Base field 4.4.14336.1
Generator \(w\), with minimal polynomial \(x^{4} - 8x^{2} + 14\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[23, 23, -w - 3]$ |
| Dimension: | $18$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $38$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{18} - 28x^{16} + 319x^{14} - 1901x^{12} + 6353x^{10} - 11894x^{8} + 11760x^{6} - 5106x^{4} + 435x^{2} - 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w^{3} + w^{2} + 5w - 6]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w^{3} - w^{2} - 5w + 7]$ | $\phantom{-}\frac{9}{40}e^{16} - \frac{713}{120}e^{14} + \frac{623}{10}e^{12} - \frac{13121}{40}e^{10} + \frac{13508}{15}e^{8} - \frac{24027}{20}e^{6} + \frac{12117}{20}e^{4} + \frac{24}{5}e^{2} - \frac{117}{40}$ |
| 7 | $[7, 7, -w - 1]$ | $-\frac{313}{720}e^{17} + \frac{8387}{720}e^{15} - \frac{7487}{60}e^{13} + \frac{489377}{720}e^{11} - \frac{178217}{90}e^{9} + \frac{357413}{120}e^{7} - \frac{82041}{40}e^{5} + \frac{6832}{15}e^{3} - \frac{3977}{240}e$ |
| 7 | $[7, 7, w - 1]$ | $\phantom{-}\frac{11}{144}e^{17} - \frac{277}{144}e^{15} + \frac{223}{12}e^{13} - \frac{11995}{144}e^{11} + \frac{5423}{36}e^{9} + \frac{1079}{24}e^{7} - \frac{3647}{8}e^{5} + \frac{4819}{12}e^{3} - \frac{2057}{48}e$ |
| 17 | $[17, 17, w^{2} - w - 5]$ | $\phantom{-}\frac{1}{72}e^{17} - \frac{17}{72}e^{15} + \frac{1}{3}e^{13} + \frac{1243}{72}e^{11} - \frac{5251}{36}e^{9} + \frac{2951}{6}e^{7} - 743e^{5} + \frac{5071}{12}e^{3} - \frac{361}{24}e$ |
| 17 | $[17, 17, w^{2} + w - 5]$ | $\phantom{-}\frac{5}{18}e^{17} - \frac{68}{9}e^{15} + \frac{248}{3}e^{13} - \frac{8365}{18}e^{11} + \frac{25631}{18}e^{9} - \frac{14021}{6}e^{7} + \frac{3795}{2}e^{5} - \frac{3719}{6}e^{3} + \frac{131}{3}e$ |
| 23 | $[23, 23, -w - 3]$ | $-1$ |
| 23 | $[23, 23, w - 3]$ | $-\frac{77}{120}e^{16} + \frac{2053}{120}e^{14} - \frac{909}{5}e^{12} + \frac{117193}{120}e^{10} - \frac{166297}{60}e^{8} + \frac{39401}{10}e^{6} - \frac{11683}{5}e^{4} + \frac{5049}{20}e^{2} + \frac{77}{40}$ |
| 25 | $[25, 5, -w^{3} + w^{2} + 4w - 3]$ | $-\frac{41}{120}e^{17} + \frac{1109}{120}e^{15} - \frac{502}{5}e^{13} + \frac{67069}{120}e^{11} - \frac{101231}{60}e^{9} + \frac{13504}{5}e^{7} - \frac{21013}{10}e^{5} + \frac{12987}{20}e^{3} - \frac{2579}{40}e$ |
| 25 | $[25, 5, -w^{3} - w^{2} + 4w + 3]$ | $-\frac{13}{20}e^{17} + \frac{1051}{60}e^{15} - \frac{946}{5}e^{13} + \frac{20877}{20}e^{11} - \frac{93229}{30}e^{9} + \frac{24342}{5}e^{7} - \frac{18307}{5}e^{5} + \frac{10543}{10}e^{3} - \frac{1741}{20}e$ |
| 41 | $[41, 41, w^{3} - 4w - 1]$ | $-\frac{151}{180}e^{17} + \frac{4109}{180}e^{15} - \frac{3749}{15}e^{13} + \frac{253199}{180}e^{11} - \frac{194383}{45}e^{9} + \frac{213671}{30}e^{7} - \frac{58447}{10}e^{5} + \frac{29236}{15}e^{3} - \frac{8099}{60}e$ |
| 41 | $[41, 41, -w^{3} + 4w - 1]$ | $-\frac{23}{720}e^{17} + \frac{517}{720}e^{15} - \frac{337}{60}e^{13} + \frac{9967}{720}e^{11} + \frac{1654}{45}e^{9} - \frac{30257}{120}e^{7} + \frac{16909}{40}e^{5} - \frac{6731}{30}e^{3} + \frac{1313}{240}e$ |
| 71 | $[71, 71, -w^{3} + 2w^{2} + 4w - 9]$ | $-\frac{109}{90}e^{17} + \frac{2951}{90}e^{15} - \frac{5347}{15}e^{13} + \frac{178721}{90}e^{11} - \frac{270149}{45}e^{9} + \frac{144809}{15}e^{7} - \frac{38038}{5}e^{5} + \frac{35648}{15}e^{3} - \frac{5111}{30}e$ |
| 71 | $[71, 71, w^{3} + 2w^{2} - 4w - 9]$ | $\phantom{-}\frac{113}{360}e^{17} - \frac{3247}{360}e^{15} + \frac{3187}{30}e^{13} - \frac{237937}{360}e^{11} + \frac{210119}{90}e^{9} - \frac{280843}{60}e^{7} + \frac{99851}{20}e^{5} - \frac{69563}{30}e^{3} + \frac{21637}{120}e$ |
| 73 | $[73, 73, w^{3} - w^{2} - 5w + 3]$ | $\phantom{-}\frac{67}{72}e^{16} - \frac{1781}{72}e^{14} + \frac{1571}{6}e^{12} - \frac{100715}{72}e^{10} + \frac{70837}{18}e^{8} - \frac{66065}{12}e^{6} + \frac{12577}{4}e^{4} - \frac{1567}{6}e^{2} - \frac{97}{24}$ |
| 73 | $[73, 73, w^{3} + w^{2} - 5w - 3]$ | $-\frac{25}{36}e^{16} + \frac{665}{36}e^{14} - \frac{587}{3}e^{12} + \frac{37685}{36}e^{10} - \frac{53249}{18}e^{8} + \frac{12619}{3}e^{6} - 2570e^{4} + \frac{2279}{6}e^{2} - \frac{119}{12}$ |
| 79 | $[79, 79, 2w^{2} - 2w - 9]$ | $-\frac{7}{30}e^{17} + \frac{104}{15}e^{15} - \frac{426}{5}e^{13} + \frac{16763}{30}e^{11} - \frac{63089}{30}e^{9} + \frac{45299}{10}e^{7} - \frac{51989}{10}e^{5} + \frac{25813}{10}e^{3} - \frac{1024}{5}e$ |
| 79 | $[79, 79, -2w^{3} + 8w + 5]$ | $\phantom{-}\frac{193}{720}e^{17} - \frac{5207}{720}e^{15} + \frac{4697}{60}e^{13} - \frac{312017}{720}e^{11} + \frac{233119}{180}e^{9} - \frac{243263}{120}e^{7} + \frac{58911}{40}e^{5} - \frac{19093}{60}e^{3} - \frac{7363}{240}e$ |
| 81 | $[81, 3, -3]$ | $-\frac{137}{360}e^{16} + \frac{3643}{360}e^{14} - \frac{3223}{30}e^{12} + \frac{208393}{360}e^{10} - \frac{74878}{45}e^{8} + \frac{147757}{60}e^{6} - \frac{33429}{20}e^{4} + \frac{5596}{15}e^{2} - \frac{1753}{120}$ |
| 89 | $[89, 89, -w^{3} - 2w^{2} + 6w + 13]$ | $\phantom{-}\frac{7}{72}e^{16} - \frac{185}{72}e^{14} + \frac{161}{6}e^{12} - \frac{10055}{72}e^{10} + \frac{6733}{18}e^{8} - \frac{5693}{12}e^{6} + \frac{841}{4}e^{4} + \frac{131}{6}e^{2} + \frac{11}{24}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $23$ | $[23,23,-w-3]$ | $1$ |