Properties

Label 2.2.305.1-10.1-b
Base field \(\Q(\sqrt{305}) \)
Weight $[2, 2]$
Level norm $10$
Level $[10, 10, w + 2]$
Dimension $13$
CM no
Base change no

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Base field \(\Q(\sqrt{305}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 76\); narrow class number \(4\) and class number \(2\).

Form

Weight: $[2, 2]$
Level: $[10, 10, w + 2]$
Dimension: $13$
CM: no
Base change: no
Newspace dimension: $116$

Hecke eigenvalues ($q$-expansion)

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

\(x^{13} + x^{12} - 19x^{11} - 21x^{10} + 133x^{9} + 159x^{8} - 422x^{7} - 538x^{6} + 603x^{5} + 822x^{4} - 327x^{3} - 492x^{2} + 45x + 81\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $-1$
2 $[2, 2, w + 1]$ $\phantom{-}e$
5 $[5, 5, -4w + 37]$ $-1$
7 $[7, 7, w + 2]$ $-\frac{59}{3}e^{12} + 5e^{11} + \frac{1102}{3}e^{10} - \frac{143}{3}e^{9} - \frac{7664}{3}e^{8} + \frac{230}{3}e^{7} + \frac{24583}{3}e^{6} + \frac{907}{3}e^{5} - \frac{36629}{3}e^{4} - 838e^{3} + 7446e^{2} + 307e - 1261$
7 $[7, 7, w + 4]$ $-\frac{86}{9}e^{12} + \frac{22}{9}e^{11} + \frac{1607}{9}e^{10} - \frac{70}{3}e^{9} - \frac{11186}{9}e^{8} + \frac{113}{3}e^{7} + \frac{35941}{9}e^{6} + \frac{1331}{9}e^{5} - 5969e^{4} - \frac{1232}{3}e^{3} + \frac{10982}{3}e^{2} + \frac{454}{3}e - 625$
9 $[9, 3, 3]$ $-\frac{130}{9}e^{12} + \frac{38}{9}e^{11} + \frac{2422}{9}e^{10} - \frac{133}{3}e^{9} - \frac{16795}{9}e^{8} + 113e^{7} + \frac{53681}{9}e^{6} + \frac{673}{9}e^{5} - \frac{26543}{3}e^{4} - \frac{1402}{3}e^{3} + \frac{16111}{3}e^{2} + \frac{569}{3}e - 908$
17 $[17, 17, w + 6]$ $-\frac{316}{3}e^{12} + \frac{83}{3}e^{11} + \frac{5899}{3}e^{10} - 271e^{9} - \frac{40999}{3}e^{8} + 511e^{7} + \frac{131411}{3}e^{6} + \frac{4033}{3}e^{5} - 65222e^{4} - 4203e^{3} + 39779e^{2} + 1587e - 6756$
17 $[17, 17, w + 10]$ $\phantom{-}\frac{596}{9}e^{12} - \frac{154}{9}e^{11} - \frac{11129}{9}e^{10} + \frac{497}{3}e^{9} + \frac{77369}{9}e^{8} - 293e^{7} - \frac{248047}{9}e^{6} - \frac{8270}{9}e^{5} + \frac{123139}{3}e^{4} + \frac{8159}{3}e^{3} - \frac{75113}{3}e^{2} - \frac{3049}{3}e + 4251$
19 $[19, 19, -2w + 19]$ $-\frac{898}{9}e^{12} + \frac{236}{9}e^{11} + \frac{16765}{9}e^{10} - \frac{770}{3}e^{9} - \frac{116536}{9}e^{8} + \frac{1444}{3}e^{7} + \frac{373610}{9}e^{6} + \frac{11605}{9}e^{5} - 61832e^{4} - \frac{12031}{3}e^{3} + \frac{113194}{3}e^{2} + \frac{4550}{3}e - 6415$
19 $[19, 19, -2w - 17]$ $-\frac{476}{9}e^{12} + \frac{124}{9}e^{11} + \frac{8888}{9}e^{10} - 134e^{9} - \frac{61796}{9}e^{8} + \frac{730}{3}e^{7} + \frac{198181}{9}e^{6} + \frac{6380}{9}e^{5} - \frac{98438}{3}e^{4} - \frac{6407}{3}e^{3} + \frac{60086}{3}e^{2} + \frac{2377}{3}e - 3403$
23 $[23, 23, w + 5]$ $\phantom{-}\frac{1126}{9}e^{12} - \frac{293}{9}e^{11} - \frac{21022}{9}e^{10} + \frac{949}{3}e^{9} + \frac{146122}{9}e^{8} - 570e^{7} - \frac{468404}{9}e^{6} - \frac{15358}{9}e^{5} + \frac{232499}{3}e^{4} + \frac{15391}{3}e^{3} - \frac{141802}{3}e^{2} - \frac{5813}{3}e + 8031$
23 $[23, 23, w + 17]$ $-\frac{94}{3}e^{12} + \frac{26}{3}e^{11} + \frac{1753}{3}e^{10} - 88e^{9} - \frac{12169}{3}e^{8} + 197e^{7} + \frac{38945}{3}e^{6} + \frac{844}{3}e^{5} - 19291e^{4} - 1125e^{3} + 11743e^{2} + 436e - 1995$
37 $[37, 37, w + 1]$ $-\frac{1714}{9}e^{12} + \frac{449}{9}e^{11} + \frac{32002}{9}e^{10} - 488e^{9} - \frac{222463}{9}e^{8} + \frac{2738}{3}e^{7} + \frac{713201}{9}e^{6} + \frac{22171}{9}e^{5} - \frac{354061}{3}e^{4} - \frac{22945}{3}e^{3} + \frac{216007}{3}e^{2} + \frac{8681}{3}e - 12238$
37 $[37, 37, w + 35]$ $\phantom{-}\frac{253}{3}e^{12} - 22e^{11} - \frac{4724}{3}e^{10} + \frac{643}{3}e^{9} + \frac{32842}{3}e^{8} - \frac{1177}{3}e^{7} - \frac{105305}{3}e^{6} - \frac{3365}{3}e^{5} + \frac{156868}{3}e^{4} + 3407e^{3} - 31908e^{2} - 1272e + 5426$
41 $[41, 41, -22w + 203]$ $\phantom{-}\frac{238}{9}e^{12} - \frac{65}{9}e^{11} - \frac{4438}{9}e^{10} + \frac{217}{3}e^{9} + \frac{30799}{9}e^{8} - 151e^{7} - \frac{98501}{9}e^{6} - \frac{2626}{9}e^{5} + \frac{48716}{3}e^{4} + \frac{3094}{3}e^{3} - \frac{29548}{3}e^{2} - \frac{1217}{3}e + 1662$
41 $[41, 41, -6w + 55]$ $\phantom{-}\frac{367}{3}e^{12} - \frac{95}{3}e^{11} - \frac{6853}{3}e^{10} + 307e^{9} + \frac{47644}{3}e^{8} - 547e^{7} - \frac{152759}{3}e^{6} - \frac{5050}{3}e^{5} + 75842e^{4} + 5012e^{3} - 46267e^{2} - 1877e + 7860$
43 $[43, 43, w + 20]$ $-92e^{12} + \frac{74}{3}e^{11} + \frac{5150}{3}e^{10} - \frac{734}{3}e^{9} - 11925e^{8} + \frac{1472}{3}e^{7} + 38198e^{6} + \frac{3218}{3}e^{5} - \frac{170477}{3}e^{4} - 3589e^{3} + 34616e^{2} + 1375e - 5872$
43 $[43, 43, w + 22]$ $-\frac{722}{9}e^{12} + \frac{187}{9}e^{11} + \frac{13484}{9}e^{10} - \frac{604}{3}e^{9} - \frac{93767}{9}e^{8} + \frac{1070}{3}e^{7} + \frac{300751}{9}e^{6} + \frac{10067}{9}e^{5} - 49798e^{4} - \frac{9950}{3}e^{3} + \frac{91187}{3}e^{2} + \frac{3736}{3}e - 5161$
53 $[53, 53, w + 13]$ $-\frac{688}{9}e^{12} + \frac{182}{9}e^{11} + \frac{12844}{9}e^{10} - \frac{598}{3}e^{9} - \frac{89272}{9}e^{8} + 388e^{7} + \frac{286142}{9}e^{6} + \frac{8377}{9}e^{5} - \frac{142007}{3}e^{4} - \frac{9025}{3}e^{3} + \frac{86593}{3}e^{2} + \frac{3422}{3}e - 4908$
53 $[53, 53, w + 39]$ $-32e^{12} + 9e^{11} + 597e^{10} - 93e^{9} - 4146e^{8} + 224e^{7} + 13274e^{6} + 219e^{5} - 19732e^{4} - 1074e^{3} + 12017e^{2} + 427e - 2046$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w]$ $1$
$5$ $[5, 5, -4w + 37]$ $1$