Base field \(\Q(\sqrt{79}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 79\); narrow class number \(6\) and class number \(3\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[5, 5, w + 2]$ |
| Dimension: | $14$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $150$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{14} - 28x^{12} + 287x^{10} - 1309x^{8} + 2595x^{6} - 1901x^{4} + 176x^{2} - 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 9]$ | $-\frac{207}{11698}e^{12} + \frac{2757}{5849}e^{10} - \frac{53423}{11698}e^{8} + \frac{227005}{11698}e^{6} - \frac{406603}{11698}e^{4} + \frac{272071}{11698}e^{2} - \frac{17602}{5849}$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 2]$ | $-\frac{5179}{46792}e^{13} + \frac{72369}{23396}e^{11} - \frac{1482465}{46792}e^{9} + \frac{6771777}{46792}e^{7} - \frac{13513587}{46792}e^{5} + \frac{10115645}{46792}e^{3} - \frac{593001}{23396}e$ |
| 5 | $[5, 5, w + 2]$ | $-1$ |
| 5 | $[5, 5, w + 3]$ | $-\frac{2941}{23396}e^{12} + \frac{40527}{11698}e^{10} - \frac{815023}{23396}e^{8} + \frac{3620019}{23396}e^{6} - \frac{6869849}{23396}e^{4} + \frac{4657867}{23396}e^{2} - \frac{111093}{11698}$ |
| 7 | $[7, 7, w + 3]$ | $\phantom{-}\frac{9101}{23396}e^{13} - \frac{126979}{11698}e^{11} + \frac{2587795}{23396}e^{9} - \frac{11672063}{23396}e^{7} + \frac{22588081}{23396}e^{5} - \frac{15527327}{23396}e^{3} + \frac{291873}{11698}e$ |
| 7 | $[7, 7, w + 4]$ | $\phantom{-}\frac{9101}{23396}e^{13} - \frac{126979}{11698}e^{11} + \frac{2587795}{23396}e^{9} - \frac{11672063}{23396}e^{7} + \frac{22588081}{23396}e^{5} - \frac{15527327}{23396}e^{3} + \frac{291873}{11698}e$ |
| 13 | $[13, 13, w + 1]$ | $\phantom{-}\frac{4503}{23396}e^{12} - \frac{63535}{11698}e^{10} + \frac{1305741}{23396}e^{8} - \frac{5915049}{23396}e^{6} + \frac{11435263}{23396}e^{4} - \frac{7820557}{23396}e^{2} + \frac{193281}{11698}$ |
| 13 | $[13, 13, w + 12]$ | $-\frac{435}{11698}e^{12} + \frac{6048}{5849}e^{10} - \frac{120573}{11698}e^{8} + \frac{514507}{11698}e^{6} - \frac{886837}{11698}e^{4} + \frac{509015}{11698}e^{2} - \frac{3252}{5849}$ |
| 43 | $[43, 43, -w - 6]$ | $-\frac{10648}{5849}e^{13} + \frac{297540}{5849}e^{11} - \frac{3039463}{5849}e^{9} + \frac{13773478}{5849}e^{7} - \frac{26902871}{5849}e^{5} + \frac{18847128}{5849}e^{3} - \frac{896543}{5849}e$ |
| 43 | $[43, 43, w - 6]$ | $-\frac{60863}{46792}e^{13} + \frac{849957}{23396}e^{11} - \frac{17355149}{46792}e^{9} + \frac{78591693}{46792}e^{7} - \frac{153469087}{46792}e^{5} + \frac{108191073}{46792}e^{3} - \frac{3343885}{23396}e$ |
| 47 | $[47, 47, w + 19]$ | $-\frac{39831}{23396}e^{13} + \frac{557459}{11698}e^{11} - \frac{11413697}{23396}e^{9} + \frac{51878801}{23396}e^{7} - \frac{101830651}{23396}e^{5} + \frac{71910189}{23396}e^{3} - \frac{1797495}{11698}e$ |
| 47 | $[47, 47, w + 28]$ | $\phantom{-}\frac{85171}{46792}e^{13} - \frac{1190665}{23396}e^{11} + \frac{24338401}{46792}e^{9} - \frac{110320273}{46792}e^{7} + \frac{215353971}{46792}e^{5} - \frac{150292413}{46792}e^{3} + \frac{3450257}{23396}e$ |
| 59 | $[59, 59, w + 16]$ | $\phantom{-}\frac{3493}{46792}e^{13} - \frac{47879}{23396}e^{11} + \frac{941887}{46792}e^{9} - \frac{3936815}{46792}e^{7} + \frac{6261813}{46792}e^{5} - \frac{1889587}{46792}e^{3} - \frac{773909}{23396}e$ |
| 59 | $[59, 59, w + 43]$ | $-\frac{3318}{5849}e^{13} + \frac{92707}{5849}e^{11} - \frac{946425}{5849}e^{9} + \frac{4282728}{5849}e^{7} - \frac{8352409}{5849}e^{5} + \frac{5896427}{5849}e^{3} - \frac{355331}{5849}e$ |
| 71 | $[71, 71, w + 24]$ | $-\frac{52413}{46792}e^{13} + \frac{733683}{23396}e^{11} - \frac{15029119}{46792}e^{9} + \frac{68385607}{46792}e^{7} - \frac{134555629}{46792}e^{5} + \frac{95657411}{46792}e^{3} - \frac{2710739}{23396}e$ |
| 71 | $[71, 71, w + 47]$ | $\phantom{-}\frac{593}{46792}e^{13} - \frac{7559}{23396}e^{11} + \frac{138067}{46792}e^{9} - \frac{537963}{46792}e^{7} + \frac{848681}{46792}e^{5} - \frac{570599}{46792}e^{3} + \frac{46667}{23396}e$ |
| 73 | $[73, 73, 3w - 28]$ | $\phantom{-}\frac{4197}{23396}e^{12} - \frac{57425}{11698}e^{10} + \frac{1152511}{23396}e^{8} - \frac{5147159}{23396}e^{6} + \frac{9881065}{23396}e^{4} - \frac{6571023}{23396}e^{2} + \frac{58927}{11698}$ |
| 73 | $[73, 73, 12w - 107]$ | $-\frac{1240}{5849}e^{12} + \frac{35489}{5849}e^{10} - \frac{369922}{5849}e^{8} + \frac{1702752}{5849}e^{6} - \frac{3368167}{5849}e^{4} + \frac{2420373}{5849}e^{2} - \frac{163555}{5849}$ |
| 79 | $[79, 79, -w]$ | $-\frac{26323}{23396}e^{13} + \frac{367715}{11698}e^{11} - \frac{7512725}{23396}e^{9} + \frac{34056877}{23396}e^{7} - \frac{66613139}{23396}e^{5} + \frac{46957857}{23396}e^{3} - \frac{1274899}{11698}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, w + 2]$ | $1$ |