Properties

Label 16.16
Level 16
Weight 16
Dimension 65
Nonzero newspaces 2
Newform subspaces 7
Sturm bound 256
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 16 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 7 \)
Sturm bound: \(256\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(16))\).

Total New Old
Modular forms 127 70 57
Cusp forms 113 65 48
Eisenstein series 14 5 9

Trace form

\( 65 q - 2 q^{2} + 2186 q^{3} - 48952 q^{4} - 68384 q^{5} + 1712848 q^{6} + 1587576 q^{7} + 11363476 q^{8} + 24885763 q^{9} + O(q^{10}) \) \( 65 q - 2 q^{2} + 2186 q^{3} - 48952 q^{4} - 68384 q^{5} + 1712848 q^{6} + 1587576 q^{7} + 11363476 q^{8} + 24885763 q^{9} - 13268 q^{10} + 199140662 q^{11} + 11982244 q^{12} + 64314920 q^{13} - 815083396 q^{14} - 2031520212 q^{15} + 1312336408 q^{16} - 1490533990 q^{17} + 11831569374 q^{18} - 4442027614 q^{19} - 18401078276 q^{20} + 7304397364 q^{21} + 46969404612 q^{22} + 19500374760 q^{23} + 58907605168 q^{24} + 47819817089 q^{25} + 46490368648 q^{26} + 186113164784 q^{27} - 136464950888 q^{28} + 111241862928 q^{29} + 409157989236 q^{30} + 281204843856 q^{31} + 259474196168 q^{32} + 171989743948 q^{33} - 1853847875852 q^{34} + 733879927724 q^{35} + 2871518054956 q^{36} + 327657750296 q^{37} + 392497290528 q^{38} + 1205007174472 q^{39} - 1981157206456 q^{40} + 982024897590 q^{41} + 6267204339640 q^{42} - 1188890599298 q^{43} - 9313276424668 q^{44} - 3844099297044 q^{45} + 6034216494124 q^{46} - 15827617351904 q^{47} + 13099182068968 q^{48} - 35922695604819 q^{49} - 34473503101434 q^{50} + 1464859163708 q^{51} + 53995605797716 q^{52} + 5429785679480 q^{53} - 29671461363680 q^{54} - 7817637861448 q^{55} - 31013323692776 q^{56} + 8949482399152 q^{57} + 128956383494552 q^{58} - 43688887573410 q^{59} - 195931903651392 q^{60} - 28019000570968 q^{61} + 126592545645616 q^{62} + 75070998202908 q^{63} + 114035599561472 q^{64} - 20800624602176 q^{65} - 112420082039468 q^{66} - 171646245612382 q^{67} + 96504941089296 q^{68} + 198917266961604 q^{69} + 44763000760960 q^{70} - 85826678557896 q^{71} + 295535605395972 q^{72} + 14903530487638 q^{73} - 79932489127764 q^{74} + 946517612119722 q^{75} + 512078041788788 q^{76} + 100215754901044 q^{77} + 2869258735676 q^{78} - 1133813197318288 q^{79} - 195148919735128 q^{80} - 722352531251439 q^{81} + 987676388017792 q^{82} + 828414968209210 q^{83} - 1742921706401624 q^{84} - 28399335116872 q^{85} + 322693053197508 q^{86} - 1328135532304248 q^{87} + 285060762932728 q^{88} - 656167737364506 q^{89} - 1921828325398824 q^{90} + 1069777750513364 q^{91} - 565578026553864 q^{92} + 152515133840432 q^{93} - 1226064450545072 q^{94} - 226663216574532 q^{95} - 1627313921745232 q^{96} + 463947620564842 q^{97} + 2497268006962938 q^{98} + 5371173965940850 q^{99} + O(q^{100}) \)

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(16))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
16.16.a \(\chi_{16}(1, \cdot)\) 16.16.a.a 1 1
16.16.a.b 1
16.16.a.c 1
16.16.a.d 1
16.16.a.e 1
16.16.a.f 2
16.16.b \(\chi_{16}(9, \cdot)\) None 0 1
16.16.e \(\chi_{16}(5, \cdot)\) 16.16.e.a 58 2

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_1(16))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_1(16)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)