Space of modular forms of level 5 and weight 26

• Label: 5.26
• Level: 5
• Weight: 26
• Dimension: 21
• Nonzero newspaces: 2
• Newform subspaces: 3
• Sturm bound: 52
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 5 \)
Weight:	\( k \)	=	\( 26 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 3 \)
Sturm bound:			\(52\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_1(5))\).

	Total	New	Old
Modular forms	27	23	4
Cusp forms	23	21	2
Eisenstein series	4	2	2

Trace form

21 * q - 4002 * q^2 - 172396 * q^3 + 16772604 * q^4 + 793683685 * q^5 + 12322944112 * q^6 + 6543128808 * q^7 - 101081972280 * q^8 - 1582903387079 * q^9 + 3165827140710 * q^10 - 28877086066308 * q^11 - 68422875582512 * q^12 + 220275163302414 * q^13 - 1226233013920392 * q^14 + 790938061497620 * q^15 + 2439776746591536 * q^16 + 2841751737326178 * q^17 + 114435516345254 * q^18 + 14037065165645700 * q^19 - 45740712208111220 * q^20 + 13529319667084032 * q^21 - 24264570707350104 * q^22 + 324730477826668824 * q^23 - 1250704138692513600 * q^24 + 1419801381445966725 * q^25 - 1353210555038154348 * q^26 - 616576469248728280 * q^27 + 7460551168186390176 * q^28 - 6010709312528680650 * q^29 + 11142996804253937920 * q^30 - 11241796156071223008 * q^31 - 17481045614240873952 * q^32 + 21495795663454819408 * q^33 - 63830509289807974692 * q^34 + 63452805294951080360 * q^35 - 2552759174209817764 * q^36 + 9156020287154409318 * q^37 + 60516990815238896280 * q^38 + 58043041771740771992 * q^39 - 269511934953092923800 * q^40 + 413443038130194670242 * q^41 + 197044147055009475936 * q^42 - 1321060245929686734756 * q^43 + 2082884792406599561808 * q^44 - 2198879184684185818055 * q^45 - 1495485905003304882408 * q^46 + 2140441407206432771088 * q^47 + 4388391998086191424 * q^48 - 1494106826159251862571 * q^49 + 4374940462801066066350 * q^50 + 4189363435545032216872 * q^51 - 5358740220726552489192 * q^52 + 5582189630338765603254 * q^53 - 4893084786761986968800 * q^54 - 216430936450509169380 * q^55 - 18596802447900878269920 * q^56 + 6463841607189211455440 * q^57 + 19528677380655136236420 * q^58 - 50741052220023733715700 * q^59 + 42026906481612094664560 * q^60 - 5438402415917345050458 * q^61 - 3387185265634263698304 * q^62 + 34818662529560120817384 * q^63 + 18369606923249935936704 * q^64 - 23464502457272716910530 * q^65 + 6954375890293241009024 * q^66 + 109602276017722838891028 * q^67 - 269493353307885380540184 * q^68 + 447907587179800790690592 * q^69 - 649633568473811878161240 * q^70 + 210941655788439155610792 * q^71 + 651674850937592404267560 * q^72 - 578107228546908018325926 * q^73 - 877816668049104816589692 * q^74 - 266725603091691226420300 * q^75 + 1371715841872415755629360 * q^76 - 501697267892420228433984 * q^77 + 822483197934526611655888 * q^78 - 533613610512044940870000 * q^79 + 1934609898980050340802160 * q^80 + 545142523246056827752141 * q^81 + 1043883358198078825109196 * q^82 + 1876801646020830546135684 * q^83 - 12051525902524259815000992 * q^84 - 588892372579193591248590 * q^85 + 4134804128142689596327872 * q^86 + 5808903586894731691339160 * q^87 - 4216063541689362176038560 * q^88 - 2192776454621002905409950 * q^89 - 9866078419131404687544130 * q^90 + 19091558339488828897549872 * q^91 + 13190242110052756103759328 * q^92 - 5779813589219968851924192 * q^93 - 27379684943189219059270392 * q^94 - 18921134823614420054472700 * q^95 + 59921726409999579279571712 * q^96 + 37152087992100438181379538 * q^97 - 46079972861881665096048114 * q^98 - 52156868102585990025471508 * q^99

Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_1(5))\)

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
5.26.a	\(\chi_{5}(1, \cdot)\)	5.26.a.a	4	1
		5.26.a.b	5
5.26.b	\(\chi_{5}(4, \cdot)\)	5.26.b.a	12	1

Decomposition of \(S_{26}^{\mathrm{old}}(\Gamma_1(5))\) into lower level spaces

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