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Properties

Label 16.11
Level 16
Weight 11
Dimension 43
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 176
Trace bound 1

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Defining parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(176\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(16))\).

Total New Old
Modular forms 87 47 40
Cusp forms 73 43 30
Eisenstein series 14 4 10

Trace form

\( 43 q - 2 q^{2} - 2 q^{3} - 1256 q^{4} + 4672 q^{5} - 17216 q^{6} - 4 q^{7} + 69124 q^{8} - 130227 q^{9} + O(q^{10}) \) \( 43 q - 2 q^{2} - 2 q^{3} - 1256 q^{4} + 4672 q^{5} - 17216 q^{6} - 4 q^{7} + 69124 q^{8} - 130227 q^{9} - 147364 q^{10} - 45906 q^{11} - 10988 q^{12} - 357936 q^{13} + 757836 q^{14} - 469032 q^{16} - 2203162 q^{17} + 2066926 q^{18} - 5107042 q^{19} + 5301516 q^{20} - 5423444 q^{21} - 20568924 q^{22} - 8279748 q^{23} + 58519728 q^{24} + 30271831 q^{25} - 18451512 q^{26} - 25871552 q^{27} - 36459784 q^{28} - 30835296 q^{29} + 132781252 q^{30} - 52661752 q^{32} + 33578492 q^{33} + 68474900 q^{34} + 14674460 q^{35} - 15810676 q^{36} - 249606160 q^{37} + 156046000 q^{38} - 279841732 q^{39} - 125381720 q^{40} + 379964826 q^{41} + 107395416 q^{42} + 172486862 q^{43} + 73663988 q^{44} - 1193615148 q^{45} - 437620836 q^{46} + 625190376 q^{48} + 2211896295 q^{49} - 875760314 q^{50} - 72924900 q^{51} - 771392444 q^{52} - 532004304 q^{53} + 913650464 q^{54} - 1427102468 q^{55} - 1385623464 q^{56} + 3496598016 q^{57} + 37561720 q^{58} + 1543683854 q^{59} + 318869600 q^{60} - 1605958320 q^{61} - 983062992 q^{62} - 867678656 q^{64} + 5467552032 q^{65} + 768197860 q^{66} - 4830427746 q^{67} - 855827792 q^{68} - 5413745972 q^{69} - 5103882496 q^{70} + 7572888316 q^{71} + 6888513460 q^{72} + 5245381658 q^{73} + 2513658844 q^{74} - 11656678318 q^{75} - 2250244316 q^{76} - 6423350036 q^{77} + 14243324268 q^{78} - 13115458328 q^{80} - 6608616565 q^{81} + 2724305648 q^{82} + 16141605438 q^{83} - 1633924184 q^{84} - 4005542352 q^{85} - 4025865500 q^{86} - 31832612676 q^{87} + 1023457912 q^{88} - 2520582342 q^{89} + 18960485240 q^{90} + 19874217404 q^{91} + 28060187160 q^{92} + 15789813088 q^{93} - 14829002256 q^{94} + 23525947312 q^{96} - 16976779898 q^{97} - 43134832310 q^{98} - 25616384098 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(16))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
16.11.c \(\chi_{16}(15, \cdot)\) 16.11.c.a 1 1
16.11.c.b 4
16.11.d \(\chi_{16}(7, \cdot)\) None 0 1
16.11.f \(\chi_{16}(3, \cdot)\) 16.11.f.a 38 2

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(16))\) into lower level spaces

\( S_{11}^{\mathrm{old}}(\Gamma_1(16)) \cong \) \(S_{11}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)