Space of modular forms of level 10 and weight 30

• Label: 10.30
• Level: 10
• Weight: 30
• Dimension: 25
• Nonzero newspaces: 2
• Newform subspaces: 5
• Sturm bound: 180
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	=	\( 30 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(180\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{30}(\Gamma_1(10))\).

	Total	New	Old
Modular forms	91	25	66
Cusp forms	83	25	58
Eisenstein series	8	0	8

Trace form

25 * q - 16384 * q^2 - 15889676 * q^3 - 805306368 * q^4 + 22023640345 * q^5 + 71793049600 * q^6 - 3301442406392 * q^7 - 4398046511104 * q^8 + 10663690441721 * q^9 + 315117647216640 * q^10 - 2792119052515700 * q^11 - 4265352422752256 * q^12 - 9994627384813646 * q^13 + 106213929274966016 * q^14 - 279651232109165660 * q^15 + 1801439850948198400 * q^16 - 521553325153684122 * q^17 - 2702288166880755712 * q^18 + 18726935387329251940 * q^19 - 9188725938790072320 * q^20 + 20656869040456316800 * q^21 - 62231466094223228928 * q^22 + 139454904901997495784 * q^23 + 17507620406100492288 * q^24 + 703197380595262999025 * q^25 - 636809360531084902400 * q^26 - 255539613774060065960 * q^27 - 886224197817573834752 * q^28 + 7812589474642566625710 * q^29 - 3803143206788405329920 * q^30 + 12502767632684144248800 * q^31 - 1180591620717411303424 * q^32 - 46119560272399813118592 * q^33 + 61985595904164559814656 * q^34 - 77373072106800846846280 * q^35 + 220176157575954510643200 * q^36 + 5288864962332411063418 * q^37 - 63027690681444729159680 * q^38 + 254277280233893983472312 * q^39 - 138275840524245889187840 * q^40 + 289639829318212996118050 * q^41 - 273000181132563988348928 * q^42 - 644710088125413611633156 * q^43 + 720132436769652441350144 * q^44 - 6726517591966911618357135 * q^45 - 1258691677707506542182400 * q^46 + 758395963760620776590688 * q^47 - 1144971822602206614388736 * q^48 + 1054967437490858935513029 * q^49 + 4963665484776910939340800 * q^50 - 2788222294536037885046200 * q^51 - 2682912359592538539032576 * q^52 - 3618019055610234593494326 * q^53 + 2191998907367641725665280 * q^54 + 44890741837545384509440540 * q^55 - 12030956810930263739596800 * q^56 + 48857138949841582726922480 * q^57 + 69910241023124646729646080 * q^58 - 189523807761360729896664980 * q^59 + 69179647375385725721640960 * q^60 - 38623566878949639841147450 * q^61 - 304121863678682287742517248 * q^62 + 214624422386392230749827544 * q^63 - 58028439341502200385896448 * q^64 - 331078787363475784239046310 * q^65 - 1135823676858042595691724800 * q^66 + 1036411244249033650454359828 * q^67 - 140003404665945467369029632 * q^68 - 1300101689567726845433979248 * q^69 + 387827346434276964285808640 * q^70 + 1523261605926403305060877800 * q^71 - 725389956320039757175324672 * q^72 - 4219319739837575148050226866 * q^73 + 8972463825302034824291188736 * q^74 - 6926575738107261702443352700 * q^75 - 2169539412925078499753984000 * q^76 + 4709185236928164902483369136 * q^77 + 3398075965103144930186100736 * q^78 - 15599022334232515661403473840 * q^79 + 1586970535217341151492177920 * q^80 + 15491665245180327319152227025 * q^81 - 15607726626299770160571383808 * q^82 + 31454671470146203377996238164 * q^83 - 6127057271370572329182560256 * q^84 + 38193025257680511409879493470 * q^85 + 366574834960142362622361600 * q^86 - 24199876236602858842852655880 * q^87 - 16705131978551351423080071168 * q^88 + 5301885253491374948644817930 * q^89 - 4942727064346779396412293120 * q^90 + 45049302760657602776909046800 * q^91 + 37434640988804333091636117504 * q^92 - 118904172807683916536560285072 * q^93 + 946508338922938849579237376 * q^94 + 26709042744754715499490591300 * q^95 + 5173234422821624590473625600 * q^96 - 193954048978928548292661906362 * q^97 - 136572537443999123729646501888 * q^98 + 622874404702336542540524301932 * q^99

Decomposition of \(S_{30}^{\mathrm{new}}(\Gamma_1(10))\)

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
10.30.a	\(\chi_{10}(1, \cdot)\)	10.30.a.a	2	1
		10.30.a.b	3
		10.30.a.c	3
		10.30.a.d	3
10.30.b	\(\chi_{10}(9, \cdot)\)	10.30.b.a	14	1

Decomposition of \(S_{30}^{\mathrm{old}}(\Gamma_1(10))\) into lower level spaces

\( S_{30}^{\mathrm{old}}(\Gamma_1(10)) \cong \) \(S_{30}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{30}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{30}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{30}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 1}\)