Properties

Label 16.8
Level 16
Weight 8
Dimension 29
Nonzero newspaces 2
Newform subspaces 4
Sturm bound 128
Trace bound 1

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Defining parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 4 \)
Sturm bound: \(128\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(16))\).

Total New Old
Modular forms 63 34 29
Cusp forms 49 29 20
Eisenstein series 14 5 9

Trace form

\( 29 q - 2 q^{2} + 26 q^{3} - 184 q^{4} + 136 q^{5} - 176 q^{6} + 664 q^{7} - 1004 q^{8} + 2575 q^{9} + O(q^{10}) \) \( 29 q - 2 q^{2} + 26 q^{3} - 184 q^{4} + 136 q^{5} - 176 q^{6} + 664 q^{7} - 1004 q^{8} + 2575 q^{9} + 12972 q^{10} + 5798 q^{11} - 27356 q^{12} - 3280 q^{13} + 22268 q^{14} - 50292 q^{15} + 13336 q^{16} - 12718 q^{17} - 29346 q^{18} + 101874 q^{19} + 46204 q^{20} + 1012 q^{21} - 44348 q^{22} - 151992 q^{23} - 59216 q^{24} + 1349 q^{25} - 35960 q^{26} + 149648 q^{27} + 220312 q^{28} + 68376 q^{29} + 27636 q^{30} - 80944 q^{31} - 248632 q^{32} + 85900 q^{33} + 924660 q^{34} + 450284 q^{35} - 1015508 q^{36} + 104320 q^{37} - 5472 q^{38} - 1191128 q^{39} - 1121976 q^{40} - 167154 q^{41} + 124600 q^{42} + 1180142 q^{43} - 758620 q^{44} + 73716 q^{45} + 2335660 q^{46} - 2151200 q^{47} + 4141288 q^{48} - 1379351 q^{49} - 787194 q^{50} + 2212316 q^{51} + 410324 q^{52} + 1522976 q^{53} - 7404512 q^{54} + 1382872 q^{55} - 4093160 q^{56} - 1066640 q^{57} - 1860712 q^{58} - 5642226 q^{59} + 5147328 q^{60} + 4110448 q^{61} + 6274096 q^{62} + 12283836 q^{63} + 10452224 q^{64} + 1797424 q^{65} + 10937812 q^{66} - 13064014 q^{67} - 7403760 q^{68} - 10755324 q^{69} - 22140800 q^{70} + 6673752 q^{71} - 25293948 q^{72} - 6370898 q^{73} - 13177044 q^{74} - 4074918 q^{75} + 17814260 q^{76} + 13737460 q^{77} + 37993916 q^{78} - 4946000 q^{79} + 40047272 q^{80} + 2649165 q^{81} + 22858240 q^{82} + 5807626 q^{83} - 30159704 q^{84} - 1792312 q^{85} - 54129468 q^{86} + 4209000 q^{87} - 59216392 q^{88} - 6818562 q^{89} - 33515304 q^{90} + 3757204 q^{91} + 21810936 q^{92} + 2686640 q^{93} + 77196112 q^{94} - 10595172 q^{95} + 116940464 q^{96} + 13548002 q^{97} + 21823866 q^{98} + 32541154 q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(16))\)

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
16.8.a \(\chi_{16}(1, \cdot)\) 16.8.a.a 1 1
16.8.a.b 1
16.8.a.c 1
16.8.b \(\chi_{16}(9, \cdot)\) None 0 1
16.8.e \(\chi_{16}(5, \cdot)\) 16.8.e.a 26 2

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(16))\) into lower level spaces

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