Space of modular forms of level 10 and weight 22

• Label: 10.22
• Level: 10
• Weight: 22
• Dimension: 17
• Nonzero newspaces: 2
• Newform subspaces: 5
• Sturm bound: 132
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	=	\( 22 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(132\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_1(10))\).

	Total	New	Old
Modular forms	67	17	50
Cusp forms	59	17	42
Eisenstein series	8	0	8

Trace form

17 * q - 1024 * q^2 - 17336 * q^3 - 3145728 * q^4 + 17956525 * q^5 - 194465792 * q^6 - 126415972 * q^7 - 1073741824 * q^8 + 28671539681 * q^9 - 32426931200 * q^10 - 63724698476 * q^11 - 18178113536 * q^12 + 1759096582034 * q^13 - 2356689362944 * q^14 - 14551191200 * q^15 + 18691697672192 * q^16 - 1550055571602 * q^17 - 35099863954432 * q^18 + 72110842518260 * q^19 - 39308781158400 * q^20 + 198772688668984 * q^21 + 178816832827392 * q^22 - 504621232645116 * q^23 + 280001802928128 * q^24 - 86272367174375 * q^25 - 1392540389906432 * q^26 + 3273499683699760 * q^27 - 132556754255872 * q^28 - 1749869050244850 * q^29 + 2840678400921600 * q^30 + 6212708341623384 * q^31 - 1125899906842624 * q^32 + 20322682714697088 * q^33 + 8485316100847616 * q^34 + 37108525058564900 * q^35 + 56723122569609216 * q^36 - 13007505623316982 * q^37 + 39391290462515200 * q^38 + 65891446401451712 * q^39 + 13030581809971200 * q^40 + 214579390253382874 * q^41 - 356378085213175808 * q^42 - 243310821507893776 * q^43 + 351425816044765184 * q^44 - 93244562278530075 * q^45 - 403823685349425152 * q^46 + 881790342543934068 * q^47 - 19061133579124736 * q^48 - 2444414702778908691 * q^49 + 33297266753920000 * q^50 - 846033831479052976 * q^51 + 1844546457602883584 * q^52 - 112497377888155926 * q^53 - 3733274589295779840 * q^54 + 8722417528423367300 * q^55 - 2251168470672605184 * q^56 - 15982097147052733600 * q^57 + 876669646172375040 * q^58 + 3629400606092644300 * q^59 + 3580907949863731200 * q^60 - 8006547167366289266 * q^61 + 128857993513787392 * q^62 + 5345077138568792204 * q^63 - 3458764513820540928 * q^64 + 644410116263066050 * q^65 - 649467003155431424 * q^66 - 22522900884194907472 * q^67 - 1625351071048138752 * q^68 + 166901122269193619032 * q^69 + 22047544156705996800 * q^70 - 147195722424120544896 * q^71 - 36804874945882488832 * q^72 + 63646881826441593494 * q^73 + 105828325499122681856 * q^74 + 294953348246231795000 * q^75 - 183252280955518320640 * q^76 - 184601145641795237424 * q^77 + 168867026027871256576 * q^78 + 226525451386698246080 * q^79 + 19743408031950438400 * q^80 - 577064776384154305983 * q^81 - 295910364070758279168 * q^82 + 5170514717007118584 * q^83 + 541791701991312850944 * q^84 + 320660213037835775150 * q^85 - 839961821943995461632 * q^86 - 1904616390843583644240 * q^87 + 187503039298815393792 * q^88 + 3111372998356599038330 * q^89 + 222206177811928857600 * q^90 - 3998320288109997400136 * q^91 - 529133713642085154816 * q^92 + 1551870277213993198688 * q^93 + 1086279960499628916736 * q^94 + 47612185879217510500 * q^95 - 213817399508669038592 * q^96 - 1671611530660787780002 * q^97 - 1282164053311481422848 * q^98 + 7599587498386605762932 * q^99

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_1(10))\)

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
10.22.a	\(\chi_{10}(1, \cdot)\)	10.22.a.a	1	1
		10.22.a.b	2
		10.22.a.c	2
		10.22.a.d	2
10.22.b	\(\chi_{10}(9, \cdot)\)	10.22.b.a	10	1

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_1(10))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_1(10)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 1}\)