Base field 4.4.9225.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 10x^{2} + 7x + 19\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[29, 29, \frac{3}{4}w^{3} + w^{2} - \frac{9}{2}w - \frac{25}{4}]$ |
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:
\(x^{8} - x^{7} - 15x^{6} + 15x^{5} + 47x^{4} - 24x^{3} - 33x^{2} + 10x + 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, -\frac{1}{4}w^{3} + \frac{1}{2}w + \frac{3}{4}]$ | $-\frac{18}{115}e^{7} + \frac{47}{115}e^{6} + \frac{239}{115}e^{5} - \frac{687}{115}e^{4} - \frac{82}{23}e^{3} + \frac{1527}{115}e^{2} + \frac{108}{115}e - \frac{469}{115}$ |
4 | $[4, 2, \frac{1}{2}w^{3} - 4w - \frac{1}{2}]$ | $\phantom{-}e$ |
9 | $[9, 3, \frac{1}{2}w^{3} + w^{2} - 3w - \frac{7}{2}]$ | $\phantom{-}\frac{83}{230}e^{7} - \frac{57}{230}e^{6} - \frac{1249}{230}e^{5} + \frac{887}{230}e^{4} + \frac{787}{46}e^{3} - \frac{521}{115}e^{2} - \frac{1763}{230}e + \frac{222}{115}$ |
11 | $[11, 11, -\frac{1}{4}w^{3} + \frac{1}{2}w + \frac{7}{4}]$ | $\phantom{-}\frac{101}{230}e^{7} + \frac{11}{230}e^{6} - \frac{1603}{230}e^{5} - \frac{151}{230}e^{4} + \frac{1191}{46}e^{3} + \frac{1303}{115}e^{2} - \frac{3711}{230}e - \frac{521}{115}$ |
11 | $[11, 11, \frac{1}{2}w^{3} - 4w - \frac{3}{2}]$ | $-\frac{83}{230}e^{7} + \frac{57}{230}e^{6} + \frac{1249}{230}e^{5} - \frac{887}{230}e^{4} - \frac{787}{46}e^{3} + \frac{521}{115}e^{2} + \frac{1993}{230}e + \frac{8}{115}$ |
19 | $[19, 19, w]$ | $\phantom{-}\frac{283}{230}e^{7} - \frac{247}{230}e^{6} - \frac{4109}{230}e^{5} + \frac{3537}{230}e^{4} + \frac{2291}{46}e^{3} - \frac{1376}{115}e^{2} - \frac{4573}{230}e + \frac{42}{115}$ |
19 | $[19, 19, \frac{1}{4}w^{3} - \frac{5}{2}w + \frac{1}{4}]$ | $-\frac{3}{23}e^{7} + \frac{4}{23}e^{6} + \frac{36}{23}e^{5} - \frac{57}{23}e^{4} - \frac{30}{23}e^{3} + \frac{59}{23}e^{2} - \frac{74}{23}e + \frac{10}{23}$ |
25 | $[25, 5, \frac{1}{2}w^{3} - 3w - \frac{1}{2}]$ | $-\frac{101}{230}e^{7} - \frac{11}{230}e^{6} + \frac{1603}{230}e^{5} + \frac{151}{230}e^{4} - \frac{1191}{46}e^{3} - \frac{1188}{115}e^{2} + \frac{3481}{230}e + \frac{291}{115}$ |
29 | $[29, 29, \frac{3}{4}w^{3} + w^{2} - \frac{9}{2}w - \frac{25}{4}]$ | $-1$ |
29 | $[29, 29, \frac{1}{2}w^{3} - w^{2} - 3w + \frac{9}{2}]$ | $-\frac{3}{230}e^{7} + \frac{27}{230}e^{6} + \frac{59}{230}e^{5} - \frac{517}{230}e^{4} - \frac{75}{46}e^{3} + \frac{1306}{115}e^{2} + \frac{823}{230}e - \frac{777}{115}$ |
41 | $[41, 41, -w^{3} + 7w + 3]$ | $-\frac{63}{115}e^{7} + \frac{107}{115}e^{6} + \frac{894}{115}e^{5} - \frac{1542}{115}e^{4} - \frac{448}{23}e^{3} + \frac{2757}{115}e^{2} + \frac{1183}{115}e - \frac{204}{115}$ |
41 | $[41, 41, -\frac{3}{4}w^{3} + \frac{11}{2}w - \frac{3}{4}]$ | $-\frac{111}{115}e^{7} + \frac{79}{115}e^{6} + \frac{1608}{115}e^{5} - \frac{1074}{115}e^{4} - \frac{889}{23}e^{3} - \frac{416}{115}e^{2} + \frac{1586}{115}e + \frac{1382}{115}$ |
41 | $[41, 41, \frac{1}{4}w^{3} + w^{2} - \frac{5}{2}w - \frac{11}{4}]$ | $\phantom{-}\frac{1}{2}e^{7} - \frac{1}{2}e^{6} - \frac{15}{2}e^{5} + \frac{15}{2}e^{4} + \frac{47}{2}e^{3} - 12e^{2} - \frac{33}{2}e + 9$ |
71 | $[71, 71, \frac{1}{2}w^{3} - 4w + \frac{5}{2}]$ | $-\frac{14}{23}e^{7} + \frac{11}{23}e^{6} + \frac{214}{23}e^{5} - \frac{151}{23}e^{4} - \frac{715}{23}e^{3} + \frac{76}{23}e^{2} + \frac{613}{23}e + \frac{16}{23}$ |
71 | $[71, 71, \frac{3}{4}w^{3} + w^{2} - \frac{11}{2}w - \frac{21}{4}]$ | $\phantom{-}\frac{106}{115}e^{7} - \frac{149}{115}e^{6} - \frac{1433}{115}e^{5} + \frac{2129}{115}e^{4} + \frac{580}{23}e^{3} - \frac{2859}{115}e^{2} - \frac{61}{115}e + \frac{858}{115}$ |
79 | $[79, 79, \frac{1}{4}w^{3} - 2w^{2} + \frac{1}{2}w + \frac{25}{4}]$ | $-\frac{24}{115}e^{7} + \frac{101}{115}e^{6} + \frac{242}{115}e^{5} - \frac{1376}{115}e^{4} + \frac{113}{23}e^{3} + \frac{2381}{115}e^{2} - \frac{1466}{115}e - \frac{472}{115}$ |
79 | $[79, 79, -\frac{3}{4}w^{3} + \frac{13}{2}w + \frac{9}{4}]$ | $-\frac{28}{115}e^{7} + \frac{22}{115}e^{6} + \frac{359}{115}e^{5} - \frac{302}{115}e^{4} - \frac{102}{23}e^{3} - \frac{78}{115}e^{2} - \frac{867}{115}e + \frac{216}{115}$ |
89 | $[89, 89, -\frac{7}{4}w^{3} - w^{2} + \frac{27}{2}w + \frac{41}{4}]$ | $-\frac{16}{115}e^{7} - \frac{86}{115}e^{6} + \frac{353}{115}e^{5} + \frac{1191}{115}e^{4} - \frac{469}{23}e^{3} - \frac{3051}{115}e^{2} + \frac{1936}{115}e + \frac{1142}{115}$ |
89 | $[89, 89, -\frac{7}{4}w^{3} - w^{2} + \frac{27}{2}w + \frac{33}{4}]$ | $\phantom{-}\frac{71}{230}e^{7} + \frac{51}{230}e^{6} - \frac{1243}{230}e^{5} - \frac{721}{230}e^{4} + \frac{1177}{46}e^{3} + \frac{1598}{115}e^{2} - \frac{6521}{230}e - \frac{931}{115}$ |
101 | $[101, 101, \frac{1}{4}w^{3} + w^{2} - \frac{1}{2}w - \frac{27}{4}]$ | $\phantom{-}\frac{8}{115}e^{7} + \frac{43}{115}e^{6} - \frac{119}{115}e^{5} - \frac{538}{115}e^{4} + \frac{108}{23}e^{3} + \frac{1353}{115}e^{2} - \frac{393}{115}e - \frac{686}{115}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$29$ | $[29, 29, \frac{3}{4}w^{3} + w^{2} - \frac{9}{2}w - \frac{25}{4}]$ | $1$ |