Properties

Label 16.26
Level 16
Weight 26
Dimension 110
Nonzero newspaces 2
Newform subspaces 7
Sturm bound 416
Trace bound 1

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Defining parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 26 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 7 \)
Sturm bound: \(416\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_1(16))\).

Total New Old
Modular forms 207 115 92
Cusp forms 193 110 83
Eisenstein series 14 5 9

Trace form

\( 110 q - 2 q^{2} - 531442 q^{3} - 35720280 q^{4} + 153134278 q^{5} + 5523305584 q^{6} + 49570129440 q^{7} - 111585796556 q^{8} + 2747998934812 q^{9} + O(q^{10}) \) \( 110 q - 2 q^{2} - 531442 q^{3} - 35720280 q^{4} + 153134278 q^{5} + 5523305584 q^{6} + 49570129440 q^{7} - 111585796556 q^{8} + 2747998934812 q^{9} + 11204469279564 q^{10} - 30416451244558 q^{11} + 4457958449476 q^{12} + 35520940152358 q^{13} + 569786063169884 q^{14} + 806839317223524 q^{15} + 2994093021729688 q^{16} - 508652996207404 q^{17} - 2867795956543938 q^{18} + 25090401388498134 q^{19} - 13833473467102628 q^{20} + 21360790375033540 q^{21} - 115557957737734140 q^{22} + 171058373102590560 q^{23} - 503381193280933712 q^{24} + 742154438320879092 q^{25} - 456252478548229112 q^{26} + 1687439738931291032 q^{27} + 1552921875587693528 q^{28} - 1155802628923769298 q^{29} + 11343158469529692756 q^{30} + 1159561357865364080 q^{31} - 11578069776901521592 q^{32} + 6200363844091350076 q^{33} + 2938852285050308020 q^{34} - 30813891593043950788 q^{35} + 157785427701797708140 q^{36} + 10269729223310826126 q^{37} + 40614359087426656128 q^{38} + 44592267118282562272 q^{39} - 112757857382560433528 q^{40} - 79427185216773458184 q^{41} + 638952664458283966840 q^{42} + 458565511862360252410 q^{43} - 684998681106129479932 q^{44} - 19223342470168786902 q^{45} + 2218094645327092722636 q^{46} + 1651653582231121905616 q^{47} + 4829126491824706742248 q^{48} - 13432703219514104969262 q^{49} - 8564647487456172003450 q^{50} + 5527703016297488495780 q^{51} + 9055573957446241741556 q^{52} - 8863031786897366151490 q^{53} - 8457040875946880191712 q^{54} - 5876894224122036981984 q^{55} + 9182602521331713530776 q^{56} - 9121300938558448139840 q^{57} + 35486130953890834044888 q^{58} - 82273566305469055871958 q^{59} - 46747865165969226000768 q^{60} + 55185202531721448649686 q^{61} - 106153381614218446625744 q^{62} - 47658577408171949580636 q^{63} - 69716836760070778346880 q^{64} - 85800012208627056419660 q^{65} + 265304266078332345263284 q^{66} - 187710608447860324176250 q^{67} - 327450239037616682015280 q^{68} + 287669619634425177380148 q^{69} - 94640137963738168435840 q^{70} + 107087933176294058805024 q^{71} + 129208915803885279184164 q^{72} + 155463632157558765980280 q^{73} - 912412751745056267684916 q^{74} + 318066264182580819308598 q^{75} + 1223073046602197915465364 q^{76} - 66485787009789472868156 q^{77} - 2096745025905732230839204 q^{78} + 2304307781328512183885376 q^{79} - 2884839085500728003108056 q^{80} - 6088629460539675734815530 q^{81} - 317812241817362320201440 q^{82} + 402960361491245370707278 q^{83} + 865387961022598778467240 q^{84} - 2770719705744889833041324 q^{85} - 4068985156002103836136572 q^{86} + 376583198260927029773280 q^{87} - 5646367645559063873022472 q^{88} + 34600911412223898467640 q^{89} + 5632032915017761814636952 q^{90} - 10435250209093337023671356 q^{91} + 3861096908689669442366136 q^{92} - 2598008703314497993550704 q^{93} + 3035350002539798965762832 q^{94} + 3438034297852793622987732 q^{95} - 7441722806018774292782416 q^{96} + 5248313571060446231270036 q^{97} + 3220121184660928876013274 q^{98} - 26080991251890017407360274 q^{99} + O(q^{100}) \)

Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_1(16))\)

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
16.26.a \(\chi_{16}(1, \cdot)\) 16.26.a.a 1 1
16.26.a.b 1
16.26.a.c 2
16.26.a.d 2
16.26.a.e 3
16.26.a.f 3
16.26.b \(\chi_{16}(9, \cdot)\) None 0 1
16.26.e \(\chi_{16}(5, \cdot)\) 16.26.e.a 98 2

Decomposition of \(S_{26}^{\mathrm{old}}(\Gamma_1(16))\) into lower level spaces

\( S_{26}^{\mathrm{old}}(\Gamma_1(16)) \cong \) \(S_{26}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)