# Properties

 Base field 4.4.19225.1 Weight [2, 2, 2, 2] Level norm 11 Level $[11,11,w + 3]$ Label 4.4.19225.1-11.2-b Dimension 12 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.19225.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 15x^{2} + 2x + 44$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[11,11,w + 3]$ Label 4.4.19225.1-11.2-b Dimension 12 Is CM no Is base change no Parent newspace dimension 19

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{12} - 3x^{11} - 24x^{10} + 66x^{9} + 208x^{8} - 461x^{7} - 919x^{6} + 1193x^{5} + 2262x^{4} - 532x^{3} - 2421x^{2} - 1391x - 251$$
Norm Prime Eigenvalue
4 $[4, 2, w + 2]$ $\phantom{-}e$
4 $[4, 2, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{9}{2}w - 10]$ $\phantom{-}\frac{183}{44}e^{11} - \frac{705}{44}e^{10} - \frac{973}{11}e^{9} + \frac{15555}{44}e^{8} + \frac{6828}{11}e^{7} - \frac{27629}{11}e^{6} - \frac{95527}{44}e^{5} + \frac{155785}{22}e^{4} + \frac{227653}{44}e^{3} - \frac{282383}{44}e^{2} - \frac{306457}{44}e - \frac{74949}{44}$
9 $[9, 3, \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - \frac{5}{2}w + 17]$ $\phantom{-}\frac{71}{11}e^{11} - \frac{260}{11}e^{10} - \frac{6137}{44}e^{9} + \frac{5705}{11}e^{8} + \frac{44203}{44}e^{7} - \frac{80209}{22}e^{6} - \frac{156867}{44}e^{5} + \frac{443457}{44}e^{4} + \frac{356481}{44}e^{3} - \frac{96308}{11}e^{2} - \frac{110595}{11}e - \frac{110795}{44}$
9 $[9, 3, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 28]$ $-\frac{155}{88}e^{11} + \frac{145}{22}e^{10} + \frac{1653}{44}e^{9} - \frac{6351}{44}e^{8} - \frac{2903}{11}e^{7} + \frac{88993}{88}e^{6} + \frac{39953}{44}e^{5} - \frac{244941}{88}e^{4} - \frac{181201}{88}e^{3} + \frac{212635}{88}e^{2} + \frac{29015}{11}e + \frac{57083}{88}$
11 $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 11]$ $\phantom{-}\frac{889}{88}e^{11} - \frac{799}{22}e^{10} - \frac{9663}{44}e^{9} + \frac{35005}{44}e^{8} + \frac{17569}{11}e^{7} - \frac{490539}{88}e^{6} - \frac{250875}{44}e^{5} + \frac{1347591}{88}e^{4} + \frac{1122851}{88}e^{3} - \frac{1154121}{88}e^{2} - \frac{169076}{11}e - \frac{340673}{88}$
11 $[11, 11, -w - 3]$ $-1$
25 $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ $-\frac{53}{88}e^{11} + \frac{135}{44}e^{10} + \frac{533}{44}e^{9} - \frac{779}{11}e^{8} - \frac{882}{11}e^{7} + \frac{47877}{88}e^{6} + \frac{3536}{11}e^{5} - \frac{151825}{88}e^{4} - \frac{101435}{88}e^{3} + \frac{162229}{88}e^{2} + \frac{91115}{44}e + \frac{48337}{88}$
29 $[29, 29, w + 1]$ $\phantom{-}\frac{289}{88}e^{11} - \frac{259}{22}e^{10} - \frac{3089}{44}e^{9} + \frac{11221}{44}e^{8} + \frac{10807}{22}e^{7} - \frac{154075}{88}e^{6} - \frac{71701}{44}e^{5} + \frac{409971}{88}e^{4} + \frac{296983}{88}e^{3} - \frac{337473}{88}e^{2} - \frac{43727}{11}e - \frac{80917}{88}$
29 $[29, 29, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 9]$ $\phantom{-}\frac{25}{22}e^{11} - \frac{45}{11}e^{10} - \frac{284}{11}e^{9} + \frac{1013}{11}e^{8} + \frac{2265}{11}e^{7} - \frac{14881}{22}e^{6} - \frac{9364}{11}e^{5} + \frac{43737}{22}e^{4} + \frac{47503}{22}e^{3} - \frac{40121}{22}e^{2} - \frac{29499}{11}e - \frac{16919}{22}$
31 $[31, 31, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 16]$ $-\frac{371}{44}e^{11} + \frac{681}{22}e^{10} + \frac{2003}{11}e^{9} - \frac{7474}{11}e^{8} - \frac{14416}{11}e^{7} + \frac{210311}{44}e^{6} + \frac{102385}{22}e^{5} - \frac{582185}{44}e^{4} - \frac{467429}{44}e^{3} + \frac{506997}{44}e^{2} + \frac{291811}{22}e + \frac{146695}{44}$
31 $[31, 31, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 5]$ $-\frac{1591}{88}e^{11} + \frac{1455}{22}e^{10} + \frac{17181}{44}e^{9} - \frac{63817}{44}e^{8} - \frac{30892}{11}e^{7} + \frac{896389}{88}e^{6} + \frac{436993}{44}e^{5} - \frac{2474885}{88}e^{4} - \frac{1976697}{88}e^{3} + \frac{2148951}{88}e^{2} + \frac{611635}{22}e + \frac{607591}{88}$
31 $[31, 31, -w + 3]$ $\phantom{-}\frac{543}{88}e^{11} - \frac{995}{44}e^{10} - \frac{2943}{22}e^{9} + \frac{5471}{11}e^{8} + \frac{42697}{44}e^{7} - \frac{308991}{88}e^{6} - \frac{153355}{44}e^{5} + \frac{859985}{88}e^{4} + \frac{704091}{88}e^{3} - \frac{754983}{88}e^{2} - \frac{437301}{44}e - \frac{218861}{88}$
31 $[31, 31, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 29]$ $\phantom{-}\frac{551}{88}e^{11} - \frac{1049}{44}e^{10} - \frac{1472}{11}e^{9} + \frac{11563}{22}e^{8} + \frac{41697}{44}e^{7} - \frac{328067}{88}e^{6} - \frac{147203}{44}e^{5} + \frac{921705}{88}e^{4} + \frac{697299}{88}e^{3} - \frac{827403}{88}e^{2} - \frac{460591}{44}e - \frac{229101}{88}$
59 $[59, 59, 2w^{2} - w - 13]$ $-\frac{251}{8}e^{11} + \frac{455}{4}e^{10} + \frac{2719}{4}e^{9} - \frac{4985}{2}e^{8} - 4915e^{7} + \frac{139807}{8}e^{6} + \frac{34915}{2}e^{5} - \frac{384691}{8}e^{4} - \frac{314045}{8}e^{3} + \frac{331099}{8}e^{2} + \frac{191651}{4}e + \frac{96143}{8}$
59 $[59, 59, \frac{9}{2}w^{3} - \frac{31}{2}w^{2} - \frac{61}{2}w + 85]$ $\phantom{-}\frac{377}{22}e^{11} - \frac{1355}{22}e^{10} - \frac{8191}{22}e^{9} + \frac{29669}{22}e^{8} + \frac{59497}{22}e^{7} - \frac{103861}{11}e^{6} - \frac{105966}{11}e^{5} + \frac{569999}{22}e^{4} + \frac{236618}{11}e^{3} - \frac{487513}{22}e^{2} - \frac{569607}{22}e - \frac{71561}{11}$
61 $[61, 61, 2w^{3} - 6w^{2} - 15w + 31]$ $\phantom{-}\frac{633}{44}e^{11} - \frac{617}{11}e^{10} - \frac{3342}{11}e^{9} + \frac{13608}{11}e^{8} + \frac{46253}{22}e^{7} - \frac{386547}{44}e^{6} - \frac{79500}{11}e^{5} + \frac{1090047}{44}e^{4} + \frac{759527}{44}e^{3} - \frac{993165}{44}e^{2} - \frac{522263}{22}e - \frac{250791}{44}$
61 $[61, 61, -\frac{3}{2}w^{3} + \frac{11}{2}w^{2} + \frac{21}{2}w - 34]$ $-\frac{317}{88}e^{11} + \frac{597}{44}e^{10} + \frac{1691}{22}e^{9} - \frac{3276}{11}e^{8} - \frac{23801}{44}e^{7} + \frac{184365}{88}e^{6} + \frac{82421}{44}e^{5} - \frac{510667}{88}e^{4} - \frac{378525}{88}e^{3} + \frac{447745}{88}e^{2} + \frac{245071}{44}e + \frac{120827}{88}$
71 $[71, 71, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 32]$ $\phantom{-}\frac{9}{8}e^{11} - \frac{7}{4}e^{10} - \frac{113}{4}e^{9} + 32e^{8} + 247e^{7} - \frac{1105}{8}e^{6} - 932e^{5} - \frac{483}{8}e^{4} + \frac{10423}{8}e^{3} + \frac{6863}{8}e^{2} + \frac{173}{4}e - \frac{349}{8}$
71 $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 13]$ $\phantom{-}\frac{1213}{44}e^{11} - \frac{2201}{22}e^{10} - \frac{6577}{11}e^{9} + \frac{24140}{11}e^{8} + \frac{95347}{22}e^{7} - \frac{678357}{44}e^{6} - \frac{340299}{22}e^{5} + \frac{1872619}{44}e^{4} + \frac{1539169}{44}e^{3} - \frac{1619853}{44}e^{2} - \frac{942257}{22}e - \frac{473903}{44}$
79 $[79, 79, -3w^{3} + 10w^{2} + 19w - 51]$ $\phantom{-}\frac{37}{11}e^{11} - \frac{425}{44}e^{10} - \frac{849}{11}e^{9} + \frac{9027}{44}e^{8} + \frac{13323}{22}e^{7} - \frac{59415}{44}e^{6} - \frac{97371}{44}e^{5} + \frac{143713}{44}e^{4} + \frac{45180}{11}e^{3} - \frac{21954}{11}e^{2} - \frac{141923}{44}e - \frac{9245}{11}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
11 $[11,11,w + 3]$ $1$