Space of modular forms of level 10 and weight 28

• Label: 10.28
• Level: 10
• Weight: 28
• Dimension: 23
• Nonzero newspaces: 2
• Newform subspaces: 5
• Sturm bound: 168
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	=	\( 28 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(168\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{28}(\Gamma_1(10))\).

	Total	New	Old
Modular forms	85	23	62
Cusp forms	77	23	54
Eisenstein series	8	0	8

Trace form

23 * q + 8192 * q^2 - 5585528 * q^3 - 335544320 * q^4 + 1147059535 * q^5 + 61841047552 * q^6 - 26881836804 * q^7 + 549755813888 * q^8 - 19906295436385 * q^9 - 23017385943040 * q^10 - 14464521837404 * q^11 - 374838438920192 * q^12 + 425308381788102 * q^13 + 527341706608640 * q^14 + 30170228973533440 * q^15 + 103582791429521408 * q^16 + 6681364551758226 * q^17 + 201364589787521024 * q^18 + 391847706867416100 * q^19 + 86862137665781760 * q^20 + 110299882556703976 * q^21 + 3495399077188829184 * q^22 - 6982312948683377628 * q^23 + 1992941791157944320 * q^24 + 19930328417185239975 * q^25 + 9518209575403896832 * q^26 - 89283751298201073680 * q^27 - 1804009530149830656 * q^28 - 285328614595335340950 * q^29 + 192664032900713840640 * q^30 + 165824795322844125656 * q^31 + 36893488147419103232 * q^32 + 1084944057566163351744 * q^33 - 546934826654125506560 * q^34 + 1779058149963547078580 * q^35 + 4043903022645676867584 * q^36 - 987703039883954851554 * q^37 + 5666409518834220236800 * q^38 - 31191042249789943630720 * q^39 + 2886847902886983106560 * q^40 - 17045922067005018135194 * q^41 + 9863265465742102626304 * q^42 - 8827063906753261149168 * q^43 + 20263192551262791925760 * q^44 - 44059180292106749129745 * q^45 - 18450730723896290050048 * q^46 + 111594255111887773270836 * q^47 - 25154981819467471781888 * q^48 + 359338621034195391779835 * q^49 - 250885731953302557286400 * q^50 + 63783638175330851237456 * q^51 + 28541962351477813936128 * q^52 + 300330320174543209438302 * q^53 - 959478085121436917760000 * q^54 + 94054880938828656801220 * q^55 + 328466925999295775637504 * q^56 - 1424768382188793206159200 * q^57 + 210492666738415258091520 * q^58 - 1602396720328640860160900 * q^59 - 662905452553715224412160 * q^60 - 4124309181172383309390134 * q^61 + 1669578868622464251265024 * q^62 + 3149316348073265634939212 * q^63 - 1511157274518286468382720 * q^64 + 10925271035845812081698590 * q^65 + 10002873745655499968610304 * q^66 - 3523566238154064750244464 * q^67 + 448378785038363749515264 * q^68 + 5414120697041743067199880 * q^69 - 609433493800660242923520 * q^70 - 41894012247154375187097024 * q^71 + 13513348870466537296756736 * q^72 - 10222732513042515682939398 * q^73 - 18144501234296814776565760 * q^74 - 40588670658508783493974600 * q^75 + 45141482442569107793510400 * q^76 - 19315729944095831187248208 * q^77 - 15765469973509183667044352 * q^78 + 27692534091719341030632000 * q^79 + 5165896894397774414479360 * q^80 + 345985476733739253520252023 * q^81 - 70431375105977767817035776 * q^82 + 151454670603188593724129592 * q^83 + 7340747598173814977986560 * q^84 + 210483960236508472772087530 * q^85 - 479203763554341924205068288 * q^86 - 21552465969231732641857680 * q^87 + 234572261296790640028286976 * q^88 - 1004920802349250792674245050 * q^89 + 285175902014605646110433280 * q^90 - 268709388343781837437497384 * q^91 - 468575090078631768298094592 * q^92 + 363824802843394270792921184 * q^93 + 438006451137641439912919040 * q^94 - 326435274989438279538655100 * q^95 + 278507318711388323857825792 * q^96 + 1466928433453302566766065346 * q^97 + 1845423955521133174021103616 * q^98 - 6328126834425397331314147420 * q^99

Decomposition of \(S_{28}^{\mathrm{new}}(\Gamma_1(10))\)

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
10.28.a	\(\chi_{10}(1, \cdot)\)	10.28.a.a	2	1
		10.28.a.b	2
		10.28.a.c	2
		10.28.a.d	3
10.28.b	\(\chi_{10}(9, \cdot)\)	10.28.b.a	14	1

Decomposition of \(S_{28}^{\mathrm{old}}(\Gamma_1(10))\) into lower level spaces

\( S_{28}^{\mathrm{old}}(\Gamma_1(10)) \cong \) \(S_{28}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{28}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{28}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{28}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 1}\)