Base field \(\Q(\sqrt{46}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 46\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[10,10,-w - 6]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} + x^{7} - 15x^{6} - 14x^{5} + 58x^{4} + 39x^{3} - 49x^{2} - 6x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, 23w - 156]$ | $\phantom{-}1$ |
| 3 | $[3, 3, -w - 7]$ | $\phantom{-}\frac{19}{98}e^{7} + \frac{8}{49}e^{6} - \frac{303}{98}e^{5} - \frac{213}{98}e^{4} + \frac{1311}{98}e^{3} + \frac{267}{49}e^{2} - \frac{1397}{98}e - \frac{43}{98}$ |
| 3 | $[3, 3, w - 7]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -9w + 61]$ | $-1$ |
| 5 | $[5, 5, -9w - 61]$ | $-\frac{23}{196}e^{7} - \frac{10}{49}e^{6} + \frac{341}{196}e^{5} + \frac{557}{196}e^{4} - \frac{1195}{196}e^{3} - \frac{839}{98}e^{2} + \frac{381}{196}e + \frac{377}{196}$ |
| 7 | $[7, 7, 4w - 27]$ | $-\frac{24}{49}e^{7} - \frac{43}{98}e^{6} + \frac{701}{98}e^{5} + \frac{300}{49}e^{4} - \frac{2577}{98}e^{3} - \frac{788}{49}e^{2} + \frac{960}{49}e - \frac{59}{98}$ |
| 7 | $[7, 7, 4w + 27]$ | $\phantom{-}\frac{39}{196}e^{7} + \frac{19}{98}e^{6} - \frac{591}{196}e^{5} - \frac{561}{196}e^{4} + \frac{2397}{196}e^{3} + \frac{873}{98}e^{2} - \frac{2589}{196}e - \frac{635}{196}$ |
| 23 | $[23, 23, 78w - 529]$ | $-\frac{17}{28}e^{7} - \frac{9}{14}e^{6} + \frac{249}{28}e^{5} + \frac{251}{28}e^{4} - \frac{907}{28}e^{3} - \frac{359}{14}e^{2} + \frac{631}{28}e + \frac{93}{28}$ |
| 37 | $[37, 37, -w - 3]$ | $-\frac{69}{196}e^{7} - \frac{11}{98}e^{6} + \frac{1121}{196}e^{5} + \frac{299}{196}e^{4} - \frac{5055}{196}e^{3} - \frac{263}{98}e^{2} + \frac{5651}{196}e - \frac{731}{196}$ |
| 37 | $[37, 37, w - 3]$ | $-\frac{65}{98}e^{7} - \frac{48}{49}e^{6} + \frac{985}{98}e^{5} + \frac{1327}{98}e^{4} - \frac{3799}{98}e^{3} - \frac{1896}{49}e^{2} + \frac{3139}{98}e + \frac{601}{98}$ |
| 41 | $[41, 41, -2w + 15]$ | $\phantom{-}\frac{73}{196}e^{7} + \frac{23}{98}e^{6} - \frac{1061}{196}e^{5} - \frac{643}{196}e^{4} + \frac{3763}{196}e^{3} + \frac{737}{98}e^{2} - \frac{1891}{196}e + \frac{103}{196}$ |
| 41 | $[41, 41, 2w + 15]$ | $-\frac{129}{196}e^{7} - \frac{93}{98}e^{6} + \frac{1985}{196}e^{5} + \frac{2519}{196}e^{4} - \frac{8019}{196}e^{3} - \frac{3551}{98}e^{2} + \frac{7463}{196}e + \frac{1437}{196}$ |
| 53 | $[53, 53, -3w - 19]$ | $\phantom{-}\frac{27}{28}e^{7} + \frac{9}{7}e^{6} - \frac{393}{28}e^{5} - \frac{481}{28}e^{4} + \frac{1387}{28}e^{3} + \frac{627}{14}e^{2} - \frac{765}{28}e - \frac{193}{28}$ |
| 53 | $[53, 53, 3w - 19]$ | $\phantom{-}\frac{19}{98}e^{7} + \frac{8}{49}e^{6} - \frac{303}{98}e^{5} - \frac{213}{98}e^{4} + \frac{1311}{98}e^{3} + \frac{169}{49}e^{2} - \frac{1299}{98}e + \frac{643}{98}$ |
| 59 | $[59, 59, 11w - 75]$ | $\phantom{-}\frac{39}{196}e^{7} + \frac{19}{98}e^{6} - \frac{591}{196}e^{5} - \frac{561}{196}e^{4} + \frac{2201}{196}e^{3} + \frac{775}{98}e^{2} - \frac{1021}{196}e + \frac{345}{196}$ |
| 59 | $[59, 59, -11w - 75]$ | $-\frac{41}{196}e^{7} - \frac{25}{98}e^{6} + \frac{561}{196}e^{5} + \frac{635}{196}e^{4} - \frac{1751}{196}e^{3} - \frac{571}{98}e^{2} + \frac{415}{196}e - \frac{1207}{196}$ |
| 61 | $[61, 61, -5w + 33]$ | $-\frac{9}{196}e^{7} + \frac{11}{49}e^{6} + \frac{159}{196}e^{5} - \frac{549}{196}e^{4} - \frac{817}{196}e^{3} + \frac{771}{98}e^{2} + \frac{507}{196}e - \frac{645}{196}$ |
| 61 | $[61, 61, 5w + 33]$ | $\phantom{-}\frac{193}{196}e^{7} + \frac{89}{98}e^{6} - \frac{2789}{196}e^{5} - \frac{2535}{196}e^{4} + \frac{9691}{196}e^{3} + \frac{3589}{98}e^{2} - \frac{4927}{196}e - \frac{1489}{196}$ |
| 73 | $[73, 73, -24w - 163]$ | $-\frac{199}{196}e^{7} - \frac{107}{98}e^{6} + \frac{2895}{196}e^{5} + \frac{2953}{196}e^{4} - \frac{10301}{196}e^{3} - \frac{4055}{98}e^{2} + \frac{6245}{196}e + \frac{1255}{196}$ |
| 73 | $[73, 73, -24w + 163]$ | $-\frac{61}{98}e^{7} - \frac{36}{49}e^{6} + \frac{947}{98}e^{5} + \frac{983}{98}e^{4} - \frac{3817}{98}e^{3} - \frac{1275}{49}e^{2} + \frac{3175}{98}e - \frac{713}{98}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,-23w - 156]$ | $-1$ |
| $5$ | $[5,5,9w - 61]$ | $1$ |