Space of modular forms of level 16 and weight 26

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

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 + 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

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 available 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

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