Base field \(\Q(\sqrt{205}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 51\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[7, 7, w + 1]$ |
| Dimension: | $34$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $68$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{34} + 76x^{32} + 2588x^{30} + 52226x^{28} + 696138x^{26} + 6466337x^{24} + 43028165x^{22} + 207533088x^{20} + 725379405x^{18} + 1816507018x^{16} + 3182392382x^{14} + 3749319102x^{12} + 2795916984x^{10} + 1207951393x^{8} + 266603777x^{6} + 24513160x^{4} + 617744x^{2} + 1024\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $...$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $...$ |
| 5 | $[5, 5, -w + 8]$ | $...$ |
| 7 | $[7, 7, w + 1]$ | $...$ |
| 7 | $[7, 7, w + 5]$ | $...$ |
| 13 | $[13, 13, w + 3]$ | $...$ |
| 13 | $[13, 13, w + 9]$ | $...$ |
| 17 | $[17, 17, w]$ | $...$ |
| 17 | $[17, 17, w + 16]$ | $...$ |
| 31 | $[31, 31, -w - 4]$ | $...$ |
| 31 | $[31, 31, w - 5]$ | $...$ |
| 41 | $[41, 41, 3w - 22]$ | $...$ |
| 47 | $[47, 47, w + 19]$ | $...$ |
| 47 | $[47, 47, w + 27]$ | $...$ |
| 53 | $[53, 53, w + 14]$ | $...$ |
| 53 | $[53, 53, w + 38]$ | $...$ |
| 59 | $[59, 59, -w - 10]$ | $...$ |
| 59 | $[59, 59, w - 11]$ | $...$ |
| 61 | $[61, 61, 2w - 13]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, w + 1]$ | $-\frac{5611208529239384832043}{93112812469159685355593728}e^{33} - \frac{425305302612245294579129}{93112812469159685355593728}e^{31} - \frac{14439167419245193093729995}{93112812469159685355593728}e^{29} - \frac{290407441855913349093008587}{93112812469159685355593728}e^{27} - \frac{3856634761726424667511637331}{93112812469159685355593728}e^{25} - \frac{4459896479594969532975051583}{11639101558644960669449216}e^{23} - \frac{236380530585057082438250548527}{93112812469159685355593728}e^{21} - \frac{1134808538473506056989082734337}{93112812469159685355593728}e^{19} - \frac{1973521905784102740784577432295}{46556406234579842677796864}e^{17} - \frac{614633477932487976241301000163}{5819550779322480334724608}e^{15} - \frac{8569575491658053184072447031845}{46556406234579842677796864}e^{13} - \frac{1255289558987812125420144605661}{5819550779322480334724608}e^{11} - \frac{1861414514838272808144032246297}{11639101558644960669449216}e^{9} - \frac{6386455821941696813171099404435}{93112812469159685355593728}e^{7} - \frac{173891806931118470275497315021}{11639101558644960669449216}e^{5} - \frac{7705329331647784084422262955}{5819550779322480334724608}e^{3} - \frac{591187698403803367005169}{22732620231728438807518}e$ |