Space of modular forms of level 10 and weight 26

• Label: 10.26
• Level: 10
• Weight: 26
• Dimension: 19
• Nonzero newspaces: 2
• Newform subspaces: 5
• Sturm bound: 156
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	=	\( 26 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(156\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_1(10))\).

	Total	New	Old
Modular forms	79	19	60
Cusp forms	71	19	52
Eisenstein series	8	0	8

Trace form

19 * q - 4096 * q^2 + 172396 * q^3 - 83886080 * q^4 - 734435965 * q^5 - 6732529664 * q^6 - 29178793288 * q^7 - 68719476736 * q^8 + 75780301535 * q^9 + 636528619520 * q^10 + 33864829109988 * q^11 + 2892324929536 * q^12 - 179593027428814 * q^13 + 121725324328960 * q^14 - 626604493100180 * q^15 + 5348024557502464 * q^16 - 278192702833218 * q^17 - 18024426694955008 * q^18 - 1352675984755300 * q^19 + 4129790822973440 * q^20 + 83856543654804928 * q^21 - 31904915250266112 * q^22 - 57464588148196344 * q^23 + 107338448272097280 * q^24 - 630321572821262525 * q^25 + 1283325007728418816 * q^26 - 1492578851865494120 * q^27 - 489538917612126208 * q^28 + 2087490831212629050 * q^29 - 2504160483574824960 * q^30 + 11869055929016480288 * q^31 - 1152921504606846976 * q^32 - 23721594650263551888 * q^33 + 24029955888834600960 * q^34 - 60807166028705596040 * q^35 + 37608737346800320512 * q^36 + 155457717802810003802 * q^37 - 17790383732468695040 * q^38 - 172205691195540720280 * q^39 - 44233610139868856320 * q^40 - 409995814233949616562 * q^41 + 19951777482209886208 * q^42 + 1010218220561249182436 * q^43 - 93639503570440028160 * q^44 + 1458127120662030176895 * q^45 - 491633554654858543104 * q^46 - 828989199456009681648 * q^47 + 48525160085010251776 * q^48 - 3970229477924855817885 * q^49 + 102490832781510963200 * q^50 + 8140582223469890298968 * q^51 - 3013071013267137101824 * q^52 - 3595408668331726645494 * q^53 + 10628295150642996019200 * q^54 - 7320145307758398813180 * q^55 - 7305754808189009788928 * q^56 + 4204922984141094699440 * q^57 + 2713638168327776378880 * q^58 + 20687333814098295590100 * q^59 + 4582948879312229498880 * q^60 - 38742837011912144250262 * q^61 + 19279033604719908487168 * q^62 - 4245583819863456185224 * q^63 - 23611832414348226068480 * q^64 + 4169551103474543339170 * q^65 + 57649422253664283983872 * q^66 + 24383692289330109140012 * q^67 - 4667299065056710361088 * q^68 - 473552809821053026827680 * q^69 + 228479849196587932549120 * q^70 + 315123431485722521859288 * q^71 - 302399699937426279497728 * q^72 + 79974919621594950676166 * q^73 - 180008157074690983485440 * q^74 + 1043172813871208888098700 * q^75 + 112037409099163872788480 * q^76 - 1568720493209389904209536 * q^77 - 9799023502584299749376 * q^78 + 1183348808192904094098800 * q^79 - 206725346143843165143040 * q^80 - 3524706653718636399732261 * q^81 + 1501915684254291799400448 * q^82 + 389721063496013168985276 * q^83 + 3298121909117199518269440 * q^84 + 52137346127954808690510 * q^85 - 606982946306929123180544 * q^86 + 1376374965251964003154920 * q^87 - 535275654615408618504192 * q^88 + 199728336584255883029550 * q^89 + 2746899836775628597309440 * q^90 - 14396868702933323806328432 * q^91 - 964095807713330073698304 * q^92 + 4622114231236669578643232 * q^93 + 4501279773320996053647360 * q^94 + 19461106695512524920070300 * q^95 - 1895038630378200664899584 * q^96 - 31710595169851658894946418 * q^97 + 24127501086126701924610048 * q^98 + 12001150330429260659354420 * q^99

Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_1(10))\)

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
10.26.a	\(\chi_{10}(1, \cdot)\)	10.26.a.a	1	1
		10.26.a.b	2
		10.26.a.c	2
		10.26.a.d	2
10.26.b	\(\chi_{10}(9, \cdot)\)	10.26.b.a	12	1

Decomposition of \(S_{26}^{\mathrm{old}}(\Gamma_1(10))\) into lower level spaces

\( S_{26}^{\mathrm{old}}(\Gamma_1(10)) \cong \) \(S_{26}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 1}\)