13, 13, w^{2} - w - 7]$ $\phantom{-}\frac{1}{8}e^{7} - \frac{9}{4}e^{5} + \frac{45}{4}e^{3} - \frac{27}{2}e$
17 $[17, 17, -w^{2} + w + 4]$ $\phantom{-}\frac{1}{16}e^{9} - \frac{9}{8}e^{7} + \frac{45}{8}e^{5} - \frac{21}{4}e^{3} - 9e$
19 $[19, 19, -w^{2} - w + 4]$ $\phantom{-}1$
29 $[29, 29, 2w^{2} - 2w - 11]$ $-\frac{3}{32}e^{9} + \frac{15}{8}e^{7} - \frac{195}{16}e^{5} + \frac{121}{4}e^{3} - \frac{51}{2}e$
31 $[31, 31, w^{2} - 2w - 4]$ $\phantom{-}\frac{1}{16}e^{7} - \frac{5}{4}e^{5} + \frac{61}{8}e^{3} - \frac{23}{2}e$
37 $[37, 37, -2w^{2} + 3w + 7]$ $-\frac{3}{32}e^{9} + 2e^{7} - \frac{223}{16}e^{5} + \frac{71}{2}e^{3} - 23e$
41 $[41, 41, w^{2} - 2]$ $\phantom{-}\frac{5}{64}e^{9} - \frac{23}{16}e^{7} + \frac{249}{32}e^{5} - \frac{85}{8}e^{3} - \frac{19}{2}e$
59 $[59, 59, 2w^{2} - 13]$ $\phantom{-}\frac{1}{4}e^{6} - 4e^{4} + \frac{33}{2}e^{2} - 6$
61 $[61, 61, w^{2} + w - 10]$ $-2e^{2} + 6$
67 $[67, 67, 2w^{2} - w - 11]$ $\phantom{-}\frac{1}{4}e^{7} - \frac{9}{2}e^{5} + \frac{45}{2}e^{3} - 28e$
73 $[73, 73, -w^{2} - 1]$ $-\frac{5}{16}e^{8} + \frac{23}{4}e^{6} - \frac{249}{8}e^{4} + \frac{101}{2}e^{2} - 18$
83 $[83, 83, w^{2} - w - 10]$ $-\frac{5}{16}e^{8} + 6e^{6} - \frac{281}{8}e^{4} + 66e^{2} - 14$
89 $[89, 89, -w^{2} + 4w - 2]$ $-\frac{3}{16}e^{8} + \frac{7}{2}e^{6} - \frac{155}{8}e^{4} + 32e^{2} - 7$
97 $[97, 97, w^{2} - 2w - 7]$ $\phantom{-}\frac{1}{8}e^{7} - \frac{3}{2}e^{5} + \frac{5}{4}e^{3} + 14e$
97 $[97, 97, -w^{2} - 4w - 5]$ $-\frac{3}{16}e^{8} + \frac{13}{4}e^{6} - \frac{127}{8}e^{4} + \frac{45}{2}e^{2} - 16$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
19 $[19, 19, -w^{2} - w + 4]$ $-1$