Properties

Label 16.5
Level 16
Weight 5
Dimension 16
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 80
Trace bound 1

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Defining parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(80\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(16))\).

Total New Old
Modular forms 39 20 19
Cusp forms 25 16 9
Eisenstein series 14 4 10

Trace form

\( 16 q - 2 q^{2} - 2 q^{3} - 8 q^{4} + 34 q^{5} + 64 q^{6} - 4 q^{7} - 92 q^{8} - 222 q^{9} + O(q^{10}) \) \( 16 q - 2 q^{2} - 2 q^{3} - 8 q^{4} + 34 q^{5} + 64 q^{6} - 4 q^{7} - 92 q^{8} - 222 q^{9} - 100 q^{10} + 94 q^{11} - 332 q^{12} + 354 q^{13} + 44 q^{14} - 168 q^{16} - 256 q^{17} + 1390 q^{18} - 706 q^{19} + 1900 q^{20} + 604 q^{21} + 900 q^{22} + 1148 q^{23} - 1872 q^{24} - 602 q^{25} - 3416 q^{26} - 1664 q^{27} - 3784 q^{28} - 1982 q^{29} - 3740 q^{30} + 3208 q^{32} + 3452 q^{33} + 7508 q^{34} + 1340 q^{35} + 11468 q^{36} - 766 q^{37} + 3568 q^{38} + 2684 q^{39} - 5144 q^{40} + 324 q^{41} - 17064 q^{42} + 1694 q^{43} - 14636 q^{44} - 2586 q^{45} - 5316 q^{46} + 6888 q^{48} + 3948 q^{49} + 20070 q^{50} - 3012 q^{51} + 20452 q^{52} + 706 q^{53} + 10784 q^{54} - 11780 q^{55} - 6952 q^{56} - 11136 q^{57} - 20456 q^{58} - 2786 q^{59} - 29920 q^{60} - 2526 q^{61} - 11472 q^{62} + 15808 q^{64} + 4388 q^{65} + 30148 q^{66} + 7998 q^{67} + 18032 q^{68} + 30364 q^{69} + 15296 q^{70} + 19964 q^{71} - 17708 q^{72} - 13372 q^{73} - 23780 q^{74} + 17570 q^{75} - 23996 q^{76} - 16420 q^{77} - 8052 q^{78} + 1384 q^{80} - 5008 q^{81} + 16016 q^{82} - 17282 q^{83} + 19624 q^{84} + 5412 q^{85} - 4796 q^{86} - 49284 q^{87} + 7288 q^{88} + 16452 q^{89} - 5416 q^{90} - 28036 q^{91} - 14632 q^{92} - 320 q^{93} + 432 q^{94} + 6064 q^{96} - 3200 q^{97} - 12246 q^{98} + 49214 q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(16))\)

We only show spaces with odd 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
16.5.c \(\chi_{16}(15, \cdot)\) 16.5.c.a 2 1
16.5.d \(\chi_{16}(7, \cdot)\) None 0 1
16.5.f \(\chi_{16}(3, \cdot)\) 16.5.f.a 14 2

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(16))\) into lower level spaces

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