# Properties

 Label 6.6.703493.1-49.1-b Base field 6.6.703493.1 Weight $[2, 2, 2, 2, 2, 2]$ Level norm $49$ Level $[49, 7, 2w^{5} - w^{4} - 12w^{3} + 5w^{2} + 13w - 4]$ Dimension $10$ CM no Base change yes

# Related objects

• L-function not available

## Base field 6.6.703493.1

Generator $$w$$, with minimal polynomial $$x^{6} - 2x^{5} - 5x^{4} + 11x^{3} + 2x^{2} - 9x + 1$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2, 2, 2]$ Level: $[49, 7, 2w^{5} - w^{4} - 12w^{3} + 5w^{2} + 13w - 4]$ Dimension: $10$ CM: no Base change: yes Newspace dimension: $16$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

 $$x^{10} - 2x^{9} - 61x^{8} + 150x^{7} + 982x^{6} - 3096x^{5} - 2013x^{4} + 10564x^{3} - 580x^{2} - 9416x + 1456$$
Norm Prime Eigenvalue
13 $[13, 13, 3w^{5} - 2w^{4} - 17w^{3} + 10w^{2} + 16w - 3]$ $\phantom{-}e$
13 $[13, 13, w^{5} - w^{4} - 5w^{3} + 5w^{2} + 3w - 3]$ $\phantom{-}e$
13 $[13, 13, 2w^{5} - w^{4} - 12w^{3} + 4w^{2} + 13w]$ $-\frac{249450329}{1561462156604}e^{9} - \frac{1574522153}{780731078302}e^{8} + \frac{18682232881}{1561462156604}e^{7} + \frac{90312154355}{780731078302}e^{6} - \frac{39277322381}{111533011186}e^{5} - \frac{647717390956}{390365539151}e^{4} + \frac{7182695299093}{1561462156604}e^{3} + \frac{626615278650}{390365539151}e^{2} - \frac{2613153633425}{390365539151}e + \frac{180949662384}{55766505593}$
13 $[13, 13, -w^{2} + 3]$ $-\frac{249450329}{1561462156604}e^{9} - \frac{1574522153}{780731078302}e^{8} + \frac{18682232881}{1561462156604}e^{7} + \frac{90312154355}{780731078302}e^{6} - \frac{39277322381}{111533011186}e^{5} - \frac{647717390956}{390365539151}e^{4} + \frac{7182695299093}{1561462156604}e^{3} + \frac{626615278650}{390365539151}e^{2} - \frac{2613153633425}{390365539151}e + \frac{180949662384}{55766505593}$
41 $[41, 41, -2w^{5} + w^{4} + 11w^{3} - 4w^{2} - 10w - 1]$ $-\frac{3210047721}{1561462156604}e^{9} + \frac{632027281}{780731078302}e^{8} + \frac{201550461341}{1561462156604}e^{7} - \frac{84157610479}{780731078302}e^{6} - \frac{258818040179}{111533011186}e^{5} + \frac{1188782656610}{390365539151}e^{4} + \frac{16485576456465}{1561462156604}e^{3} - \frac{4349721961251}{390365539151}e^{2} - \frac{4580339003552}{390365539151}e + \frac{257564496808}{55766505593}$
41 $[41, 41, -4w^{5} + 3w^{4} + 23w^{3} - 14w^{2} - 22w + 4]$ $-\frac{3210047721}{1561462156604}e^{9} + \frac{632027281}{780731078302}e^{8} + \frac{201550461341}{1561462156604}e^{7} - \frac{84157610479}{780731078302}e^{6} - \frac{258818040179}{111533011186}e^{5} + \frac{1188782656610}{390365539151}e^{4} + \frac{16485576456465}{1561462156604}e^{3} - \frac{4349721961251}{390365539151}e^{2} - \frac{4580339003552}{390365539151}e + \frac{257564496808}{55766505593}$
41 $[41, 41, w^{5} - 6w^{3} + w^{2} + 7w - 2]$ $-\frac{12164277169}{7807310783020}e^{9} - \frac{2972779856}{1951827695755}e^{8} + \frac{740084960717}{7807310783020}e^{7} + \frac{69994951409}{1951827695755}e^{6} - \frac{186554964711}{111533011186}e^{5} + \frac{1450660439831}{1951827695755}e^{4} + \frac{67147958117729}{7807310783020}e^{3} - \frac{29554207783757}{3903655391510}e^{2} - \frac{21761170194903}{1951827695755}e + \frac{2903223230266}{278832527965}$
41 $[41, 41, -3w^{5} + w^{4} + 18w^{3} - 4w^{2} - 20w - 1]$ $-\frac{12164277169}{7807310783020}e^{9} - \frac{2972779856}{1951827695755}e^{8} + \frac{740084960717}{7807310783020}e^{7} + \frac{69994951409}{1951827695755}e^{6} - \frac{186554964711}{111533011186}e^{5} + \frac{1450660439831}{1951827695755}e^{4} + \frac{67147958117729}{7807310783020}e^{3} - \frac{29554207783757}{3903655391510}e^{2} - \frac{21761170194903}{1951827695755}e + \frac{2903223230266}{278832527965}$
43 $[43, 43, 3w^{5} - 2w^{4} - 17w^{3} + 11w^{2} + 16w - 6]$ $-\frac{49914469183}{15614621566040}e^{9} - \frac{6776563797}{3903655391510}e^{8} + \frac{3006956162339}{15614621566040}e^{7} + \frac{5364819034}{1951827695755}e^{6} - \frac{728125133955}{223066022372}e^{5} + \frac{8149880708507}{3903655391510}e^{4} + \frac{219198911878843}{15614621566040}e^{3} - \frac{53081483918989}{7807310783020}e^{2} - \frac{37504947529333}{1951827695755}e + \frac{1436269741226}{278832527965}$
43 $[43, 43, -2w^{5} + w^{4} + 12w^{3} - 6w^{2} - 14w + 5]$ $-\frac{49914469183}{15614621566040}e^{9} - \frac{6776563797}{3903655391510}e^{8} + \frac{3006956162339}{15614621566040}e^{7} + \frac{5364819034}{1951827695755}e^{6} - \frac{728125133955}{223066022372}e^{5} + \frac{8149880708507}{3903655391510}e^{4} + \frac{219198911878843}{15614621566040}e^{3} - \frac{53081483918989}{7807310783020}e^{2} - \frac{37504947529333}{1951827695755}e + \frac{1436269741226}{278832527965}$
49 $[49, 7, 2w^{5} - w^{4} - 12w^{3} + 5w^{2} + 13w - 4]$ $-1$
64 $[64, 2, -2]$ $-\frac{681241697}{557665055930}e^{9} + \frac{594595139}{278832527965}e^{8} + \frac{44860175061}{557665055930}e^{7} - \frac{41328227721}{278832527965}e^{6} - \frac{87113199411}{55766505593}e^{5} + \frac{782468452711}{278832527965}e^{4} + \frac{4761115525577}{557665055930}e^{3} - \frac{2092447839461}{278832527965}e^{2} - \frac{5635615680058}{278832527965}e + \frac{2193369114692}{278832527965}$
71 $[71, 71, -2w^{5} + w^{4} + 12w^{3} - 4w^{2} - 12w - 1]$ $-\frac{77231672163}{15614621566040}e^{9} + \frac{64722616461}{7807310783020}e^{8} + \frac{4647691330839}{15614621566040}e^{7} - \frac{4864672579659}{7807310783020}e^{6} - \frac{1038655012547}{223066022372}e^{5} + \frac{24281052287461}{1951827695755}e^{4} + \frac{122058728606583}{15614621566040}e^{3} - \frac{54239879733296}{1951827695755}e^{2} + \frac{2872781079029}{3903655391510}e + \frac{2412201965181}{278832527965}$
71 $[71, 71, -3w^{5} + 2w^{4} + 17w^{3} - 9w^{2} - 15w]$ $-\frac{77231672163}{15614621566040}e^{9} + \frac{64722616461}{7807310783020}e^{8} + \frac{4647691330839}{15614621566040}e^{7} - \frac{4864672579659}{7807310783020}e^{6} - \frac{1038655012547}{223066022372}e^{5} + \frac{24281052287461}{1951827695755}e^{4} + \frac{122058728606583}{15614621566040}e^{3} - \frac{54239879733296}{1951827695755}e^{2} + \frac{2872781079029}{3903655391510}e + \frac{2412201965181}{278832527965}$
83 $[83, 83, 4w^{5} - 2w^{4} - 24w^{3} + 9w^{2} + 26w - 1]$ $-\frac{5623871639}{780731078302}e^{9} - \frac{1627640631}{780731078302}e^{8} + \frac{337434562873}{780731078302}e^{7} - \frac{69561449857}{780731078302}e^{6} - \frac{399480447896}{55766505593}e^{5} + \frac{2232436518495}{390365539151}e^{4} + \frac{20877089825203}{780731078302}e^{3} - \frac{8608283087879}{780731078302}e^{2} - \frac{11854997277815}{390365539151}e + \frac{45422950652}{55766505593}$
83 $[83, 83, -4w^{5} + 2w^{4} + 23w^{3} - 9w^{2} - 23w]$ $-\frac{5623871639}{780731078302}e^{9} - \frac{1627640631}{780731078302}e^{8} + \frac{337434562873}{780731078302}e^{7} - \frac{69561449857}{780731078302}e^{6} - \frac{399480447896}{55766505593}e^{5} + \frac{2232436518495}{390365539151}e^{4} + \frac{20877089825203}{780731078302}e^{3} - \frac{8608283087879}{780731078302}e^{2} - \frac{11854997277815}{390365539151}e + \frac{45422950652}{55766505593}$
97 $[97, 97, -w^{5} + 7w^{3} + w^{2} - 11w - 3]$ $\phantom{-}\frac{4328363029}{1951827695755}e^{9} - \frac{34050091067}{3903655391510}e^{8} - \frac{244623647437}{1951827695755}e^{7} + \frac{2288848122943}{3903655391510}e^{6} + \frac{81753236518}{55766505593}e^{5} - \frac{20582365555459}{1951827695755}e^{4} + \frac{17309461333446}{1951827695755}e^{3} + \frac{87763082418563}{3903655391510}e^{2} - \frac{45989835048438}{1951827695755}e - \frac{1803157679484}{278832527965}$
97 $[97, 97, -2w^{5} + w^{4} + 11w^{3} - 6w^{2} - 9w + 3]$ $\phantom{-}\frac{4328363029}{1951827695755}e^{9} - \frac{34050091067}{3903655391510}e^{8} - \frac{244623647437}{1951827695755}e^{7} + \frac{2288848122943}{3903655391510}e^{6} + \frac{81753236518}{55766505593}e^{5} - \frac{20582365555459}{1951827695755}e^{4} + \frac{17309461333446}{1951827695755}e^{3} + \frac{87763082418563}{3903655391510}e^{2} - \frac{45989835048438}{1951827695755}e - \frac{1803157679484}{278832527965}$
113 $[113, 113, -4w^{5} + 2w^{4} + 24w^{3} - 9w^{2} - 27w + 2]$ $\phantom{-}\frac{72396986927}{15614621566040}e^{9} - \frac{4170926659}{7807310783020}e^{8} - \frac{4208949752131}{15614621566040}e^{7} + \frac{1396836034641}{7807310783020}e^{6} + \frac{904166138711}{223066022372}e^{5} - \frac{10991129685429}{1951827695755}e^{4} - \frac{118826974935827}{15614621566040}e^{3} + \frac{23417740337553}{3903655391510}e^{2} - \frac{5287234505731}{3903655391510}e + \frac{3734445566721}{278832527965}$
113 $[113, 113, 3w^{5} - 2w^{4} - 18w^{3} + 10w^{2} + 20w - 6]$ $\phantom{-}\frac{20831980091}{15614621566040}e^{9} + \frac{2527345617}{1951827695755}e^{8} - \frac{1253405372763}{15614621566040}e^{7} - \frac{192839272221}{3903655391510}e^{6} + \frac{301212860129}{223066022372}e^{5} + \frac{1300563974231}{3903655391510}e^{4} - \frac{84199630658511}{15614621566040}e^{3} - \frac{40128708299697}{7807310783020}e^{2} + \frac{13368538840227}{3903655391510}e + \frac{2066877600978}{278832527965}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$49$ $[49, 7, 2w^{5} - w^{4} - 12w^{3} + 5w^{2} + 13w - 4]$ $1$