# Properties

 Label 4.4.19225.1-16.1-h Base field 4.4.19225.1 Weight $[2, 2, 2, 2]$ Level norm $16$ Level $[16, 2, 2]$ Dimension $10$ CM no Base change yes

# 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: $[16, 2, 2]$ Dimension: $10$ CM: no Base change: yes Newspace dimension: $29$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{10} - 2x^{9} - 46x^{8} + 98x^{7} + 704x^{6} - 1518x^{5} - 4006x^{4} + 7949x^{3} + 7326x^{2} - 12004x + 3400$$
Norm Prime Eigenvalue
4 $[4, 2, w + 2]$ $\phantom{-}1$
4 $[4, 2, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{9}{2}w - 10]$ $\phantom{-}1$
9 $[9, 3, \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - \frac{5}{2}w + 17]$ $\phantom{-}e$
9 $[9, 3, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 28]$ $\phantom{-}e$
11 $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 11]$ $\phantom{-}\frac{16447}{990128}e^{9} + \frac{9619}{247532}e^{8} - \frac{371797}{495064}e^{7} - \frac{707687}{495064}e^{6} + \frac{2920447}{247532}e^{5} + \frac{8065355}{495064}e^{4} - \frac{35631315}{495064}e^{3} - \frac{51634817}{990128}e^{2} + \frac{29786763}{247532}e - \frac{9019997}{247532}$
11 $[11, 11, -w - 3]$ $\phantom{-}\frac{16447}{990128}e^{9} + \frac{9619}{247532}e^{8} - \frac{371797}{495064}e^{7} - \frac{707687}{495064}e^{6} + \frac{2920447}{247532}e^{5} + \frac{8065355}{495064}e^{4} - \frac{35631315}{495064}e^{3} - \frac{51634817}{990128}e^{2} + \frac{29786763}{247532}e - \frac{9019997}{247532}$
25 $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ $\phantom{-}\frac{4953}{990128}e^{9} + \frac{5365}{247532}e^{8} - \frac{125331}{495064}e^{7} - \frac{360281}{495064}e^{6} + \frac{1267065}{247532}e^{5} + \frac{3207757}{495064}e^{4} - \frac{22655853}{495064}e^{3} - \frac{515271}{990128}e^{2} + \frac{31730861}{247532}e - \frac{15364923}{247532}$
29 $[29, 29, w + 1]$ $-\frac{37877}{990128}e^{9} - \frac{8893}{247532}e^{8} + \frac{796519}{495064}e^{7} + \frac{486053}{495064}e^{6} - \frac{5488909}{247532}e^{5} - \frac{4126657}{495064}e^{4} + \frac{52090713}{495064}e^{3} + \frac{30885579}{990128}e^{2} - \frac{28069165}{247532}e + \frac{9932815}{247532}$
29 $[29, 29, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 9]$ $-\frac{37877}{990128}e^{9} - \frac{8893}{247532}e^{8} + \frac{796519}{495064}e^{7} + \frac{486053}{495064}e^{6} - \frac{5488909}{247532}e^{5} - \frac{4126657}{495064}e^{4} + \frac{52090713}{495064}e^{3} + \frac{30885579}{990128}e^{2} - \frac{28069165}{247532}e + \frac{9932815}{247532}$
31 $[31, 31, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 16]$ $\phantom{-}\frac{4719}{495064}e^{9} + \frac{4137}{123766}e^{8} - \frac{96021}{247532}e^{7} - \frac{319871}{247532}e^{6} + \frac{652693}{123766}e^{5} + \frac{4034643}{247532}e^{4} - \frac{6080639}{247532}e^{3} - \frac{33371753}{495064}e^{2} + \frac{989855}{123766}e + \frac{2499159}{123766}$
31 $[31, 31, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 5]$ $-\frac{24647}{990128}e^{9} - \frac{6107}{247532}e^{8} + \frac{548405}{495064}e^{7} + \frac{371999}{495064}e^{6} - \frac{4122479}{247532}e^{5} - \frac{3427539}{495064}e^{4} + \frac{46111875}{495064}e^{3} + \frac{18150649}{990128}e^{2} - \frac{35767971}{247532}e + \frac{13797133}{247532}$
31 $[31, 31, -w + 3]$ $-\frac{24647}{990128}e^{9} - \frac{6107}{247532}e^{8} + \frac{548405}{495064}e^{7} + \frac{371999}{495064}e^{6} - \frac{4122479}{247532}e^{5} - \frac{3427539}{495064}e^{4} + \frac{46111875}{495064}e^{3} + \frac{18150649}{990128}e^{2} - \frac{35767971}{247532}e + \frac{13797133}{247532}$
31 $[31, 31, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 29]$ $\phantom{-}\frac{4719}{495064}e^{9} + \frac{4137}{123766}e^{8} - \frac{96021}{247532}e^{7} - \frac{319871}{247532}e^{6} + \frac{652693}{123766}e^{5} + \frac{4034643}{247532}e^{4} - \frac{6080639}{247532}e^{3} - \frac{33371753}{495064}e^{2} + \frac{989855}{123766}e + \frac{2499159}{123766}$
59 $[59, 59, 2w^{2} - w - 13]$ $-\frac{55515}{990128}e^{9} - \frac{13655}{247532}e^{8} + \frac{1165169}{495064}e^{7} + \frac{790107}{495064}e^{6} - \frac{7996327}{247532}e^{5} - \frac{7558127}{495064}e^{4} + \frac{75227615}{495064}e^{3} + \frac{65135045}{990128}e^{2} - \frac{39247999}{247532}e + \frac{8721505}{247532}$
59 $[59, 59, \frac{9}{2}w^{3} - \frac{31}{2}w^{2} - \frac{61}{2}w + 85]$ $-\frac{55515}{990128}e^{9} - \frac{13655}{247532}e^{8} + \frac{1165169}{495064}e^{7} + \frac{790107}{495064}e^{6} - \frac{7996327}{247532}e^{5} - \frac{7558127}{495064}e^{4} + \frac{75227615}{495064}e^{3} + \frac{65135045}{990128}e^{2} - \frac{39247999}{247532}e + \frac{8721505}{247532}$
61 $[61, 61, 2w^{3} - 6w^{2} - 15w + 31]$ $-\frac{44473}{495064}e^{9} + \frac{196}{61883}e^{8} + \frac{949931}{247532}e^{7} - \frac{240879}{247532}e^{6} - \frac{6537437}{123766}e^{5} + \frac{4619559}{247532}e^{4} + \frac{60283301}{247532}e^{3} - \frac{27735753}{495064}e^{2} - \frac{16327387}{61883}e + \frac{15118569}{123766}$
61 $[61, 61, -\frac{3}{2}w^{3} + \frac{11}{2}w^{2} + \frac{21}{2}w - 34]$ $-\frac{44473}{495064}e^{9} + \frac{196}{61883}e^{8} + \frac{949931}{247532}e^{7} - \frac{240879}{247532}e^{6} - \frac{6537437}{123766}e^{5} + \frac{4619559}{247532}e^{4} + \frac{60283301}{247532}e^{3} - \frac{27735753}{495064}e^{2} - \frac{16327387}{61883}e + \frac{15118569}{123766}$
71 $[71, 71, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 32]$ $-\frac{10579}{123766}e^{9} - \frac{15263}{123766}e^{8} + \frac{227061}{61883}e^{7} + \frac{260796}{61883}e^{6} - \frac{3241663}{61883}e^{5} - \frac{2900696}{61883}e^{4} + \frac{16469850}{61883}e^{3} + \frac{22007789}{123766}e^{2} - \frac{38069917}{123766}e + \frac{5019937}{61883}$
71 $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 13]$ $-\frac{10579}{123766}e^{9} - \frac{15263}{123766}e^{8} + \frac{227061}{61883}e^{7} + \frac{260796}{61883}e^{6} - \frac{3241663}{61883}e^{5} - \frac{2900696}{61883}e^{4} + \frac{16469850}{61883}e^{3} + \frac{22007789}{123766}e^{2} - \frac{38069917}{123766}e + \frac{5019937}{61883}$
79 $[79, 79, -3w^{3} + 10w^{2} + 19w - 51]$ $\phantom{-}\frac{34657}{495064}e^{9} + \frac{3631}{123766}e^{8} - \frac{729583}{247532}e^{7} - \frac{120393}{247532}e^{6} + \frac{4963159}{123766}e^{5} + \frac{261857}{247532}e^{4} - \frac{45185913}{247532}e^{3} - \frac{8978879}{495064}e^{2} + \frac{22254395}{123766}e - \frac{7168215}{123766}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, w + 2]$ $-1$
$4$ $[4, 2, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{9}{2}w - 10]$ $-1$