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Properties

Label 16.22.a
Level $16$
Weight $22$
Character orbit 16.a
Rep. character $\chi_{16}(1,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $6$
Sturm bound $44$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 22 \)
Character orbit: \([\chi]\) \(=\) 16.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(44\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_0(16))\).

Total New Old
Modular forms 45 11 34
Cusp forms 39 10 29
Eisenstein series 6 1 5

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)Dim
\(+\)\(5\)
\(-\)\(5\)

Trace form

\( 10 q - 59048 q^{3} - 10391780 q^{5} - 286396624 q^{7} + 36243817378 q^{9} + O(q^{10}) \) \( 10 q - 59048 q^{3} - 10391780 q^{5} - 286396624 q^{7} + 36243817378 q^{9} - 44145613432 q^{11} - 53827631700 q^{13} - 409034126192 q^{15} - 1849642826188 q^{17} - 64445589026888 q^{19} - 6335038461120 q^{21} + 333505906879376 q^{23} + 512198372079702 q^{25} - 3179712712147856 q^{27} + 4339955132705484 q^{29} - 544217111281472 q^{31} + 277341305837024 q^{33} + 16343014300785696 q^{35} - 19463787357296804 q^{37} - 61106929702818224 q^{39} - 54372406343966748 q^{41} + 104523248903382600 q^{43} - 105167698877440724 q^{45} + 874784109581930784 q^{47} + 281167627130179834 q^{49} - 1699907057117920720 q^{51} - 10180307078564228 q^{53} - 1215488655761389904 q^{55} + 1041229908777309472 q^{57} + 1660839230536236200 q^{59} + 1888770384295213836 q^{61} - 12251256396388940688 q^{63} + 7397352098231670856 q^{65} + 26576033182092256984 q^{67} - 28834712558382134848 q^{69} + 41200641038922856624 q^{71} - 37765020242610577116 q^{73} - 73979495734498489048 q^{75} + 24391643967118988736 q^{77} + 13899556848849002976 q^{79} + 234173317447560005626 q^{81} - 47026879772027908808 q^{83} - 244084099503461631752 q^{85} - 227604522934813134384 q^{87} - 240584055283923843516 q^{89} + 402710460549494674336 q^{91} + 913461579600302447872 q^{93} + 23588040578229740752 q^{95} + 710462713306615232468 q^{97} - 775806929716913573272 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_0(16))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2
16.22.a.a 16.a 1.a $1$ $44.716$ \(\Q\) None \(0\) \(-71604\) \(-28693770\) \(853202392\) $-$ $\mathrm{SU}(2)$ \(q-71604q^{3}-28693770q^{5}+853202392q^{7}+\cdots\)
16.22.a.b 16.a 1.a $1$ $44.716$ \(\Q\) None \(0\) \(-59316\) \(4975350\) \(-1427425832\) $-$ $\mathrm{SU}(2)$ \(q-59316q^{3}+4975350q^{5}-1427425832q^{7}+\cdots\)
16.22.a.c 16.a 1.a $1$ $44.716$ \(\Q\) None \(0\) \(128844\) \(21640950\) \(768078808\) $-$ $\mathrm{SU}(2)$ \(q+128844q^{3}+21640950q^{5}+768078808q^{7}+\cdots\)
16.22.a.d 16.a 1.a $2$ $44.716$ \(\Q(\sqrt{2161}) \) None \(0\) \(-65640\) \(13689324\) \(260508080\) $-$ $\mathrm{SU}(2)$ \(q+(-32820-\beta )q^{3}+(6844662+204\beta )q^{5}+\cdots\)
16.22.a.e 16.a 1.a $2$ $44.716$ \(\Q(\sqrt{358549}) \) None \(0\) \(105432\) \(2108140\) \(-444771792\) $+$ $\mathrm{SU}(2)$ \(q+(52716-\beta )q^{3}+(1054070-20\beta )q^{5}+\cdots\)
16.22.a.f 16.a 1.a $3$ $44.716$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(-96764\) \(-24111774\) \(-295988280\) $+$ $\mathrm{SU}(2)$ \(q+(-32255+\beta _{1})q^{3}+(-8037261+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_0(16))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_0(16)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)