Properties

Label 4.4.8525.1-31.2-d
Base field 4.4.8525.1
Weight $[2, 2, 2, 2]$
Level norm $31$
Level $[31, 31, -w^{2} + 2w + 7]$
Dimension $8$
CM no
Base change no

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Base field 4.4.8525.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 8x^{2} + 9x + 19\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[31, 31, -w^{2} + 2w + 7]$
Dimension: $8$
CM: no
Base change: no
Newspace dimension: $18$

Hecke eigenvalues ($q$-expansion)

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

\(x^{8} + 6x^{7} - 8x^{6} - 92x^{5} - 58x^{4} + 308x^{3} + 300x^{2} - 232x - 236\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, w + 1]$ $\phantom{-}e$
5 $[5, 5, -w + 2]$ $-\frac{677}{13281}e^{7} - \frac{1196}{4427}e^{6} + \frac{2719}{4427}e^{5} + \frac{18947}{4427}e^{4} - \frac{4775}{13281}e^{3} - \frac{203453}{13281}e^{2} - \frac{40715}{13281}e + \frac{136370}{13281}$
11 $[11, 11, w^{2} - 2w - 4]$ $-\frac{707}{8854}e^{7} - \frac{9155}{26562}e^{6} + \frac{32173}{26562}e^{5} + \frac{70838}{13281}e^{4} - \frac{53146}{13281}e^{3} - \frac{244160}{13281}e^{2} + \frac{16638}{4427}e + \frac{170690}{13281}$
11 $[11, 11, -w^{2} + 3]$ $\phantom{-}\frac{677}{13281}e^{7} + \frac{1196}{4427}e^{6} - \frac{2719}{4427}e^{5} - \frac{18947}{4427}e^{4} + \frac{4775}{13281}e^{3} + \frac{203453}{13281}e^{2} + \frac{27434}{13281}e - \frac{136370}{13281}$
11 $[11, 11, w^{2} - 5]$ $\phantom{-}\frac{959}{13281}e^{7} + \frac{4154}{13281}e^{6} - \frac{29459}{26562}e^{5} - \frac{64438}{13281}e^{4} + \frac{53290}{13281}e^{3} + \frac{74542}{4427}e^{2} - \frac{73978}{13281}e - \frac{65224}{4427}$
16 $[16, 2, 2]$ $\phantom{-}\frac{640}{13281}e^{7} + \frac{941}{4427}e^{6} - \frac{3172}{4427}e^{5} - \frac{15407}{4427}e^{4} + \frac{23386}{13281}e^{3} + \frac{181858}{13281}e^{2} + \frac{21148}{13281}e - \frac{188809}{13281}$
19 $[19, 19, -w]$ $\phantom{-}\frac{25}{26562}e^{7} - \frac{67}{8854}e^{6} - \frac{1369}{8854}e^{5} - \frac{837}{4427}e^{4} + \frac{26915}{13281}e^{3} + \frac{41216}{13281}e^{2} - \frac{59974}{13281}e - \frac{66098}{13281}$
19 $[19, 19, -w + 1]$ $\phantom{-}\frac{17}{699}e^{7} + \frac{29}{233}e^{6} - \frac{119}{466}e^{5} - \frac{430}{233}e^{4} - \frac{163}{699}e^{3} + \frac{4160}{699}e^{2} + \frac{470}{699}e - \frac{4112}{699}$
31 $[31, 31, -w^{3} + 3w^{2} + 2w - 9]$ $-\frac{223}{8854}e^{7} - \frac{1472}{13281}e^{6} + \frac{11801}{26562}e^{5} + \frac{28768}{13281}e^{4} - \frac{28748}{13281}e^{3} - \frac{164062}{13281}e^{2} + \frac{16832}{4427}e + \frac{209416}{13281}$
31 $[31, 31, -w^{2} + 2w + 7]$ $\phantom{-}1$
31 $[31, 31, -w^{3} + 5w + 5]$ $-\frac{395}{13281}e^{7} - \frac{539}{8854}e^{6} + \frac{6959}{8854}e^{5} + \frac{6085}{4427}e^{4} - \frac{80216}{13281}e^{3} - \frac{112448}{13281}e^{2} + \frac{163336}{13281}e + \frac{112484}{13281}$
41 $[41, 41, -w^{3} + 2w^{2} + 4w - 2]$ $-\frac{262}{13281}e^{7} - \frac{2339}{26562}e^{6} + \frac{188}{13281}e^{5} + \frac{7121}{13281}e^{4} + \frac{43246}{13281}e^{3} + \frac{22931}{4427}e^{2} - \frac{122044}{13281}e - \frac{44408}{4427}$
41 $[41, 41, -w^{3} + w^{2} + 5w - 3]$ $\phantom{-}\frac{730}{13281}e^{7} + \frac{2285}{8854}e^{6} - \frac{2788}{4427}e^{5} - \frac{16121}{4427}e^{4} + \frac{4678}{13281}e^{3} + \frac{130651}{13281}e^{2} - \frac{28172}{13281}e - \frac{72382}{13281}$
59 $[59, 59, -w^{3} + w^{2} + 6w - 2]$ $-\frac{605}{13281}e^{7} - \frac{2219}{13281}e^{6} + \frac{9964}{13281}e^{5} + \frac{32107}{13281}e^{4} - \frac{45418}{13281}e^{3} - \frac{28644}{4427}e^{2} + \frac{119044}{13281}e + \frac{10394}{4427}$
59 $[59, 59, -w^{3} + w^{2} + 4w + 5]$ $\phantom{-}\frac{212}{4427}e^{7} + \frac{2501}{13281}e^{6} - \frac{11338}{13281}e^{5} - \frac{39928}{13281}e^{4} + \frac{56387}{13281}e^{3} + \frac{131305}{13281}e^{2} - \frac{36490}{4427}e - \frac{37858}{13281}$
59 $[59, 59, w^{3} - 5w^{2} - w + 18]$ $\phantom{-}\frac{515}{13281}e^{7} + \frac{1276}{4427}e^{6} - \frac{754}{4427}e^{5} - \frac{20318}{4427}e^{4} - \frac{46549}{13281}e^{3} + \frac{234533}{13281}e^{2} + \frac{116210}{13281}e - \frac{231722}{13281}$
59 $[59, 59, w^{3} - 2w^{2} - 5w + 4]$ $\phantom{-}\frac{137}{13281}e^{7} - \frac{13}{4427}e^{6} - \frac{596}{4427}e^{5} + \frac{3045}{4427}e^{4} - \frac{2506}{13281}e^{3} - \frac{113512}{13281}e^{2} + \frac{31172}{13281}e + \frac{200986}{13281}$
81 $[81, 3, -3]$ $-\frac{2111}{26562}e^{7} - \frac{4259}{8854}e^{6} + \frac{3170}{4427}e^{5} + \frac{32427}{4427}e^{4} + \frac{32879}{13281}e^{3} - \frac{308245}{13281}e^{2} - \frac{112198}{13281}e + \frac{195604}{13281}$
89 $[89, 89, -w^{3} + 3w^{2} - 3]$ $\phantom{-}\frac{139}{4427}e^{7} + \frac{122}{4427}e^{6} - \frac{6181}{8854}e^{5} - \frac{652}{4427}e^{4} + \frac{18623}{4427}e^{3} - \frac{6336}{4427}e^{2} - \frac{27475}{4427}e + \frac{3768}{4427}$
89 $[89, 89, -4w^{2} + 5w + 20]$ $-\frac{875}{8854}e^{7} - \frac{14311}{26562}e^{6} + \frac{23951}{26562}e^{5} + \frac{99856}{13281}e^{4} + \frac{38194}{13281}e^{3} - \frac{232705}{13281}e^{2} - \frac{39151}{4427}e - \frac{10100}{13281}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$31$ $[31, 31, -w^{2} + 2w + 7]$ $-1$