Base field 3.3.1345.1
Generator \(w\), with minimal polynomial \(x^{3} - 7x - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[25, 5, w^{2} - 2w - 3]$ |
Dimension: | $8$ |
CM: | no |
Base change: | no |
Newspace dimension: | $25$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} + x^{7} - 39x^{6} - 19x^{5} + 469x^{4} - 32x^{3} - 1808x^{2} + 960x + 576\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, -w - 1]$ | $-1$ |
5 | $[5, 5, w + 2]$ | $\phantom{-}1$ |
7 | $[7, 7, w + 3]$ | $\phantom{-}e$ |
7 | $[7, 7, -w + 2]$ | $\phantom{-}\frac{209}{66862}e^{7} + \frac{797}{267448}e^{6} - \frac{25883}{267448}e^{5} - \frac{20395}{267448}e^{4} + \frac{194089}{267448}e^{3} + \frac{219045}{267448}e^{2} - \frac{20554}{33431}e - \frac{136977}{33431}$ |
7 | $[7, 7, -w + 1]$ | $\phantom{-}\frac{2861}{802344}e^{7} + \frac{5695}{1604688}e^{6} - \frac{72835}{534896}e^{5} - \frac{111841}{1604688}e^{4} + \frac{2423107}{1604688}e^{3} + \frac{295657}{1604688}e^{2} - \frac{434003}{100293}e + \frac{14679}{66862}$ |
8 | $[8, 2, 2]$ | $\phantom{-}\frac{5761}{802344}e^{7} + \frac{31379}{1604688}e^{6} - \frac{131519}{534896}e^{5} - \frac{864053}{1604688}e^{4} + \frac{3986879}{1604688}e^{3} + \frac{5285453}{1604688}e^{2} - \frac{1562297}{200586}e - \frac{30807}{66862}$ |
13 | $[13, 13, -w^{2} + w + 4]$ | $\phantom{-}\frac{872}{100293}e^{7} + \frac{13781}{1604688}e^{6} - \frac{171553}{534896}e^{5} - \frac{284867}{1604688}e^{4} + \frac{5428481}{1604688}e^{3} + \frac{446105}{1604688}e^{2} - \frac{898837}{100293}e + \frac{226691}{66862}$ |
19 | $[19, 19, -w^{2} + 5]$ | $\phantom{-}\frac{26585}{3209376}e^{7} + \frac{76571}{3209376}e^{6} - \frac{275095}{1069792}e^{5} - \frac{1944497}{3209376}e^{4} + \frac{7203359}{3209376}e^{3} + \frac{4778113}{1604688}e^{2} - \frac{2789927}{401172}e + \frac{185711}{66862}$ |
23 | $[23, 23, -w^{2} - w + 3]$ | $-\frac{8413}{1604688}e^{7} - \frac{43411}{1604688}e^{6} + \frac{69375}{534896}e^{5} + \frac{1193257}{1604688}e^{4} - \frac{807943}{1604688}e^{3} - \frac{3871043}{802344}e^{2} - \frac{260951}{200586}e + \frac{219805}{33431}$ |
27 | $[27, 3, 3]$ | $\phantom{-}\frac{4115}{401172}e^{7} + \frac{4043}{401172}e^{6} - \frac{49359}{133724}e^{5} - \frac{86513}{401172}e^{4} + \frac{1502687}{401172}e^{3} + \frac{18806}{100293}e^{2} - \frac{1029961}{100293}e + \frac{145150}{33431}$ |
29 | $[29, 29, w^{2} - w - 3]$ | $\phantom{-}\frac{6623}{802344}e^{7} + \frac{3217}{401172}e^{6} - \frac{37621}{133724}e^{5} - \frac{73849}{401172}e^{4} + \frac{1042477}{401172}e^{3} + \frac{732359}{802344}e^{2} - \frac{626789}{100293}e + \frac{35891}{33431}$ |
31 | $[31, 31, w^{2} - w - 8]$ | $\phantom{-}\frac{3313}{1069792}e^{7} - \frac{13757}{1069792}e^{6} - \frac{129405}{1069792}e^{5} + \frac{369655}{1069792}e^{4} + \frac{1155175}{1069792}e^{3} - \frac{666375}{534896}e^{2} + \frac{12041}{133724}e - \frac{387883}{66862}$ |
37 | $[37, 37, -w - 4]$ | $-\frac{1733}{534896}e^{7} - \frac{13369}{534896}e^{6} + \frac{22423}{534896}e^{5} + \frac{380867}{534896}e^{4} + \frac{344299}{534896}e^{3} - \frac{608435}{133724}e^{2} - \frac{355765}{66862}e + \frac{128478}{33431}$ |
43 | $[43, 43, 2w^{2} - 4w - 3]$ | $\phantom{-}\frac{383}{267448}e^{7} - \frac{9427}{534896}e^{6} - \frac{56267}{534896}e^{5} + \frac{232845}{534896}e^{4} + \frac{1086153}{534896}e^{3} - \frac{910277}{534896}e^{2} - \frac{349245}{33431}e + \frac{43007}{66862}$ |
47 | $[47, 47, w^{2} - 3]$ | $\phantom{-}\frac{11627}{1604688}e^{7} + \frac{46715}{1604688}e^{6} - \frac{116327}{534896}e^{5} - \frac{1243913}{1604688}e^{4} + \frac{2648783}{1604688}e^{3} + \frac{1022869}{200586}e^{2} - \frac{344807}{200586}e - \frac{244270}{33431}$ |
53 | $[53, 53, 2w^{2} - w - 11]$ | $\phantom{-}\frac{4471}{401172}e^{7} + \frac{10349}{200586}e^{6} - \frac{27103}{66862}e^{5} - \frac{307529}{200586}e^{4} + \frac{902879}{200586}e^{3} + \frac{4174783}{401172}e^{2} - \frac{1576124}{100293}e - \frac{126314}{33431}$ |
59 | $[59, 59, w^{2} - 2w - 4]$ | $\phantom{-}\frac{6619}{534896}e^{7} + \frac{18267}{534896}e^{6} - \frac{215045}{534896}e^{5} - \frac{472313}{534896}e^{4} + \frac{1884719}{534896}e^{3} + \frac{347225}{66862}e^{2} - \frac{491687}{66862}e - \frac{138264}{33431}$ |
67 | $[67, 67, w^{2} + w - 8]$ | $-\frac{1529}{1604688}e^{7} + \frac{18337}{1604688}e^{6} + \frac{37627}{534896}e^{5} - \frac{615043}{1604688}e^{4} - \frac{2582099}{1604688}e^{3} + \frac{2236853}{802344}e^{2} + \frac{2382161}{200586}e - \frac{118143}{33431}$ |
71 | $[71, 71, w^{2} + w - 11]$ | $\phantom{-}\frac{9119}{802344}e^{7} + \frac{11081}{200586}e^{6} - \frac{22611}{66862}e^{5} - \frac{147841}{100293}e^{4} + \frac{516629}{200586}e^{3} + \frac{6723473}{802344}e^{2} - \frac{483731}{100293}e - \frac{150977}{33431}$ |
73 | $[73, 73, -w^{2} + 4w - 2]$ | $\phantom{-}\frac{2005}{401172}e^{7} - \frac{11293}{802344}e^{6} - \frac{64551}{267448}e^{5} + \frac{293347}{802344}e^{4} + \frac{2840783}{802344}e^{3} - \frac{1217587}{802344}e^{2} - \frac{1582031}{100293}e + \frac{28843}{33431}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5, 5, -w - 1]$ | $1$ |
$5$ | $[5, 5, w + 2]$ | $-1$ |