Base field \(\Q(\sqrt{197}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 49\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[29,29,w - 5]$ |
| Dimension: | $54$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $108$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{54} - 2x^{53} - 133x^{52} + 268x^{51} + 8272x^{50} - 16825x^{49} - 319968x^{48} + 658156x^{47} + 8635374x^{46} - 17997267x^{45} - 172916084x^{44} + 365848673x^{43} + 2667090220x^{42} - 5739839502x^{41} - 32472185366x^{40} + 71227837755x^{39} + 317270452161x^{38} - 710816206353x^{37} - 2515682661239x^{36} + 5769334196574x^{35} + 16307659528406x^{34} - 38370404064539x^{33} - 86809096479215x^{32} + 210050912308636x^{31} + 380258680278329x^{30} - 948415449414785x^{29} - 1370820599982757x^{28} + 3531478092699099x^{27} + 4060707677770986x^{26} - 10819933462379680x^{25} - 9856286602143674x^{24} + 27157216473285106x^{23} + 19532084214774691x^{22} - 55458170873705714x^{21} - 31489192390349172x^{20} + 91247033035128753x^{19} + 41205074292366178x^{18} - 119327103748831662x^{17} - 43768164702389378x^{16} + 121698334645265535x^{15} + 37801593280749129x^{14} - 94197277643225408x^{13} - 26449205068330345x^{12} + 53108649404187061x^{11} + 14617124361915842x^{10} - 20388549058815510x^{9} - 5952451278417886x^{8} + 4690502963946844x^{7} + 1549335598754155x^{6} - 465440763513095x^{5} - 189336779355386x^{4} - 5101809736052x^{3} + 2128987298472x^{2} + 108011083502x - 1904936045\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w - 7]$ | $...$ |
| 7 | $[7, 7, w + 6]$ | $...$ |
| 9 | $[9, 3, 3]$ | $...$ |
| 19 | $[19, 19, w + 5]$ | $...$ |
| 19 | $[19, 19, w - 6]$ | $...$ |
| 23 | $[23, 23, w + 8]$ | $...$ |
| 23 | $[23, 23, -w + 9]$ | $...$ |
| 25 | $[25, 5, 5]$ | $...$ |
| 29 | $[29, 29, -w - 4]$ | $...$ |
| 29 | $[29, 29, w - 5]$ | $-1$ |
| 37 | $[37, 37, -w - 3]$ | $...$ |
| 37 | $[37, 37, w - 4]$ | $...$ |
| 41 | $[41, 41, -w - 9]$ | $...$ |
| 41 | $[41, 41, w - 10]$ | $...$ |
| 43 | $[43, 43, -w - 2]$ | $...$ |
| 43 | $[43, 43, w - 3]$ | $...$ |
| 47 | $[47, 47, -w - 1]$ | $...$ |
| 47 | $[47, 47, w - 2]$ | $...$ |
| 53 | $[53, 53, 2w - 13]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29,29,w - 5]$ | $1$ |