Base field \(\Q(\sqrt{229}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 57\); narrow class number \(3\) and class number \(3\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[9, 9, w + 3]$ |
| Dimension: | $16$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $99$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{16} + 21x^{14} + 320x^{12} + 2309x^{10} + 12189x^{8} + 13364x^{6} + 11520x^{4} + 1856x^{2} + 256\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}\frac{911}{156640}e^{15} + \frac{41805}{344608}e^{13} + \frac{158859}{86152}e^{11} + \frac{22689837}{1723040}e^{9} + \frac{23787045}{344608}e^{7} + \frac{1463175}{21538}e^{5} + \frac{24466869}{430760}e^{3} + \frac{16722}{10769}e$ |
| 5 | $[5, 5, w + 1]$ | $-\frac{6279}{27568640}e^{15} - \frac{2289}{501248}e^{13} - \frac{94185}{1378432}e^{11} - \frac{2517879}{5513728}e^{9} - \frac{62754191}{27568640}e^{7} - \frac{194649}{430760}e^{5} - \frac{6279}{86152}e^{3} - \frac{311403}{430760}e$ |
| 5 | $[5, 5, w + 3]$ | $-\frac{9421}{6892160}e^{14} - \frac{3563}{125312}e^{12} - \frac{67697}{156640}e^{10} - \frac{21227313}{6892160}e^{8} - \frac{2027347}{125312}e^{6} - \frac{124705}{7832}e^{4} - \frac{673437}{43076}e^{2} - \frac{3563}{9790}$ |
| 11 | $[11, 11, w + 1]$ | $\phantom{-}\frac{25277}{3446080}e^{15} + \frac{106373}{689216}e^{13} + \frac{1013703}{430760}e^{11} + \frac{58678993}{3446080}e^{9} + \frac{310202593}{3446080}e^{7} + \frac{87070887}{861520}e^{5} + \frac{4582348}{53845}e^{3} + \frac{738273}{53845}e$ |
| 11 | $[11, 11, w + 9]$ | $-\frac{10993}{3446080}e^{14} - \frac{46485}{689216}e^{12} - \frac{887309}{861520}e^{10} - \frac{25854437}{3446080}e^{8} - \frac{137145537}{3446080}e^{6} - \frac{20329129}{430760}e^{4} - \frac{2027472}{53845}e^{2} - \frac{326657}{53845}$ |
| 17 | $[17, 17, w + 2]$ | $\phantom{-}\frac{30213}{13784320}e^{14} + \frac{126513}{2756864}e^{12} + \frac{2403747}{3446080}e^{10} + \frac{6261467}{1253120}e^{8} + \frac{71985897}{2756864}e^{6} + \frac{4427955}{172304}e^{4} + \frac{3243993}{215380}e^{2} + \frac{126513}{215380}$ |
| 17 | $[17, 17, w + 14]$ | $-\frac{4339}{3446080}e^{15} - \frac{86931}{3446080}e^{13} - \frac{65085}{172304}e^{11} - \frac{1739939}{689216}e^{9} - \frac{43519963}{3446080}e^{7} - \frac{134509}{53845}e^{5} - \frac{4339}{10769}e^{3} + \frac{1686541}{107690}e$ |
| 19 | $[19, 19, w]$ | $-\frac{3373}{3446080}e^{14} - \frac{71013}{3446080}e^{12} - \frac{270953}{861520}e^{10} - \frac{7842257}{3446080}e^{8} - \frac{41474397}{3446080}e^{6} - \frac{5749037}{430760}e^{4} - \frac{122544}{10769}e^{2} - \frac{98717}{53845}$ |
| 19 | $[19, 19, w + 18]$ | $\phantom{-}\frac{39481}{6892160}e^{14} + \frac{164821}{1378432}e^{12} + \frac{3131599}{1723040}e^{10} + \frac{89520429}{6892160}e^{8} + \frac{93783149}{1378432}e^{6} + \frac{5768735}{86152}e^{4} + \frac{5519071}{107690}e^{2} + \frac{164821}{107690}$ |
| 37 | $[37, 37, -w - 4]$ | $-\frac{1675}{2756864}e^{14} - \frac{167863}{13784320}e^{12} - \frac{125625}{689216}e^{10} - \frac{3358375}{2756864}e^{8} - \frac{83717631}{13784320}e^{6} - \frac{51925}{43076}e^{4} - \frac{8375}{43076}e^{2} - \frac{109187}{215380}$ |
| 37 | $[37, 37, w - 5]$ | $-\frac{19163}{13784320}e^{14} - \frac{383707}{13784320}e^{12} - \frac{287445}{689216}e^{10} - \frac{7684363}{2756864}e^{8} - \frac{17483241}{1253120}e^{6} - \frac{594053}{215380}e^{4} - \frac{19163}{43076}e^{2} + \frac{1682041}{215380}$ |
| 43 | $[43, 43, w + 16]$ | $\phantom{-}\frac{19933}{1253120}e^{15} + \frac{924739}{2756864}e^{13} + \frac{17636969}{3446080}e^{11} + \frac{512029867}{13784320}e^{9} + \frac{2711036567}{13784320}e^{7} + \frac{195167657}{861520}e^{5} + \frac{10015418}{53845}e^{3} + \frac{6454487}{215380}e$ |
| 43 | $[43, 43, w + 26]$ | $\phantom{-}\frac{7779}{6892160}e^{15} + \frac{31175}{1378432}e^{13} + \frac{116685}{344608}e^{11} + \frac{3119379}{1378432}e^{9} + \frac{77990091}{6892160}e^{7} + \frac{241149}{107690}e^{5} + \frac{7779}{21538}e^{3} - \frac{125067}{9790}e$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}\frac{5683}{13784320}e^{14} + \frac{113907}{13784320}e^{12} + \frac{85245}{689216}e^{10} + \frac{2278883}{2756864}e^{8} + \frac{5184241}{1253120}e^{6} + \frac{176173}{215380}e^{4} + \frac{5683}{43076}e^{2} - \frac{1388901}{215380}$ |
| 53 | $[53, 53, -w - 10]$ | $-\frac{41009}{13784320}e^{14} - \frac{821361}{13784320}e^{12} - \frac{615135}{689216}e^{10} - \frac{16444609}{2756864}e^{8} - \frac{411186153}{13784320}e^{6} - \frac{1271279}{215380}e^{4} - \frac{41009}{43076}e^{2} + \frac{2670983}{215380}$ |
| 53 | $[53, 53, w - 11]$ | $\phantom{-}\frac{75685}{5513728}e^{15} + \frac{143455}{501248}e^{13} + \frac{545129}{125312}e^{11} + \frac{171223049}{5513728}e^{9} + \frac{81625895}{501248}e^{7} + \frac{5020925}{31328}e^{5} + \frac{12098123}{86152}e^{3} + \frac{28691}{7832}e$ |
| 61 | $[61, 61, w + 15]$ | $\phantom{-}\frac{6661}{3446080}e^{15} + \frac{12127}{313280}e^{13} + \frac{99915}{172304}e^{11} + \frac{2671061}{689216}e^{9} + \frac{66860493}{3446080}e^{7} + \frac{206491}{53845}e^{5} + \frac{6661}{10769}e^{3} - \frac{498483}{21538}e$ |
| 61 | $[61, 61, w + 45]$ | $-\frac{32983}{2506240}e^{15} - \frac{1525897}{5513728}e^{13} - \frac{29076059}{6892160}e^{11} - \frac{840858817}{27568640}e^{9} - \frac{4443203717}{27568640}e^{7} - \frac{309868387}{1723040}e^{5} - \frac{8203639}{53845}e^{3} - \frac{10573637}{430760}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w]$ | $-\frac{1795}{2756864}e^{14} - \frac{37395}{2756864}e^{12} - \frac{142101}{689216}e^{10} - \frac{368605}{250624}e^{8} - \frac{21277755}{2756864}e^{6} - \frac{1308825}{172304}e^{4} - \frac{78450}{10769}e^{2} - \frac{50555}{43076}$ |