Properties

Base field 3.3.316.1
Weight [2, 2, 2]
Level norm 27
Level $[27, 3, 3]$
Label 3.3.316.1-27.1-b
Dimension 8
CM no
Base change no

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Base field 3.3.316.1

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

Form

Weight [2, 2, 2]
Level $[27, 3, 3]$
Label 3.3.316.1-27.1-b
Dimension 8
Is CM no
Is base change no
Parent newspace dimension 10

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} \) \(\mathstrut -\mathstrut 4x^{7} \) \(\mathstrut -\mathstrut 6x^{6} \) \(\mathstrut +\mathstrut 37x^{5} \) \(\mathstrut -\mathstrut 8x^{4} \) \(\mathstrut -\mathstrut 88x^{3} \) \(\mathstrut +\mathstrut 62x^{2} \) \(\mathstrut +\mathstrut 40x \) \(\mathstrut -\mathstrut 32\)

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Norm Prime Eigenvalue
2 $[2, 2, -w]$ $\phantom{-}e$
2 $[2, 2, w - 1]$ $\phantom{-}\frac{1}{4}e^{7} - \frac{1}{2}e^{6} - \frac{5}{2}e^{5} + \frac{17}{4}e^{4} + \frac{13}{2}e^{3} - 8e^{2} - \frac{5}{2}e + 1$
11 $[11, 11, w^{2} - w - 1]$ $\phantom{-}e^{7} - 3e^{6} - 9e^{5} + 27e^{4} + 20e^{3} - 60e^{2} - 4e + 24$
17 $[17, 17, -w^{2} - w + 3]$ $-\frac{3}{2}e^{7} + 4e^{6} + 14e^{5} - \frac{73}{2}e^{4} - 34e^{3} + 86e^{2} + 15e - 42$
19 $[19, 19, w^{2} - w + 1]$ $-\frac{5}{2}e^{7} + \frac{13}{2}e^{6} + 24e^{5} - \frac{117}{2}e^{4} - \frac{123}{2}e^{3} + 131e^{2} + 29e - 54$
23 $[23, 23, 2w - 3]$ $-e^{7} + 3e^{6} + 9e^{5} - 28e^{4} - 19e^{3} + 66e^{2} - 28$
27 $[27, 3, 3]$ $\phantom{-}1$
29 $[29, 29, 2w + 1]$ $-\frac{1}{2}e^{7} + e^{6} + 5e^{5} - \frac{19}{2}e^{4} - 14e^{3} + 26e^{2} + 11e - 18$
31 $[31, 31, 2w^{2} - 2w - 9]$ $-\frac{3}{2}e^{7} + \frac{7}{2}e^{6} + 15e^{5} - \frac{63}{2}e^{4} - \frac{83}{2}e^{3} + 71e^{2} + 25e - 30$
37 $[37, 37, 2w^{2} - 2w - 5]$ $\phantom{-}3e^{7} - \frac{15}{2}e^{6} - 29e^{5} + 68e^{4} + \frac{147}{2}e^{3} - 155e^{2} - 32e + 68$
41 $[41, 41, 2w^{2} - 9]$ $-2e^{7} + 5e^{6} + 20e^{5} - 45e^{4} - 56e^{3} + 100e^{2} + 34e - 38$
43 $[43, 43, w^{2} + w - 5]$ $-\frac{1}{2}e^{7} + \frac{3}{2}e^{6} + 5e^{5} - \frac{29}{2}e^{4} - \frac{27}{2}e^{3} + 35e^{2} + 5e - 14$
43 $[43, 43, -3w^{2} + w + 15]$ $\phantom{-}\frac{3}{2}e^{7} - 4e^{6} - 14e^{5} + \frac{75}{2}e^{4} + 33e^{3} - 92e^{2} - 13e + 46$
43 $[43, 43, -2w^{2} + 2w + 11]$ $\phantom{-}e^{7} - \frac{5}{2}e^{6} - 9e^{5} + 23e^{4} + \frac{37}{2}e^{3} - 56e^{2} + 2e + 28$
53 $[53, 53, w^{2} - w - 7]$ $-\frac{1}{2}e^{7} + 2e^{6} + 3e^{5} - \frac{37}{2}e^{4} + 2e^{3} + 44e^{2} - 17e - 18$
61 $[61, 61, 4w^{2} - 2w - 15]$ $\phantom{-}e^{7} - \frac{5}{2}e^{6} - 9e^{5} + 21e^{4} + \frac{39}{2}e^{3} - 41e^{2} - 4e + 12$
67 $[67, 67, -5w^{2} + 3w + 23]$ $-\frac{3}{2}e^{7} + 4e^{6} + 15e^{5} - \frac{73}{2}e^{4} - 41e^{3} + 82e^{2} + 23e - 34$
73 $[73, 73, 2w^{2} - 3]$ $-5e^{7} + 13e^{6} + 47e^{5} - 116e^{4} - 115e^{3} + 258e^{2} + 46e - 108$
73 $[73, 73, -3w^{2} - w + 7]$ $-e^{7} + \frac{5}{2}e^{6} + 10e^{5} - 22e^{4} - \frac{53}{2}e^{3} + 46e^{2} + 8e - 10$
73 $[73, 73, -6w^{2} + 4w + 25]$ $\phantom{-}2e^{7} - \frac{11}{2}e^{6} - 18e^{5} + 51e^{4} + \frac{77}{2}e^{3} - 121e^{2} - 8e + 52$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
27 $[27, 3, 3]$ $-1$