Base field \(\Q(\sqrt{449}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 112\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $10$ |
| 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:
| \(x^{10} - 3x^{9} - 13x^{8} + 40x^{7} + 55x^{6} - 177x^{5} - 80x^{4} + 287x^{3} + 20x^{2} - 104x - 25\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 10]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w - 11]$ | $\phantom{-}\frac{109}{3467}e^{9} - \frac{291}{3467}e^{8} - \frac{1036}{3467}e^{7} + \frac{3000}{3467}e^{6} + \frac{1674}{3467}e^{5} - \frac{8689}{3467}e^{4} + \frac{6445}{3467}e^{3} + \frac{6439}{3467}e^{2} - \frac{17545}{3467}e + \frac{1413}{3467}$ |
| 5 | $[5, 5, -116w - 1171]$ | $-\frac{218}{3467}e^{9} + \frac{582}{3467}e^{8} + \frac{2072}{3467}e^{7} - \frac{6000}{3467}e^{6} - \frac{3348}{3467}e^{5} + \frac{17378}{3467}e^{4} - \frac{9423}{3467}e^{3} - \frac{16345}{3467}e^{2} + \frac{14288}{3467}e + \frac{11042}{3467}$ |
| 5 | $[5, 5, 116w - 1287]$ | $\phantom{-}\frac{342}{3467}e^{9} - \frac{1581}{3467}e^{8} - \frac{2519}{3467}e^{7} + \frac{19623}{3467}e^{6} - \frac{3272}{3467}e^{5} - \frac{79554}{3467}e^{4} + \frac{48276}{3467}e^{3} + \frac{119442}{3467}e^{2} - \frac{71303}{3467}e - \frac{41719}{3467}$ |
| 7 | $[7, 7, -1002w - 10115]$ | $-\frac{283}{3467}e^{9} + \frac{183}{3467}e^{8} + \frac{5298}{3467}e^{7} - \frac{3495}{3467}e^{6} - \frac{30969}{3467}e^{5} + \frac{20333}{3467}e^{4} + \frac{55851}{3467}e^{3} - \frac{37647}{3467}e^{2} - \frac{3049}{3467}e + \frac{3329}{3467}$ |
| 7 | $[7, 7, 1002w - 11117]$ | $\phantom{-}\frac{528}{3467}e^{9} - \frac{1346}{3467}e^{8} - \frac{8390}{3467}e^{7} + \frac{20989}{3467}e^{6} + \frac{42270}{3467}e^{5} - \frac{106945}{3467}e^{4} - \frac{61594}{3467}e^{3} + \frac{185679}{3467}e^{2} - \frac{23346}{3467}e - \frac{40930}{3467}$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}\frac{267}{3467}e^{9} - \frac{1508}{3467}e^{8} - \frac{1997}{3467}e^{7} + \frac{18513}{3467}e^{6} + \frac{61}{3467}e^{5} - \frac{72144}{3467}e^{4} + \frac{17982}{3467}e^{3} + \frac{97263}{3467}e^{2} - \frac{23034}{3467}e - \frac{33817}{3467}$ |
| 11 | $[11, 11, 10w - 111]$ | $\phantom{-}\frac{683}{3467}e^{9} - \frac{1728}{3467}e^{8} - \frac{8082}{3467}e^{7} + \frac{19816}{3467}e^{6} + \frac{30528}{3467}e^{5} - \frac{70254}{3467}e^{4} - \frac{43364}{3467}e^{3} + \frac{83128}{3467}e^{2} + \frac{20663}{3467}e - \frac{10803}{3467}$ |
| 11 | $[11, 11, -10w - 101]$ | $-\frac{150}{3467}e^{9} + \frac{146}{3467}e^{8} + \frac{1044}{3467}e^{7} + \frac{1247}{3467}e^{6} - \frac{268}{3467}e^{5} - \frac{19850}{3467}e^{4} - \frac{1649}{3467}e^{3} + \frac{45784}{3467}e^{2} - \frac{14406}{3467}e + \frac{1936}{3467}$ |
| 23 | $[23, 23, -32w + 355]$ | $-\frac{150}{3467}e^{9} + \frac{146}{3467}e^{8} + \frac{1044}{3467}e^{7} + \frac{1247}{3467}e^{6} - \frac{268}{3467}e^{5} - \frac{23317}{3467}e^{4} + \frac{1818}{3467}e^{3} + \frac{66586}{3467}e^{2} - \frac{28274}{3467}e - \frac{15399}{3467}$ |
| 23 | $[23, 23, 32w + 323]$ | $-\frac{1337}{3467}e^{9} + \frac{3474}{3467}e^{8} + \frac{17765}{3467}e^{7} - \frac{44750}{3467}e^{6} - \frac{75242}{3467}e^{5} + \frac{184794}{3467}e^{4} + \frac{94836}{3467}e^{3} - \frac{253508}{3467}e^{2} + \frac{29135}{3467}e + \frac{33528}{3467}$ |
| 41 | $[41, 41, -8w - 81]$ | $\phantom{-}\frac{203}{3467}e^{9} + \frac{126}{3467}e^{8} - \frac{6128}{3467}e^{7} + \frac{5778}{3467}e^{6} + \frac{42845}{3467}e^{5} - \frac{64434}{3467}e^{4} - \frac{78457}{3467}e^{3} + \frac{162377}{3467}e^{2} - \frac{19889}{3467}e - \frac{48292}{3467}$ |
| 41 | $[41, 41, -8w + 89]$ | $-\frac{341}{3467}e^{9} + \frac{147}{3467}e^{8} + \frac{5563}{3467}e^{7} - \frac{193}{3467}e^{6} - \frac{30333}{3467}e^{5} - \frac{9300}{3467}e^{4} + \frac{56970}{3467}e^{3} + \frac{29380}{3467}e^{2} - \frac{15692}{3467}e - \frac{10114}{3467}$ |
| 53 | $[53, 53, 4w - 45]$ | $-\frac{1093}{3467}e^{9} + \frac{3745}{3467}e^{8} + \frac{11629}{3467}e^{7} - \frac{43219}{3467}e^{6} - \frac{33803}{3467}e^{5} + \frac{152366}{3467}e^{4} + \frac{15050}{3467}e^{3} - \frac{178024}{3467}e^{2} + \frac{23862}{3467}e + \frac{37359}{3467}$ |
| 53 | $[53, 53, 4w + 41]$ | $\phantom{-}\frac{1105}{3467}e^{9} - \frac{3618}{3467}e^{8} - \frac{13238}{3467}e^{7} + \frac{51024}{3467}e^{6} + \frac{39649}{3467}e^{5} - \frac{240920}{3467}e^{4} + \frac{30985}{3467}e^{3} + \frac{407205}{3467}e^{2} - \frac{183717}{3467}e - \frac{118503}{3467}$ |
| 59 | $[59, 59, -3892w + 43181]$ | $\phantom{-}\frac{617}{3467}e^{9} - \frac{4160}{3467}e^{8} - \frac{966}{3467}e^{7} + \frac{44495}{3467}e^{6} - \frac{36295}{3467}e^{5} - \frac{134460}{3467}e^{4} + \frac{131618}{3467}e^{3} + \frac{107156}{3467}e^{2} - \frac{69161}{3467}e - \frac{18688}{3467}$ |
| 59 | $[59, 59, 3892w + 39289]$ | $\phantom{-}\frac{498}{3467}e^{9} + \frac{70}{3467}e^{8} - \frac{9568}{3467}e^{7} - \frac{3724}{3467}e^{6} + \frac{65792}{3467}e^{5} + \frac{34699}{3467}e^{4} - \frac{185349}{3467}e^{3} - \frac{90845}{3467}e^{2} + \frac{170005}{3467}e + \frac{40585}{3467}$ |
| 61 | $[61, 61, 770w - 8543]$ | $-\frac{2580}{3467}e^{9} + \frac{7365}{3467}e^{8} + \frac{30438}{3467}e^{7} - \frac{86722}{3467}e^{6} - \frac{112780}{3467}e^{5} + \frac{320777}{3467}e^{4} + \frac{132506}{3467}e^{3} - \frac{399616}{3467}e^{2} + \frac{14322}{3467}e + \frac{83224}{3467}$ |
| 61 | $[61, 61, -770w - 7773]$ | $\phantom{-}\frac{1842}{3467}e^{9} - \frac{3041}{3467}e^{8} - \frac{26827}{3467}e^{7} + \frac{38356}{3467}e^{6} + \frac{131154}{3467}e^{5} - \frac{158414}{3467}e^{4} - \frac{229929}{3467}e^{3} + \frac{223256}{3467}e^{2} + \frac{69290}{3467}e + \frac{1327}{3467}$ |
| 67 | $[67, 67, 158w + 1595]$ | $-\frac{1079}{3467}e^{9} + \frac{1004}{3467}e^{8} + \frac{19575}{3467}e^{7} - \frac{17356}{3467}e^{6} - \frac{115969}{3467}e^{5} + \frac{94124}{3467}e^{4} + \frac{240374}{3467}e^{3} - \frac{157381}{3467}e^{2} - \frac{101963}{3467}e + \frac{18965}{3467}$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).