Base field 4.4.16317.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 5x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[25, 5, w^{2} - w - 3]$ |
| Dimension: | $20$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $50$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{20} - 72x^{18} + 2108x^{16} - 32352x^{14} + 280256x^{12} - 1377024x^{10} + 3659776x^{8} - 4729344x^{6} + 2489088x^{4} - 285696x^{2} + 9216\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w + 1]$ | $\phantom{-}\frac{237655451}{260390520576}e^{19} - \frac{2137429757}{32548815072}e^{17} + \frac{83354707229}{43398420096}e^{15} - \frac{212878198577}{7233070016}e^{13} + \frac{8277103929407}{32548815072}e^{11} - \frac{20240375647199}{16274407536}e^{9} + \frac{370022356443}{113016719}e^{7} - \frac{5603570404057}{1356200628}e^{5} + \frac{455410446749}{226033438}e^{3} - \frac{13682688419}{113016719}e$ |
| 5 | $[5, 5, -w + 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w^{2} + 2w + 1]$ | $-\frac{33993895}{260390520576}e^{18} + \frac{1222657081}{130195260288}e^{16} - \frac{5957397497}{21699210048}e^{14} + \frac{91207628969}{21699210048}e^{12} - \frac{295031809699}{8137203768}e^{10} + \frac{2876330039041}{16274407536}e^{8} - \frac{52229386852}{113016719}e^{6} + \frac{259741303509}{452066876}e^{4} - \frac{30635164210}{113016719}e^{2} + \frac{1768346987}{113016719}$ |
| 7 | $[7, 7, -w^{2} + 2]$ | $\phantom{-}\frac{49721651}{260390520576}e^{18} - \frac{3579047887}{260390520576}e^{16} + \frac{4364509339}{10849605024}e^{14} - \frac{44629468807}{7233070016}e^{12} + \frac{108618901271}{2034300942}e^{10} - \frac{4259665492487}{16274407536}e^{8} + \frac{937666316363}{1356200628}e^{6} - \frac{1188188954023}{1356200628}e^{4} + \frac{48406752832}{113016719}e^{2} - \frac{3148525128}{113016719}$ |
| 9 | $[9, 3, w^{3} - w^{2} - 4w]$ | $\phantom{-}\frac{3931939}{65097630144}e^{18} - \frac{1133733725}{260390520576}e^{16} + \frac{923873727}{7233070016}e^{14} - \frac{10670194363}{5424802512}e^{12} + \frac{139443795385}{8137203768}e^{10} - \frac{691667726723}{8137203768}e^{8} + \frac{310913674139}{1356200628}e^{6} - \frac{102241260874}{339050157}e^{4} + \frac{17771588622}{113016719}e^{2} - \frac{1380178141}{113016719}$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}\frac{9489251}{65097630144}e^{18} - \frac{1360486547}{130195260288}e^{16} + \frac{4398466183}{14466140032}e^{14} - \frac{50169659059}{10849605024}e^{12} + \frac{1285715203967}{32548815072}e^{10} - \frac{771965331371}{4068601884}e^{8} + \frac{1314886089221}{2712401256}e^{6} - \frac{394732519501}{678100314}e^{4} + \frac{60892707339}{226033438}e^{2} - \frac{2177201013}{113016719}$ |
| 17 | $[17, 17, -w^{3} + 2w^{2} + 3w - 2]$ | $-\frac{6230521}{8137203768}e^{19} + \frac{2390636035}{43398420096}e^{17} - \frac{209726753159}{130195260288}e^{15} + \frac{178477223709}{7233070016}e^{13} - \frac{6934890162113}{32548815072}e^{11} + \frac{5645211327809}{5424802512}e^{9} - \frac{22229856492175}{8137203768}e^{7} + \frac{1161724860656}{339050157}e^{5} - \frac{1117518364361}{678100314}e^{3} + \frac{10517792601}{113016719}e$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 4w - 2]$ | $-\frac{14744475}{57864560128}e^{19} + \frac{4774115909}{260390520576}e^{17} - \frac{34910362687}{65097630144}e^{15} + \frac{22291121783}{2712401256}e^{13} - \frac{128429165649}{1808267504}e^{11} + \frac{353540913211}{1017150471}e^{9} - \frac{933002916203}{1017150471}e^{7} + \frac{132231688463}{113016719}e^{5} - \frac{204239858236}{339050157}e^{3} + \frac{7320137611}{113016719}e$ |
| 25 | $[25, 5, w^{2} - w - 3]$ | $-1$ |
| 37 | $[37, 37, 2w - 1]$ | $\phantom{-}\frac{4215835}{65097630144}e^{18} - \frac{604431019}{130195260288}e^{16} + \frac{366810511}{2712401256}e^{14} - \frac{11196003481}{5424802512}e^{12} + \frac{289342808933}{16274407536}e^{10} - \frac{176975961845}{2034300942}e^{8} + \frac{104536939631}{452066876}e^{6} - \frac{102432993973}{339050157}e^{4} + \frac{18700177146}{113016719}e^{2} - \frac{2023728952}{113016719}$ |
| 43 | $[43, 43, -w^{3} + 2w^{2} + 2w - 2]$ | $\phantom{-}\frac{22626545}{65097630144}e^{18} - \frac{406284475}{16274407536}e^{16} + \frac{15804156823}{21699210048}e^{14} - \frac{3769627769}{339050157}e^{12} + \frac{777073788287}{8137203768}e^{10} - \frac{1881646465775}{4068601884}e^{8} + \frac{270517103101}{226033438}e^{6} - \frac{496782047276}{339050157}e^{4} + \frac{77735707437}{113016719}e^{2} - \frac{4638962480}{113016719}$ |
| 43 | $[43, 43, w^{3} - w^{2} - 3w + 1]$ | $\phantom{-}\frac{22626545}{65097630144}e^{18} - \frac{406284475}{16274407536}e^{16} + \frac{15804156823}{21699210048}e^{14} - \frac{3769627769}{339050157}e^{12} + \frac{777073788287}{8137203768}e^{10} - \frac{1881646465775}{4068601884}e^{8} + \frac{270517103101}{226033438}e^{6} - \frac{496782047276}{339050157}e^{4} + \frac{77735707437}{113016719}e^{2} - \frac{4638962480}{113016719}$ |
| 59 | $[59, 59, 2w - 5]$ | $-\frac{287646283}{520781041152}e^{19} + \frac{323191909}{8137203768}e^{17} - \frac{151106668237}{130195260288}e^{15} + \frac{385330290665}{21699210048}e^{13} - \frac{4981197590855}{32548815072}e^{11} + \frac{12123247670233}{16274407536}e^{9} - \frac{3952488074897}{2034300942}e^{7} + \frac{3259322512735}{1356200628}e^{5} - \frac{756402567013}{678100314}e^{3} + \frac{4257784301}{113016719}e$ |
| 59 | $[59, 59, -2w - 3]$ | $\phantom{-}\frac{364203841}{520781041152}e^{19} - \frac{2182960489}{43398420096}e^{17} + \frac{191444036765}{130195260288}e^{15} - \frac{488533215269}{21699210048}e^{13} + \frac{6323411358149}{32548815072}e^{11} - \frac{5142663111335}{5424802512}e^{9} + \frac{20221705471309}{8137203768}e^{7} - \frac{351332789514}{113016719}e^{5} + \frac{502388246371}{339050157}e^{3} - \frac{6631563086}{113016719}e$ |
| 79 | $[79, 79, -w^{3} + 2w^{2} + 5w - 4]$ | $\phantom{-}\frac{42135577}{130195260288}e^{18} - \frac{6071154439}{260390520576}e^{16} + \frac{3705814369}{5424802512}e^{14} - \frac{227685318137}{21699210048}e^{12} + \frac{370107503533}{4068601884}e^{10} - \frac{7274954791331}{16274407536}e^{8} + \frac{535683329995}{452066876}e^{6} - \frac{2049322790621}{1356200628}e^{4} + \frac{84631176077}{113016719}e^{2} - \frac{4592047894}{113016719}$ |
| 79 | $[79, 79, -w^{3} + w^{2} + 6w - 2]$ | $\phantom{-}\frac{9562513}{130195260288}e^{18} - \frac{169246601}{32548815072}e^{16} + \frac{1076087473}{7233070016}e^{14} - \frac{47968648901}{21699210048}e^{12} + \frac{148687934135}{8137203768}e^{10} - \frac{1361241225227}{16274407536}e^{8} + \frac{134554219175}{678100314}e^{6} - \frac{287074917149}{1356200628}e^{4} + \frac{9819707389}{113016719}e^{2} - \frac{1189020325}{113016719}$ |
| 83 | $[83, 83, -w^{3} + 7w]$ | $\phantom{-}\frac{315073717}{173593680384}e^{19} - \frac{4246982635}{32548815072}e^{17} + \frac{31016875193}{8137203768}e^{15} - \frac{421723293907}{7233070016}e^{13} + \frac{2725448472325}{5424802512}e^{11} - \frac{39811532201347}{16274407536}e^{9} + \frac{26000963991605}{4068601884}e^{7} - \frac{5391116079737}{678100314}e^{5} + \frac{2560377485387}{678100314}e^{3} - \frac{22026614172}{113016719}e$ |
| 83 | $[83, 83, -w^{3} + 2w^{2} + 4w - 2]$ | $-\frac{500918557}{520781041152}e^{19} + \frac{9003320285}{130195260288}e^{17} - \frac{87682216331}{43398420096}e^{15} + \frac{335372461067}{10849605024}e^{13} - \frac{8672811321317}{32548815072}e^{11} + \frac{10563539670469}{8137203768}e^{9} - \frac{3068477413387}{904133752}e^{7} + \frac{953744337285}{226033438}e^{5} - \frac{223256140556}{113016719}e^{3} + \frac{8457940694}{113016719}e$ |
| 83 | $[83, 83, -w^{3} + w^{2} + 5w - 3]$ | $\phantom{-}\frac{29780709}{14466140032}e^{19} - \frac{12851293655}{86796840192}e^{17} + \frac{46957662949}{10849605024}e^{15} - \frac{479285444331}{7233070016}e^{13} + \frac{516963707065}{904133752}e^{11} - \frac{15137365917241}{5424802512}e^{9} + \frac{2481785000278}{339050157}e^{7} - \frac{4153231289669}{452066876}e^{5} + \frac{505250991691}{113016719}e^{3} - \frac{33179244634}{113016719}e$ |
| 83 | $[83, 83, w^{2} - 2w - 6]$ | $\phantom{-}\frac{182244671}{57864560128}e^{19} - \frac{29496966895}{130195260288}e^{17} + \frac{862463919305}{130195260288}e^{15} - \frac{183466711021}{1808267504}e^{13} + \frac{3168158833635}{3616535008}e^{11} - \frac{34822350961793}{8137203768}e^{9} + \frac{45750735067385}{4068601884}e^{7} - \frac{4799107677202}{339050157}e^{5} + \frac{4682469364529}{678100314}e^{3} - \frac{48502439592}{113016719}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $25$ | $[25, 5, w^{2} - w - 3]$ | $1$ |