Base field \(\Q(\sqrt{145}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 36\); narrow class number \(4\) and class number \(4\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[2, 2, w]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} + 59x^{8} + 411x^{4} + 625\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $-\frac{199}{39500}e^{11} - \frac{2779}{9875}e^{7} - \frac{45289}{39500}e^{3}$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w]$ | $\phantom{-}\frac{7}{395}e^{9} + \frac{393}{395}e^{5} + \frac{1867}{395}e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}\frac{223}{19750}e^{11} + \frac{12407}{19750}e^{7} + \frac{26889}{9875}e^{3}$ |
| 5 | $[5, 5, w + 2]$ | $\phantom{-}\frac{83}{3950}e^{10} + \frac{4547}{3950}e^{6} + \frac{8219}{1975}e^{2}$ |
| 17 | $[17, 17, w + 1]$ | $-\frac{199}{19750}e^{11} - \frac{5558}{9875}e^{7} - \frac{45289}{19750}e^{3}$ |
| 17 | $[17, 17, w + 15]$ | $-\frac{73}{1580}e^{9} - \frac{2021}{790}e^{5} - \frac{15633}{1580}e$ |
| 29 | $[29, 29, w + 14]$ | $\phantom{-}\frac{99}{7900}e^{10} + \frac{3033}{3950}e^{6} + \frac{53039}{7900}e^{2}$ |
| 37 | $[37, 37, w + 10]$ | $-\frac{51}{1580}e^{9} - \frac{1347}{790}e^{5} - \frac{2091}{1580}e$ |
| 37 | $[37, 37, w + 26]$ | $-\frac{673}{39500}e^{11} - \frac{19541}{19750}e^{7} - \frac{220353}{39500}e^{3}$ |
| 43 | $[43, 43, w + 19]$ | $\phantom{-}\frac{37}{1580}e^{9} + \frac{477}{395}e^{5} + \frac{2307}{1580}e$ |
| 43 | $[43, 43, w + 23]$ | $-\frac{501}{19750}e^{11} - \frac{14092}{9875}e^{7} - \frac{121661}{19750}e^{3}$ |
| 47 | $[47, 47, w + 22]$ | $-\frac{17}{19750}e^{11} - \frac{503}{19750}e^{7} + \frac{4194}{9875}e^{3}$ |
| 47 | $[47, 47, w + 24]$ | $-\frac{67}{1580}e^{9} - \frac{1909}{790}e^{5} - \frac{21707}{1580}e$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}\frac{19}{316}e^{8} + \frac{539}{158}e^{4} + \frac{3939}{316}$ |
| 59 | $[59, 59, w + 16]$ | $-\frac{11}{1580}e^{10} - \frac{337}{790}e^{6} - \frac{5191}{1580}e^{2}$ |
| 59 | $[59, 59, w + 42]$ | $\phantom{-}\frac{72}{1975}e^{10} + \frac{3873}{1975}e^{6} + \frac{9667}{1975}e^{2}$ |
| 71 | $[71, 71, w + 21]$ | $-\frac{129}{7900}e^{10} - \frac{3593}{3950}e^{6} - \frac{14769}{7900}e^{2}$ |
| 71 | $[71, 71, w + 49]$ | $-\frac{277}{7900}e^{10} - \frac{7409}{3950}e^{6} - \frac{39797}{7900}e^{2}$ |
| 73 | $[73, 73, w + 13]$ | $\phantom{-}\frac{247}{39500}e^{11} + \frac{6849}{19750}e^{7} + \frac{62267}{39500}e^{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $\frac{199}{39500}e^{11} + \frac{2779}{9875}e^{7} + \frac{45289}{39500}e^{3}$ |