Properties

Label 4.4.9792.1-28.2-d
Base field 4.4.9792.1
Weight $[2, 2, 2, 2]$
Level norm $28$
Level $[28,14,2w^{3} - 7w^{2} - 5w + 13]$
Dimension $8$
CM no
Base change no

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Base field 4.4.9792.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[28,14,2w^{3} - 7w^{2} - 5w + 13]$
Dimension: $8$
CM: no
Base change: no
Newspace dimension: $16$

Hecke eigenvalues ($q$-expansion)

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

\(x^{8} - 41x^{6} + 526x^{4} - 2336x^{2} + 2312\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, w^{3} - 3w^{2} - 3w + 4]$ $\phantom{-}1$
7 $[7, 7, w]$ $\phantom{-}\frac{3}{358}e^{6} - \frac{73}{358}e^{4} + \frac{121}{179}e^{2} + \frac{422}{179}$
7 $[7, 7, w^{3} - 3w^{2} - 4w + 5]$ $\phantom{-}1$
9 $[9, 3, w^{3} - 4w^{2} - w + 9]$ $\phantom{-}e$
17 $[17, 17, 2w^{3} - 6w^{2} - 7w + 8]$ $-\frac{49}{12172}e^{7} + \frac{1431}{12172}e^{5} - \frac{1913}{3043}e^{3} - \frac{3327}{3043}e$
17 $[17, 17, -w^{3} + 3w^{2} + 4w - 3]$ $-\frac{49}{12172}e^{7} + \frac{1431}{12172}e^{5} - \frac{1913}{3043}e^{3} - \frac{3327}{3043}e$
17 $[17, 17, -w + 2]$ $\phantom{-}\frac{45}{6086}e^{7} - \frac{1811}{6086}e^{5} + \frac{10407}{3043}e^{3} - \frac{30902}{3043}e$
23 $[23, 23, 2w^{3} - 7w^{2} - 4w + 12]$ $\phantom{-}\frac{47}{12172}e^{7} - \frac{1621}{12172}e^{5} + \frac{4319}{3043}e^{3} - \frac{18234}{3043}e$
23 $[23, 23, -w^{2} + 2w + 3]$ $\phantom{-}\frac{1}{6086}e^{7} + \frac{95}{6086}e^{5} - \frac{2406}{3043}e^{3} + \frac{21561}{3043}e$
31 $[31, 31, -2w^{3} + 7w^{2} + 5w - 12]$ $-\frac{7}{179}e^{6} + \frac{230}{179}e^{4} - \frac{1937}{179}e^{2} + \frac{3878}{179}$
31 $[31, 31, -w^{3} + 4w^{2} + 2w - 8]$ $\phantom{-}\frac{11}{358}e^{6} - \frac{387}{358}e^{4} + \frac{1816}{179}e^{2} - \frac{3226}{179}$
41 $[41, 41, 3w^{3} - 10w^{2} - 7w + 16]$ $-\frac{93}{6086}e^{7} + \frac{3337}{6086}e^{5} - \frac{16639}{3043}e^{3} + \frac{45809}{3043}e$
41 $[41, 41, 2w^{3} - 7w^{2} - 5w + 10]$ $-\frac{47}{12172}e^{7} + \frac{1621}{12172}e^{5} - \frac{4319}{3043}e^{3} + \frac{18234}{3043}e$
49 $[49, 7, 2w^{3} - 6w^{2} - 6w + 9]$ $\phantom{-}\frac{3}{358}e^{6} - \frac{73}{358}e^{4} - \frac{58}{179}e^{2} + \frac{2212}{179}$
71 $[71, 71, w^{2} - 2w - 2]$ $-\frac{141}{6086}e^{7} + \frac{4863}{6086}e^{5} - \frac{22871}{3043}e^{3} + \frac{51587}{3043}e$
71 $[71, 71, 2w^{3} - 7w^{2} - 4w + 13]$ $\phantom{-}\frac{24}{3043}e^{7} - \frac{763}{3043}e^{5} + \frac{6232}{3043}e^{3} - \frac{14907}{3043}e$
73 $[73, 73, 3w^{3} - 11w^{2} - 5w + 19]$ $\phantom{-}\frac{11}{358}e^{6} - \frac{387}{358}e^{4} + \frac{1637}{179}e^{2} - \frac{1436}{179}$
73 $[73, 73, -4w^{3} + 13w^{2} + 10w - 17]$ $\phantom{-}\frac{11}{358}e^{6} - \frac{387}{358}e^{4} + \frac{1637}{179}e^{2} - \frac{1436}{179}$
79 $[79, 79, 3w^{3} - 9w^{2} - 10w + 13]$ $\phantom{-}\frac{3}{179}e^{6} - \frac{73}{179}e^{4} + \frac{242}{179}e^{2} + \frac{486}{179}$
79 $[79, 79, -2w^{3} + 6w^{2} + 5w - 8]$ $\phantom{-}\frac{3}{179}e^{6} - \frac{73}{179}e^{4} + \frac{242}{179}e^{2} + \frac{486}{179}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4,2,w^{3} - 3w^{2} - 3w + 4]$ $-1$
$7$ $[7,7,w^{3} - 3w^{2} - 4w + 5]$ $-1$