Base field \(\Q(\sqrt{241}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 60\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[10, 10, 23w - 190]$ |
| Dimension: | $11$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $49$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{11} + x^{10} - 20x^{9} - 20x^{8} + 146x^{7} + 138x^{6} - 476x^{5} - 384x^{4} + 681x^{3} + 369x^{2} - 348x - 48\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -393w - 2854]$ | $-1$ |
| 2 | $[2, 2, -393w + 3247]$ | $\phantom{-}e$ |
| 3 | $[3, 3, 4w - 33]$ | $-\frac{2}{3}e^{10} + \frac{3}{4}e^{9} + \frac{139}{12}e^{8} - \frac{45}{4}e^{7} - \frac{847}{12}e^{6} + \frac{697}{12}e^{5} + \frac{705}{4}e^{4} - \frac{489}{4}e^{3} - \frac{609}{4}e^{2} + 89e + 13$ |
| 3 | $[3, 3, 4w + 29]$ | $-\frac{1}{6}e^{10} + \frac{1}{4}e^{9} + \frac{17}{6}e^{8} - \frac{15}{4}e^{7} - \frac{101}{6}e^{6} + \frac{229}{12}e^{5} + \frac{81}{2}e^{4} - \frac{153}{4}e^{3} - 32e^{2} + 25e + 1$ |
| 5 | $[5, 5, 42w + 305]$ | $-1$ |
| 5 | $[5, 5, -42w + 347]$ | $\phantom{-}\frac{1}{2}e^{10} - \frac{1}{2}e^{9} - \frac{35}{4}e^{8} + \frac{15}{2}e^{7} + \frac{215}{4}e^{6} - 39e^{5} - \frac{543}{4}e^{4} + 84e^{3} + \frac{481}{4}e^{2} - 65e - 12$ |
| 29 | $[29, 29, 1820w + 13217]$ | $-\frac{5}{12}e^{10} + \frac{1}{2}e^{9} + \frac{22}{3}e^{8} - \frac{15}{2}e^{7} - \frac{275}{6}e^{6} + \frac{233}{6}e^{5} + 120e^{4} - \frac{165}{2}e^{3} - \frac{455}{4}e^{2} + 62e + 14$ |
| 29 | $[29, 29, 1820w - 15037]$ | $\phantom{-}\frac{1}{2}e^{10} - \frac{1}{4}e^{9} - 9e^{8} + \frac{15}{4}e^{7} + 57e^{6} - \frac{83}{4}e^{5} - 149e^{4} + \frac{209}{4}e^{3} + \frac{277}{2}e^{2} - 50e - 18$ |
| 41 | $[41, 41, -80w - 581]$ | $-\frac{7}{6}e^{10} + \frac{3}{2}e^{9} + \frac{61}{3}e^{8} - 23e^{7} - \frac{749}{6}e^{6} + \frac{731}{6}e^{5} + 316e^{4} - 263e^{3} - 279e^{2} + 196e + 26$ |
| 41 | $[41, 41, 80w - 661]$ | $\phantom{-}\frac{17}{12}e^{10} - \frac{3}{2}e^{9} - \frac{149}{6}e^{8} + 23e^{7} + \frac{917}{6}e^{6} - \frac{737}{6}e^{5} - \frac{771}{2}e^{4} + 271e^{3} + \frac{1335}{4}e^{2} - 209e - 23$ |
| 47 | $[47, 47, 34w - 281]$ | $-\frac{1}{3}e^{10} + \frac{1}{2}e^{9} + \frac{17}{3}e^{8} - \frac{15}{2}e^{7} - \frac{101}{3}e^{6} + \frac{229}{6}e^{5} + 81e^{4} - \frac{153}{2}e^{3} - 65e^{2} + 52e + 7$ |
| 47 | $[47, 47, 34w + 247]$ | $-\frac{13}{6}e^{10} + \frac{5}{2}e^{9} + \frac{451}{12}e^{8} - 38e^{7} - \frac{2749}{12}e^{6} + \frac{601}{3}e^{5} + \frac{2301}{4}e^{4} - \frac{869}{2}e^{3} - \frac{2029}{4}e^{2} + 330e + 47$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}\frac{13}{6}e^{10} - \frac{5}{2}e^{9} - \frac{227}{6}e^{8} + 38e^{7} + \frac{697}{3}e^{6} - \frac{1199}{6}e^{5} - \frac{1175}{2}e^{4} + 430e^{3} + \frac{1041}{2}e^{2} - 319e - 51$ |
| 53 | $[53, 53, 6w + 43]$ | $-\frac{3}{4}e^{10} + e^{9} + \frac{51}{4}e^{8} - 15e^{7} - \frac{303}{4}e^{6} + 77e^{5} + \frac{737}{4}e^{4} - 159e^{3} - \frac{315}{2}e^{2} + 110e + 18$ |
| 53 | $[53, 53, 6w - 49]$ | $\phantom{-}\frac{3}{2}e^{10} - \frac{7}{4}e^{9} - \frac{105}{4}e^{8} + \frac{107}{4}e^{7} + \frac{647}{4}e^{6} - \frac{567}{4}e^{5} - \frac{1641}{4}e^{4} + \frac{1231}{4}e^{3} + \frac{1437}{4}e^{2} - 232e - 24$ |
| 59 | $[59, 59, 10w + 73]$ | $\phantom{-}\frac{2}{3}e^{10} - \frac{3}{4}e^{9} - \frac{71}{6}e^{8} + \frac{47}{4}e^{7} + \frac{223}{3}e^{6} - \frac{769}{12}e^{5} - 193e^{4} + \frac{571}{4}e^{3} + \frac{339}{2}e^{2} - 109e - 2$ |
| 59 | $[59, 59, 10w - 83]$ | $-\frac{7}{12}e^{10} + \frac{1}{2}e^{9} + \frac{61}{6}e^{8} - \frac{15}{2}e^{7} - \frac{185}{3}e^{6} + \frac{235}{6}e^{5} + \frac{301}{2}e^{4} - \frac{167}{2}e^{3} - \frac{483}{4}e^{2} + 60e + 7$ |
| 61 | $[61, 61, 4178w + 30341]$ | $-\frac{23}{12}e^{10} + \frac{5}{2}e^{9} + \frac{100}{3}e^{8} - 38e^{7} - \frac{613}{3}e^{6} + \frac{1187}{6}e^{5} + 518e^{4} - 413e^{3} - \frac{1851}{4}e^{2} + 290e + 45$ |
| 61 | $[61, 61, 4178w - 34519]$ | $\phantom{-}\frac{1}{4}e^{9} - \frac{1}{4}e^{8} - \frac{15}{4}e^{7} + \frac{11}{4}e^{6} + \frac{73}{4}e^{5} - \frac{29}{4}e^{4} - \frac{123}{4}e^{3} + \frac{3}{4}e^{2} + 10e + 1$ |
| 67 | $[67, 67, -332w + 2743]$ | $\phantom{-}\frac{5}{3}e^{10} - \frac{7}{4}e^{9} - \frac{349}{12}e^{8} + \frac{105}{4}e^{7} + \frac{2143}{12}e^{6} - \frac{1633}{12}e^{5} - \frac{1811}{4}e^{4} + \frac{1161}{4}e^{3} + \frac{1621}{4}e^{2} - 220e - 46$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -393w - 2854]$ | $1$ |
| $5$ | $[5, 5, 42w + 305]$ | $1$ |