# Properties

 Label 4.4.14272.1-17.1-d Base field 4.4.14272.1 Weight $[2, 2, 2, 2]$ Level norm $17$ Level $[17, 17, w^{3} - 3w^{2} - 2w + 2]$ Dimension $12$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.14272.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[17, 17, w^{3} - 3w^{2} - 2w + 2]$ Dimension: $12$ CM: no Base change: no Newspace dimension: $26$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{12} + 6x^{11} - 4x^{10} - 78x^{9} - 62x^{8} + 336x^{7} + 436x^{6} - 512x^{5} - 832x^{4} + 152x^{3} + 316x^{2} - 72x + 4$$
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
4 $[4, 2, -w^{3} + 3w^{2} + w - 2]$ $-\frac{269}{222}e^{11} - \frac{1327}{222}e^{10} + \frac{399}{37}e^{9} + \frac{2994}{37}e^{8} - \frac{760}{111}e^{7} - \frac{41177}{111}e^{6} - \frac{15563}{111}e^{5} + \frac{70438}{111}e^{4} + \frac{11127}{37}e^{3} - \frac{29573}{111}e^{2} - \frac{2366}{111}e + \frac{236}{111}$
11 $[11, 11, -w^{3} + 3w^{2} + 2w - 5]$ $-\frac{31}{74}e^{11} - \frac{225}{74}e^{10} - \frac{30}{37}e^{9} + \frac{1404}{37}e^{8} + \frac{2232}{37}e^{7} - \frac{5582}{37}e^{6} - \frac{12729}{37}e^{5} + \frac{6740}{37}e^{4} + \frac{23439}{37}e^{3} + \frac{1005}{37}e^{2} - \frac{9673}{37}e + \frac{1146}{37}$
13 $[13, 13, w^{3} - 2w^{2} - 4w + 2]$ $\phantom{-}\frac{193}{222}e^{11} + \frac{773}{222}e^{10} - \frac{853}{74}e^{9} - \frac{1855}{37}e^{8} + \frac{6269}{111}e^{7} + \frac{27880}{111}e^{6} - \frac{15344}{111}e^{5} - \frac{55418}{111}e^{4} + \frac{7519}{37}e^{3} + \frac{33826}{111}e^{2} - \frac{19841}{111}e + \frac{2120}{111}$
13 $[13, 13, -w + 2]$ $\phantom{-}\frac{581}{222}e^{11} + \frac{3169}{222}e^{10} - \frac{623}{37}e^{9} - \frac{6963}{37}e^{8} - \frac{8162}{111}e^{7} + \frac{91757}{111}e^{6} + \frac{79484}{111}e^{5} - \frac{143830}{111}e^{4} - \frac{51404}{37}e^{3} + \frac{42539}{111}e^{2} + \frac{45194}{111}e - \frac{5246}{111}$
17 $[17, 17, w^{3} - 3w^{2} - 2w + 2]$ $\phantom{-}1$
19 $[19, 19, -w^{2} + w + 4]$ $\phantom{-}\frac{281}{222}e^{11} + \frac{1099}{222}e^{10} - \frac{641}{37}e^{9} - \frac{2650}{37}e^{8} + \frac{9997}{111}e^{7} + \frac{40151}{111}e^{6} - \frac{26545}{111}e^{5} - \frac{81193}{111}e^{4} + \frac{13342}{37}e^{3} + \frac{52451}{111}e^{2} - \frac{31225}{111}e + \frac{2056}{111}$
19 $[19, 19, w^{3} - 2w^{2} - 3w + 2]$ $-\frac{385}{111}e^{11} - \frac{2120}{111}e^{10} + \frac{790}{37}e^{9} + \frac{9278}{37}e^{8} + \frac{12224}{111}e^{7} - \frac{121496}{111}e^{6} - \frac{111698}{111}e^{5} + \frac{188152}{111}e^{4} + \frac{71898}{37}e^{3} - \frac{52718}{111}e^{2} - \frac{66113}{111}e + \frac{7664}{111}$
23 $[23, 23, w^{2} - 2w - 1]$ $-\frac{257}{74}e^{11} - \frac{1333}{74}e^{10} + \frac{989}{37}e^{9} + \frac{8904}{37}e^{8} + \frac{1410}{37}e^{7} - \frac{39946}{37}e^{6} - \frac{25000}{37}e^{5} + \frac{65381}{37}e^{4} + \frac{50437}{37}e^{3} - \frac{23419}{37}e^{2} - \frac{11722}{37}e + \frac{1418}{37}$
27 $[27, 3, w^{3} - 2w^{2} - 5w - 1]$ $-\frac{8}{37}e^{11} + \frac{41}{37}e^{10} + \frac{450}{37}e^{9} - \frac{266}{37}e^{8} - \frac{5249}{37}e^{7} - \frac{889}{37}e^{6} + \frac{23436}{37}e^{5} + \frac{8568}{37}e^{4} - \frac{41266}{37}e^{3} - \frac{13410}{37}e^{2} + \frac{20220}{37}e - \frac{2168}{37}$
29 $[29, 29, -w^{3} + 2w^{2} + 5w - 1]$ $\phantom{-}\frac{40}{37}e^{11} + \frac{737}{74}e^{10} + \frac{451}{37}e^{9} - \frac{4368}{37}e^{8} - \frac{10829}{37}e^{7} + \frac{15582}{37}e^{6} + \frac{56276}{37}e^{5} - \frac{12056}{37}e^{4} - \frac{101584}{37}e^{3} - \frac{15164}{37}e^{2} + \frac{44162}{37}e - \frac{4626}{37}$
37 $[37, 37, -w^{3} + 2w^{2} + 5w - 4]$ $-\frac{61}{37}e^{11} - \frac{605}{74}e^{10} + \frac{536}{37}e^{9} + \frac{4086}{37}e^{8} - \frac{281}{37}e^{7} - \frac{18725}{37}e^{6} - \frac{7207}{37}e^{5} + \frac{32253}{37}e^{4} + \frac{15174}{37}e^{3} - \frac{14256}{37}e^{2} - \frac{1130}{37}e + \frac{378}{37}$
41 $[41, 41, 2w^{3} - 5w^{2} - 6w + 4]$ $-\frac{169}{74}e^{11} - \frac{522}{37}e^{10} + \frac{253}{37}e^{9} + \frac{6667}{37}e^{8} + \frac{6322}{37}e^{7} - \frac{27712}{37}e^{6} - \frac{41307}{37}e^{5} + \frac{38052}{37}e^{4} + \frac{76305}{37}e^{3} - \frac{3018}{37}e^{2} - \frac{27102}{37}e + \frac{2760}{37}$
53 $[53, 53, w^{3} - 2w^{2} - 3w - 2]$ $-\frac{89}{74}e^{11} - \frac{677}{74}e^{10} - \frac{331}{74}e^{9} + \frac{4149}{37}e^{8} + \frac{7444}{37}e^{7} - \frac{15904}{37}e^{6} - \frac{41123}{37}e^{5} + \frac{16931}{37}e^{4} + \frac{75028}{37}e^{3} + \frac{7089}{37}e^{2} - \frac{31521}{37}e + \frac{3240}{37}$
59 $[59, 59, w - 4]$ $-\frac{131}{74}e^{11} - \frac{693}{74}e^{10} + \frac{470}{37}e^{9} + \frac{4607}{37}e^{8} + \frac{1218}{37}e^{7} - \frac{20490}{37}e^{6} - \frac{15290}{37}e^{5} + \frac{32910}{37}e^{4} + \frac{30798}{37}e^{3} - \frac{11083}{37}e^{2} - \frac{8876}{37}e + \frac{1508}{37}$
67 $[67, 67, 2w^{2} - 3w - 8]$ $\phantom{-}\frac{359}{222}e^{11} + \frac{2059}{222}e^{10} - \frac{290}{37}e^{9} - \frac{4410}{37}e^{8} - \frac{8828}{111}e^{7} + \frac{55571}{111}e^{6} + \frac{66386}{111}e^{5} - \frac{78340}{111}e^{4} - \frac{42006}{37}e^{3} + \frac{9905}{111}e^{2} + \frac{43862}{111}e - \frac{3692}{111}$
73 $[73, 73, 2w^{3} - 5w^{2} - 6w + 5]$ $\phantom{-}\frac{733}{222}e^{11} + \frac{2416}{111}e^{10} - \frac{124}{37}e^{9} - \frac{10129}{37}e^{8} - \frac{37384}{111}e^{7} + \frac{122680}{111}e^{6} + \frac{226213}{111}e^{5} - \frac{155000}{111}e^{4} - \frac{138905}{37}e^{3} - \frac{11033}{111}e^{2} + \frac{160648}{111}e - \frac{17062}{111}$
89 $[89, 89, -2w^{3} + 6w^{2} + 5w - 7]$ $\phantom{-}\frac{7}{2}e^{11} + 19e^{10} - 23e^{9} - 251e^{8} - 91e^{7} + 1109e^{6} + 919e^{5} - 1772e^{4} - 1781e^{3} + 591e^{2} + 512e - 74$
97 $[97, 97, -2w^{3} + 6w^{2} + 3w - 7]$ $-\frac{145}{222}e^{11} - \frac{121}{111}e^{10} + \frac{587}{37}e^{9} + \frac{826}{37}e^{8} - \frac{15719}{111}e^{7} - \frac{17332}{111}e^{6} + \frac{63140}{111}e^{5} + \frac{49028}{111}e^{4} - \frac{36072}{37}e^{3} - \frac{46876}{111}e^{2} + \frac{56750}{111}e - \frac{6938}{111}$
97 $[97, 97, -w^{3} + 3w^{2} + 3w - 1]$ $\phantom{-}\frac{115}{37}e^{11} + \frac{516}{37}e^{10} - \frac{1261}{37}e^{9} - \frac{7156}{37}e^{8} + \frac{3901}{37}e^{7} + \frac{34022}{37}e^{6} - \frac{1765}{37}e^{5} - \frac{62226}{37}e^{4} - \frac{2529}{37}e^{3} + \frac{31976}{37}e^{2} - \frac{9148}{37}e + \frac{714}{37}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$17$ $[17, 17, w^{3} - 3w^{2} - 2w + 2]$ $-1$