Base field \(\Q(\sqrt{377}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 94\); narrow class number \(4\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[4, 2, 2]$ |
Dimension: | $9$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $52$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{9} - 13x^{8} + 8x^{7} + 486x^{6} - 1439x^{5} - 4545x^{4} + 16830x^{3} + 18488x^{2} - 55656x - 43856\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $-1$ |
2 | $[2, 2, w + 1]$ | $-1$ |
9 | $[9, 3, 3]$ | $\phantom{-}e$ |
11 | $[11, 11, w + 2]$ | $\phantom{-}\frac{263}{36348}e^{8} - \frac{2903}{48464}e^{7} - \frac{16261}{72696}e^{6} + \frac{44363}{18174}e^{5} + \frac{28863}{24232}e^{4} - \frac{1305121}{48464}e^{3} - \frac{105341}{12116}e^{2} + \frac{1777613}{18174}e + \frac{1322759}{18174}$ |
11 | $[11, 11, w + 8]$ | $\phantom{-}\frac{263}{36348}e^{8} - \frac{2903}{48464}e^{7} - \frac{16261}{72696}e^{6} + \frac{44363}{18174}e^{5} + \frac{28863}{24232}e^{4} - \frac{1305121}{48464}e^{3} - \frac{105341}{12116}e^{2} + \frac{1777613}{18174}e + \frac{1322759}{18174}$ |
13 | $[13, 13, 4w - 41]$ | $\phantom{-}\frac{3137}{436176}e^{8} - \frac{1449}{24232}e^{7} - \frac{47185}{218088}e^{6} + \frac{131519}{54522}e^{5} + \frac{127259}{145392}e^{4} - \frac{1878905}{72696}e^{3} - \frac{71717}{18174}e^{2} + \frac{4792907}{54522}e + \frac{1436989}{27261}$ |
19 | $[19, 19, w + 7]$ | $-\frac{1255}{218088}e^{8} + \frac{2733}{48464}e^{7} + \frac{2714}{27261}e^{6} - \frac{455141}{218088}e^{5} + \frac{121553}{72696}e^{4} + \frac{2720407}{145392}e^{3} - \frac{86288}{9087}e^{2} - \frac{1652245}{27261}e - \frac{1983323}{54522}$ |
19 | $[19, 19, w + 11]$ | $-\frac{1255}{218088}e^{8} + \frac{2733}{48464}e^{7} + \frac{2714}{27261}e^{6} - \frac{455141}{218088}e^{5} + \frac{121553}{72696}e^{4} + \frac{2720407}{145392}e^{3} - \frac{86288}{9087}e^{2} - \frac{1652245}{27261}e - \frac{1983323}{54522}$ |
23 | $[23, 23, -2w + 21]$ | $-\frac{719}{72696}e^{8} + \frac{1843}{24232}e^{7} + \frac{25769}{72696}e^{6} - \frac{235687}{72696}e^{5} - \frac{38013}{12116}e^{4} + \frac{470745}{12116}e^{3} + \frac{111883}{6058}e^{2} - \frac{1355681}{9087}e - \frac{911732}{9087}$ |
23 | $[23, 23, -2w - 19]$ | $-\frac{719}{72696}e^{8} + \frac{1843}{24232}e^{7} + \frac{25769}{72696}e^{6} - \frac{235687}{72696}e^{5} - \frac{38013}{12116}e^{4} + \frac{470745}{12116}e^{3} + \frac{111883}{6058}e^{2} - \frac{1355681}{9087}e - \frac{911732}{9087}$ |
25 | $[25, 5, -5]$ | $\phantom{-}\frac{655}{218088}e^{8} - \frac{823}{48464}e^{7} - \frac{10327}{54522}e^{6} + \frac{224945}{218088}e^{5} + \frac{270643}{72696}e^{4} - \frac{2703217}{145392}e^{3} - \frac{222724}{9087}e^{2} + \frac{2347237}{27261}e + \frac{4313609}{54522}$ |
29 | $[29, 29, 6w - 61]$ | $\phantom{-}\frac{423}{48464}e^{8} - \frac{232}{3029}e^{7} - \frac{2165}{12116}e^{6} + \frac{65363}{24232}e^{5} - \frac{77515}{48464}e^{4} - \frac{499295}{24232}e^{3} + \frac{56181}{6058}e^{2} + \frac{300115}{6058}e + \frac{104573}{3029}$ |
31 | $[31, 31, w + 12]$ | $-\frac{4883}{436176}e^{8} + \frac{2157}{24232}e^{7} + \frac{41777}{109044}e^{6} - \frac{823391}{218088}e^{5} - \frac{424259}{145392}e^{4} + \frac{1628707}{36348}e^{3} + \frac{150367}{9087}e^{2} - \frac{9245513}{54522}e - \frac{3072046}{27261}$ |
31 | $[31, 31, w + 18]$ | $-\frac{4883}{436176}e^{8} + \frac{2157}{24232}e^{7} + \frac{41777}{109044}e^{6} - \frac{823391}{218088}e^{5} - \frac{424259}{145392}e^{4} + \frac{1628707}{36348}e^{3} + \frac{150367}{9087}e^{2} - \frac{9245513}{54522}e - \frac{3072046}{27261}$ |
37 | $[37, 37, w + 4]$ | $-\frac{4883}{436176}e^{8} + \frac{2157}{24232}e^{7} + \frac{41777}{109044}e^{6} - \frac{823391}{218088}e^{5} - \frac{424259}{145392}e^{4} + \frac{1628707}{36348}e^{3} + \frac{150367}{9087}e^{2} - \frac{9300035}{54522}e - \frac{2963002}{27261}$ |
37 | $[37, 37, w + 32]$ | $-\frac{4883}{436176}e^{8} + \frac{2157}{24232}e^{7} + \frac{41777}{109044}e^{6} - \frac{823391}{218088}e^{5} - \frac{424259}{145392}e^{4} + \frac{1628707}{36348}e^{3} + \frac{150367}{9087}e^{2} - \frac{9300035}{54522}e - \frac{2963002}{27261}$ |
41 | $[41, 41, w + 3]$ | $\phantom{-}\frac{473}{48464}e^{8} - \frac{3671}{48464}e^{7} - \frac{8057}{24232}e^{6} + \frac{76469}{24232}e^{5} + \frac{118249}{48464}e^{4} - \frac{1749659}{48464}e^{3} - \frac{75567}{6058}e^{2} + \frac{793477}{6058}e + \frac{515665}{6058}$ |
41 | $[41, 41, w + 37]$ | $\phantom{-}\frac{473}{48464}e^{8} - \frac{3671}{48464}e^{7} - \frac{8057}{24232}e^{6} + \frac{76469}{24232}e^{5} + \frac{118249}{48464}e^{4} - \frac{1749659}{48464}e^{3} - \frac{75567}{6058}e^{2} + \frac{793477}{6058}e + \frac{515665}{6058}$ |
47 | $[47, 47, w]$ | $-\frac{1451}{145392}e^{8} + \frac{1609}{24232}e^{7} + \frac{31645}{72696}e^{6} - \frac{109231}{36348}e^{5} - \frac{282949}{48464}e^{4} + \frac{955933}{24232}e^{3} + \frac{113083}{3029}e^{2} - \frac{2847875}{18174}e - \frac{1192597}{9087}$ |
47 | $[47, 47, w + 46]$ | $-\frac{1451}{145392}e^{8} + \frac{1609}{24232}e^{7} + \frac{31645}{72696}e^{6} - \frac{109231}{36348}e^{5} - \frac{282949}{48464}e^{4} + \frac{955933}{24232}e^{3} + \frac{113083}{3029}e^{2} - \frac{2847875}{18174}e - \frac{1192597}{9087}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, w]$ | $1$ |
$2$ | $[2, 2, w + 1]$ | $1$ |