Base field 3.3.1957.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x + 10\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[11, 11, 10w + 4]$ |
| Dimension: | $46$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $96$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{46} + 75x^{44} + 2605x^{42} + 55618x^{40} + 817072x^{38} + 8760902x^{36} + 70974445x^{34} + 443725504x^{32} + 2168255811x^{30} + 8337514243x^{28} + 25283598959x^{26} + 60361088034x^{24} + 112831908217x^{22} + 163631847938x^{20} + 181658214560x^{18} + 151577789167x^{16} + 92764565661x^{14} + 40316063474x^{12} + 11932703144x^{10} + 2283928184x^{8} + 266910304x^{6} + 17819092x^{4} + 603021x^{2} + 7569\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{2}]$ | $\phantom{-}e$ |
| 4 | $[4, 2, w^{2} + w + 1]$ | $...$ |
| 5 | $[5, 5, w]$ | $...$ |
| 11 | $[11, 11, 10w + 4]$ | $...$ |
| 13 | $[13, 13, 12w^{2} + w + 7]$ | $...$ |
| 17 | $[17, 17, w + 1]$ | $...$ |
| 17 | $[17, 17, 16w^{2} + 16]$ | $...$ |
| 17 | $[17, 17, 16w^{2} + 16w + 8]$ | $...$ |
| 19 | $[19, 19, 18w^{2} + 18w + 1]$ | $...$ |
| 19 | $[19, 19, -w^{2} + 7]$ | $...$ |
| 25 | $[25, 5, 4w^{2} + w + 4]$ | $...$ |
| 27 | $[27, 3, -3]$ | $...$ |
| 29 | $[29, 29, w + 7]$ | $...$ |
| 41 | $[41, 41, 40w^{2} + 18]$ | $...$ |
| 43 | $[43, 43, w^{2} - 11]$ | $...$ |
| 47 | $[47, 47, 2w^{2} + 2w - 13]$ | $...$ |
| 59 | $[59, 59, w^{2} - 3]$ | $...$ |
| 73 | $[73, 73, w^{2} + 2w - 1]$ | $...$ |
| 79 | $[79, 79, w^{2} + 37]$ | $...$ |
| 97 | $[97, 97, w^{2} + 2w - 7]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, 10w + 4]$ | $-\frac{7220791746370377708714882713508691}{17194268127926806554207296363233680}e^{45} - \frac{90135041334843907312856878982175913}{2865711354654467759034549393872280}e^{43} - \frac{18754054740642040196988548913784921573}{17194268127926806554207296363233680}e^{41} - \frac{399660287892817097953498107994020934789}{17194268127926806554207296363233680}e^{39} - \frac{5858442083874194459481585590150600167411}{17194268127926806554207296363233680}e^{37} - \frac{62652829162367747204298297086191697139971}{17194268127926806554207296363233680}e^{35} - \frac{126497824433529979349238622859423482874803}{4298567031981701638551824090808420}e^{33} - \frac{393943846488611187435570244208806343938283}{2149283515990850819275912045404210}e^{31} - \frac{5109843877690822110965988243627516252988487}{5731422709308935518069098787744560}e^{29} - \frac{7326611756470340185781716213667715517940039}{2149283515990850819275912045404210}e^{27} - \frac{176485923602061119002631105153965094453344109}{17194268127926806554207296363233680}e^{25} - \frac{46393580851333445676490036162094646715452361}{1910474236436311839356366262581520}e^{23} - \frac{77140940598448826186336892455205298414130563}{1719426812792680655420729636323368}e^{21} - \frac{68843999946656984729620274866934226537100679}{1074641757995425409637956022702105}e^{19} - \frac{74838266717005091145598761361868116376842397}{1074641757995425409637956022702105}e^{17} - \frac{970251866544307339628127319339776398059885069}{17194268127926806554207296363233680}e^{15} - \frac{94857407103051013083164899557640930222642291}{2865711354654467759034549393872280}e^{13} - \frac{14503053830773665574669853753902351617892223}{1074641757995425409637956022702105}e^{11} - \frac{15520371934050189438449371679486447636150723}{4298567031981701638551824090808420}e^{9} - \frac{1256116357911428611562288698815656007501799}{2149283515990850819275912045404210}e^{7} - \frac{221111616490662603468657070098400114707517}{4298567031981701638551824090808420}e^{5} - \frac{9222042370279346625987765534967525307551}{4298567031981701638551824090808420}e^{3} - \frac{35125506748338157193170294534440666889}{1146284541861787103613819757548912}e$ |