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: | $[1, 1, 1]$ |
| Dimension: | $16$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $44$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{16} + 22x^{14} + 191x^{12} + 830x^{10} + 1891x^{8} + 2169x^{6} + 1134x^{4} + 243x^{2} + 15\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $-e$ |
| 9 | $[9, 3, 3]$ | $-\frac{1}{22}e^{14} - \frac{12}{11}e^{12} - \frac{114}{11}e^{10} - \frac{544}{11}e^{8} - \frac{2725}{22}e^{6} - \frac{3395}{22}e^{4} - \frac{1797}{22}e^{2} - \frac{109}{11}$ |
| 11 | $[11, 11, w + 2]$ | $\phantom{-}\frac{25}{44}e^{15} + \frac{545}{44}e^{13} + \frac{2333}{22}e^{11} + \frac{4952}{11}e^{9} + \frac{43199}{44}e^{7} + \frac{22555}{22}e^{5} + \frac{4667}{11}e^{3} + \frac{2227}{44}e$ |
| 11 | $[11, 11, w + 8]$ | $-\frac{25}{44}e^{15} - \frac{545}{44}e^{13} - \frac{2333}{22}e^{11} - \frac{4952}{11}e^{9} - \frac{43199}{44}e^{7} - \frac{22555}{22}e^{5} - \frac{4667}{11}e^{3} - \frac{2227}{44}e$ |
| 13 | $[13, 13, 4w - 41]$ | $-\frac{15}{44}e^{14} - \frac{327}{44}e^{12} - \frac{1391}{22}e^{10} - \frac{2903}{11}e^{8} - \frac{24441}{44}e^{6} - \frac{11905}{22}e^{4} - \frac{2182}{11}e^{2} - \frac{949}{44}$ |
| 19 | $[19, 19, w + 7]$ | $\phantom{-}\frac{9}{11}e^{15} + \frac{194}{11}e^{13} + \frac{1634}{11}e^{11} + \frac{6767}{11}e^{9} + \frac{14174}{11}e^{7} + \frac{13736}{11}e^{5} + \frac{4832}{11}e^{3} + \frac{444}{11}e$ |
| 19 | $[19, 19, w + 11]$ | $-\frac{9}{11}e^{15} - \frac{194}{11}e^{13} - \frac{1634}{11}e^{11} - \frac{6767}{11}e^{9} - \frac{14174}{11}e^{7} - \frac{13736}{11}e^{5} - \frac{4832}{11}e^{3} - \frac{444}{11}e$ |
| 23 | $[23, 23, -2w + 21]$ | $\phantom{-}\frac{5}{11}e^{14} + \frac{109}{11}e^{12} + \frac{931}{11}e^{10} + \frac{3922}{11}e^{8} + \frac{8389}{11}e^{6} + \frac{8362}{11}e^{4} + \frac{3078}{11}e^{2} + \frac{276}{11}$ |
| 23 | $[23, 23, -2w - 19]$ | $\phantom{-}\frac{5}{11}e^{14} + \frac{109}{11}e^{12} + \frac{931}{11}e^{10} + \frac{3922}{11}e^{8} + \frac{8389}{11}e^{6} + \frac{8362}{11}e^{4} + \frac{3078}{11}e^{2} + \frac{276}{11}$ |
| 25 | $[25, 5, -5]$ | $\phantom{-}\frac{15}{44}e^{14} + \frac{327}{44}e^{12} + \frac{1391}{22}e^{10} + \frac{2903}{11}e^{8} + \frac{24397}{44}e^{6} + \frac{11685}{22}e^{4} + \frac{1896}{11}e^{2} + \frac{641}{44}$ |
| 29 | $[29, 29, 6w - 61]$ | $\phantom{-}\frac{3}{22}e^{14} + \frac{61}{22}e^{12} + \frac{243}{11}e^{10} + \frac{972}{11}e^{8} + \frac{4193}{22}e^{6} + \frac{2436}{11}e^{4} + \frac{1359}{11}e^{2} + \frac{423}{22}$ |
| 31 | $[31, 31, w + 12]$ | $-\frac{5}{44}e^{15} - \frac{109}{44}e^{13} - \frac{471}{22}e^{11} - \frac{1030}{11}e^{9} - \frac{9643}{44}e^{7} - \frac{5809}{22}e^{5} - \frac{1523}{11}e^{3} - \frac{903}{44}e$ |
| 31 | $[31, 31, w + 18]$ | $\phantom{-}\frac{5}{44}e^{15} + \frac{109}{44}e^{13} + \frac{471}{22}e^{11} + \frac{1030}{11}e^{9} + \frac{9643}{44}e^{7} + \frac{5809}{22}e^{5} + \frac{1523}{11}e^{3} + \frac{903}{44}e$ |
| 37 | $[37, 37, w + 4]$ | $-\frac{3}{44}e^{15} - \frac{61}{44}e^{13} - \frac{243}{22}e^{11} - \frac{486}{11}e^{9} - \frac{4193}{44}e^{7} - \frac{1207}{11}e^{5} - \frac{1227}{22}e^{3} - \frac{159}{44}e$ |
| 37 | $[37, 37, w + 32]$ | $\phantom{-}\frac{3}{44}e^{15} + \frac{61}{44}e^{13} + \frac{243}{22}e^{11} + \frac{486}{11}e^{9} + \frac{4193}{44}e^{7} + \frac{1207}{11}e^{5} + \frac{1227}{22}e^{3} + \frac{159}{44}e$ |
| 41 | $[41, 41, w + 3]$ | $-\frac{9}{44}e^{15} - \frac{183}{44}e^{13} - \frac{707}{22}e^{11} - \frac{1271}{11}e^{9} - \frac{8003}{44}e^{7} - \frac{651}{11}e^{5} + \frac{2083}{22}e^{3} + \frac{1899}{44}e$ |
| 41 | $[41, 41, w + 37]$ | $\phantom{-}\frac{9}{44}e^{15} + \frac{183}{44}e^{13} + \frac{707}{22}e^{11} + \frac{1271}{11}e^{9} + \frac{8003}{44}e^{7} + \frac{651}{11}e^{5} - \frac{2083}{22}e^{3} - \frac{1899}{44}e$ |
| 47 | $[47, 47, w]$ | $\phantom{-}\frac{5}{44}e^{15} + \frac{109}{44}e^{13} + \frac{471}{22}e^{11} + \frac{1030}{11}e^{9} + \frac{9687}{44}e^{7} + \frac{6029}{22}e^{5} + \frac{1798}{11}e^{3} + \frac{1255}{44}e$ |
| 47 | $[47, 47, w + 46]$ | $-\frac{5}{44}e^{15} - \frac{109}{44}e^{13} - \frac{471}{22}e^{11} - \frac{1030}{11}e^{9} - \frac{9687}{44}e^{7} - \frac{6029}{22}e^{5} - \frac{1798}{11}e^{3} - \frac{1255}{44}e$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).