Properties

Label 3.3.1076.1-13.3-a
Base field 3.3.1076.1
Weight $[2, 2, 2]$
Level norm $13$
Level $[13, 13, w - 1]$
Dimension $10$
CM no
Base change no

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Base field 3.3.1076.1

Generator \(w\), with minimal polynomial \(x^{3} - 8x - 6\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[13, 13, w - 1]$
Dimension: $10$
CM: no
Base change: no
Newspace dimension: $20$

Hecke eigenvalues ($q$-expansion)

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

\(x^{10} - 2x^{9} - 11x^{8} + 20x^{7} + 37x^{6} - 54x^{5} - 49x^{4} + 44x^{3} + 20x^{2} - 8x - 3\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $\phantom{-}e$
3 $[3, 3, -w^{2} + 2w + 3]$ $-\frac{8}{5}e^{9} + \frac{17}{5}e^{8} + \frac{84}{5}e^{7} - \frac{168}{5}e^{6} - 51e^{5} + \frac{442}{5}e^{4} + \frac{273}{5}e^{3} - \frac{343}{5}e^{2} - \frac{39}{5}e + \frac{52}{5}$
7 $[7, 7, -2w^{2} + 5w + 5]$ $-8e^{9} + 19e^{8} + 81e^{7} - 191e^{6} - 225e^{5} + 522e^{4} + 195e^{3} - 436e^{2} + 6e + 65$
9 $[9, 3, -w^{2} + 5]$ $\phantom{-}\frac{1}{5}e^{9} - \frac{4}{5}e^{8} - \frac{8}{5}e^{7} + \frac{46}{5}e^{6} + e^{5} - \frac{164}{5}e^{4} + \frac{44}{5}e^{3} + \frac{211}{5}e^{2} - \frac{42}{5}e - \frac{44}{5}$
13 $[13, 13, -w^{2} + 3w + 1]$ $\phantom{-}\frac{23}{5}e^{9} - \frac{57}{5}e^{8} - \frac{229}{5}e^{7} + \frac{573}{5}e^{6} + 123e^{5} - \frac{1567}{5}e^{4} - \frac{513}{5}e^{3} + \frac{1323}{5}e^{2} - \frac{11}{5}e - \frac{202}{5}$
13 $[13, 13, 2w + 5]$ $-\frac{49}{5}e^{9} + \frac{116}{5}e^{8} + \frac{497}{5}e^{7} - \frac{1164}{5}e^{6} - 278e^{5} + \frac{3166}{5}e^{4} + \frac{1239}{5}e^{3} - \frac{2614}{5}e^{2} + \frac{3}{5}e + \frac{386}{5}$
13 $[13, 13, w - 1]$ $\phantom{-}1$
17 $[17, 17, w^{2} - w - 5]$ $-\frac{16}{5}e^{9} + \frac{39}{5}e^{8} + \frac{163}{5}e^{7} - \frac{396}{5}e^{6} - 92e^{5} + \frac{1104}{5}e^{4} + \frac{416}{5}e^{3} - \frac{951}{5}e^{2} - \frac{8}{5}e + \frac{159}{5}$
19 $[19, 19, w^{2} - 2w - 5]$ $-\frac{28}{5}e^{9} + \frac{72}{5}e^{8} + \frac{274}{5}e^{7} - \frac{728}{5}e^{6} - 140e^{5} + \frac{2017}{5}e^{4} + \frac{488}{5}e^{3} - \frac{1743}{5}e^{2} + \frac{116}{5}e + \frac{272}{5}$
29 $[29, 29, w^{2} - 7]$ $\phantom{-}\frac{43}{5}e^{9} - \frac{97}{5}e^{8} - \frac{439}{5}e^{7} + \frac{958}{5}e^{6} + 250e^{5} - \frac{2517}{5}e^{4} - \frac{1178}{5}e^{3} + \frac{1953}{5}e^{2} + \frac{64}{5}e - \frac{267}{5}$
31 $[31, 31, 2w^{2} - 3w - 11]$ $-\frac{53}{5}e^{9} + \frac{122}{5}e^{8} + \frac{544}{5}e^{7} - \frac{1218}{5}e^{6} - 313e^{5} + \frac{3272}{5}e^{4} + \frac{1483}{5}e^{3} - \frac{2618}{5}e^{2} - \frac{59}{5}e + \frac{362}{5}$
49 $[49, 7, -2w^{2} - 4w + 1]$ $\phantom{-}7e^{9} - 17e^{8} - 70e^{7} + 169e^{6} + 190e^{5} - 450e^{4} - 161e^{3} + 357e^{2} - 7e - 52$
59 $[59, 59, w^{2} - 2w - 11]$ $\phantom{-}\frac{124}{5}e^{9} - \frac{301}{5}e^{8} - \frac{1242}{5}e^{7} + \frac{3014}{5}e^{6} + 676e^{5} - \frac{8166}{5}e^{4} - \frac{2874}{5}e^{3} + \frac{6729}{5}e^{2} - \frac{78}{5}e - \frac{996}{5}$
71 $[71, 71, -2w + 7]$ $\phantom{-}\frac{158}{5}e^{9} - \frac{382}{5}e^{8} - \frac{1584}{5}e^{7} + \frac{3828}{5}e^{6} + 863e^{5} - \frac{10392}{5}e^{4} - \frac{3658}{5}e^{3} + \frac{8608}{5}e^{2} - \frac{121}{5}e - \frac{1272}{5}$
73 $[73, 73, w^{2} - 3w - 13]$ $\phantom{-}\frac{57}{5}e^{9} - \frac{138}{5}e^{8} - \frac{571}{5}e^{7} + \frac{1382}{5}e^{6} + 309e^{5} - \frac{3738}{5}e^{4} - \frac{1252}{5}e^{3} + \frac{3042}{5}e^{2} - \frac{129}{5}e - \frac{428}{5}$
73 $[73, 73, 2w^{2} - 2w - 17]$ $\phantom{-}\frac{78}{5}e^{9} - \frac{182}{5}e^{8} - \frac{794}{5}e^{7} + \frac{1818}{5}e^{6} + 448e^{5} - \frac{4887}{5}e^{4} - \frac{2038}{5}e^{3} + \frac{3908}{5}e^{2} + \frac{24}{5}e - \frac{532}{5}$
73 $[73, 73, -w^{2} - 4w - 5]$ $\phantom{-}\frac{42}{5}e^{9} - \frac{103}{5}e^{8} - \frac{416}{5}e^{7} + \frac{1032}{5}e^{6} + 220e^{5} - \frac{2803}{5}e^{4} - \frac{872}{5}e^{3} + \frac{2327}{5}e^{2} - \frac{44}{5}e - \frac{343}{5}$
79 $[79, 79, 2w - 1]$ $\phantom{-}\frac{81}{5}e^{9} - \frac{189}{5}e^{8} - \frac{823}{5}e^{7} + \frac{1891}{5}e^{6} + 462e^{5} - \frac{5109}{5}e^{4} - \frac{2071}{5}e^{3} + \frac{4146}{5}e^{2} + \frac{8}{5}e - \frac{569}{5}$
79 $[79, 79, w^{2} + w - 5]$ $-\frac{88}{5}e^{9} + \frac{217}{5}e^{8} + \frac{874}{5}e^{7} - \frac{2178}{5}e^{6} - 464e^{5} + \frac{5937}{5}e^{4} + \frac{1818}{5}e^{3} - \frac{4968}{5}e^{2} + \frac{171}{5}e + \frac{752}{5}$
79 $[79, 79, w - 5]$ $\phantom{-}26e^{9} - 62e^{8} - 262e^{7} + 620e^{6} + 722e^{5} - 1675e^{4} - 624e^{3} + 1372e^{2} - 22e - 200$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13, 13, w - 1]$ $-1$