Base field 3.3.1825.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x + 7\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[7, 7, w]$ |
| Dimension: | $9$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{9} + x^{8} - 28x^{7} - 13x^{6} + 234x^{5} + 8x^{4} - 598x^{3} + 309x^{2} + 115x - 25\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w + 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w]$ | $-1$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}\frac{12247}{544250}e^{8} + \frac{24531}{272125}e^{7} - \frac{156088}{272125}e^{6} - \frac{1095981}{544250}e^{5} + \frac{2458553}{544250}e^{4} + \frac{895023}{77750}e^{3} - \frac{5564361}{544250}e^{2} - \frac{2283261}{272125}e + \frac{442643}{108850}$ |
| 11 | $[11, 11, w + 2]$ | $\phantom{-}\frac{1321}{54425}e^{8} + \frac{4141}{54425}e^{7} - \frac{32268}{54425}e^{6} - \frac{85233}{54425}e^{5} + \frac{225054}{54425}e^{4} + \frac{63039}{7775}e^{3} - \frac{351373}{54425}e^{2} - \frac{191771}{54425}e - \frac{21706}{10885}$ |
| 13 | $[13, 13, w + 1]$ | $-\frac{24848}{272125}e^{8} - \frac{89741}{544250}e^{7} + \frac{1287793}{544250}e^{6} + \frac{1674283}{544250}e^{5} - \frac{4732977}{272125}e^{4} - \frac{1150039}{77750}e^{3} + \frac{8914249}{272125}e^{2} - \frac{645479}{544250}e - \frac{34799}{108850}$ |
| 17 | $[17, 17, -w^{2} - w + 4]$ | $\phantom{-}\frac{15551}{544250}e^{8} + \frac{5571}{544250}e^{7} - \frac{403883}{544250}e^{6} + \frac{14526}{272125}e^{5} + \frac{2735599}{544250}e^{4} - \frac{45758}{38875}e^{3} - \frac{4126113}{544250}e^{2} + \frac{1959249}{544250}e - \frac{100703}{54425}$ |
| 23 | $[23, 23, -w^{2} + 6]$ | $\phantom{-}\frac{1264}{272125}e^{8} - \frac{17956}{272125}e^{7} - \frac{48262}{272125}e^{6} + \frac{443578}{272125}e^{5} + \frac{355711}{272125}e^{4} - \frac{388524}{38875}e^{3} - \frac{488857}{272125}e^{2} + \frac{3558686}{272125}e - \frac{272484}{54425}$ |
| 23 | $[23, 23, -w^{2} - w + 3]$ | $-\frac{12142}{272125}e^{8} - \frac{8357}{272125}e^{7} + \frac{355961}{272125}e^{6} + \frac{64566}{272125}e^{5} - \frac{3128908}{272125}e^{4} + \frac{108672}{38875}e^{3} + \frac{8266746}{272125}e^{2} - \frac{6595958}{272125}e - \frac{201248}{54425}$ |
| 23 | $[23, 23, -w + 4]$ | $-\frac{3701}{544250}e^{8} - \frac{18923}{272125}e^{7} + \frac{9729}{272125}e^{6} + \frac{932023}{544250}e^{5} + \frac{837301}{544250}e^{4} - \frac{965709}{77750}e^{3} - \frac{6477687}{544250}e^{2} + \frac{6007263}{272125}e + \frac{286481}{108850}$ |
| 27 | $[27, 3, 3]$ | $-\frac{25537}{272125}e^{8} - \frac{30777}{272125}e^{7} + \frac{679246}{272125}e^{6} + \frac{518276}{272125}e^{5} - \frac{5079513}{272125}e^{4} - \frac{346383}{38875}e^{3} + \frac{10245756}{272125}e^{2} - \frac{664688}{272125}e - \frac{355078}{54425}$ |
| 29 | $[29, 29, -w^{2} - 2w + 4]$ | $\phantom{-}\frac{214}{10885}e^{8} - \frac{491}{10885}e^{7} - \frac{7172}{10885}e^{6} + \frac{14233}{10885}e^{5} + \frac{71091}{10885}e^{4} - \frac{14749}{1555}e^{3} - \frac{234897}{10885}e^{2} + \frac{172576}{10885}e + \frac{13046}{2177}$ |
| 31 | $[31, 31, w^{2} - 10]$ | $-\frac{1001}{7775}e^{8} - \frac{1896}{7775}e^{7} + \frac{25758}{7775}e^{6} + \frac{36323}{7775}e^{5} - \frac{189524}{7775}e^{4} - \frac{192663}{7775}e^{3} + \frac{384588}{7775}e^{2} + \frac{121026}{7775}e - \frac{18559}{1555}$ |
| 41 | $[41, 41, w + 4]$ | $\phantom{-}\frac{58197}{544250}e^{8} + \frac{41756}{272125}e^{7} - \frac{760763}{272125}e^{6} - \frac{1435081}{544250}e^{5} + \frac{11260853}{544250}e^{4} + \frac{921323}{77750}e^{3} - \frac{22631711}{544250}e^{2} + \frac{1015639}{272125}e + \frac{606043}{108850}$ |
| 41 | $[41, 41, w^{2} - 5]$ | $\phantom{-}\frac{43349}{544250}e^{8} + \frac{30102}{272125}e^{7} - \frac{559971}{272125}e^{6} - \frac{1037877}{544250}e^{5} + \frac{7929751}{544250}e^{4} + \frac{711991}{77750}e^{3} - \frac{12728087}{544250}e^{2} - \frac{51887}{272125}e - \frac{830969}{108850}$ |
| 41 | $[41, 41, -2w - 5]$ | $-\frac{30399}{544250}e^{8} - \frac{28879}{544250}e^{7} + \frac{805467}{544250}e^{6} + \frac{184076}{272125}e^{5} - \frac{6066701}{544250}e^{4} - \frac{58908}{38875}e^{3} + \frac{13485487}{544250}e^{2} - \frac{5182801}{544250}e - \frac{400103}{54425}$ |
| 43 | $[43, 43, w^{2} - w - 4]$ | $-\frac{5321}{54425}e^{8} - \frac{12766}{54425}e^{7} + \frac{129193}{54425}e^{6} + \frac{261208}{54425}e^{5} - \frac{840229}{54425}e^{4} - \frac{217089}{7775}e^{3} + \frac{1098548}{54425}e^{2} + \frac{1460946}{54425}e - \frac{52664}{10885}$ |
| 47 | $[47, 47, w^{2} - w - 9]$ | $\phantom{-}\frac{10992}{272125}e^{8} + \frac{16082}{272125}e^{7} - \frac{330136}{272125}e^{6} - \frac{313991}{272125}e^{5} + \frac{3110558}{272125}e^{4} + \frac{211103}{38875}e^{3} - \frac{9407796}{272125}e^{2} + \frac{706733}{272125}e + \frac{441923}{54425}$ |
| 49 | $[49, 7, w^{2} - w - 8]$ | $\phantom{-}\frac{117357}{544250}e^{8} + \frac{79686}{272125}e^{7} - \frac{1526778}{272125}e^{6} - \frac{2626511}{544250}e^{5} + \frac{22313693}{544250}e^{4} + \frac{1578013}{77750}e^{3} - \frac{43212791}{544250}e^{2} + \frac{3627809}{272125}e + \frac{552383}{108850}$ |
| 53 | $[53, 53, 2w^{2} + w - 12]$ | $\phantom{-}\frac{4731}{54425}e^{8} + \frac{21627}{108850}e^{7} - \frac{229521}{108850}e^{6} - \frac{430501}{108850}e^{5} + \frac{747994}{54425}e^{4} + \frac{342783}{15550}e^{3} - \frac{1052153}{54425}e^{2} - \frac{1858737}{108850}e - \frac{5977}{21770}$ |
| 59 | $[59, 59, w^{2} - 3]$ | $\phantom{-}\frac{3712}{54425}e^{8} + \frac{5827}{54425}e^{7} - \frac{100396}{54425}e^{6} - \frac{99301}{54425}e^{5} + \frac{805563}{54425}e^{4} + \frac{52333}{7775}e^{3} - \frac{1877231}{54425}e^{2} + \frac{533763}{54425}e - \frac{21722}{10885}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, w]$ | $1$ |