Space of modular forms of level 20 and weight 22

• Label: 20.22
• Level: 20
• Weight: 22
• Dimension: 139
• Nonzero newspaces: 3
• Newform subspaces: 5
• Sturm bound: 528
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	=	\( 22 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(528\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_1(20))\).

	Total	New	Old
Modular forms	262	147	115
Cusp forms	242	139	103
Eisenstein series	20	8	12

Trace form

139 * q - 2 * q^2 - 253532 * q^3 - 20857359 * q^5 + 89518280 * q^6 - 505663888 * q^7 - 5437750796 * q^8 - 832771423 * q^9 - 79518119114 * q^10 - 77552212340 * q^11 - 570336694400 * q^12 - 1667127995880 * q^13 + 951283537180 * q^15 - 6370955606088 * q^16 + 3727380262060 * q^17 + 39757563907794 * q^18 + 235940544932 * q^19 + 81412210813996 * q^20 + 43140070830472 * q^21 - 111247266264200 * q^22 + 327711485500176 * q^23 + 1002327945981031 * q^25 + 3891111195786164 * q^26 - 3507898276619576 * q^27 + 777483915869600 * q^28 + 2681807716818222 * q^29 - 6430271285067880 * q^30 - 7260345839730768 * q^31 + 16802430346808008 * q^32 + 9278014126739120 * q^33 + 14816468394417080 * q^35 + 28959930876598012 * q^36 - 8998767555014972 * q^37 - 33903927989238800 * q^38 + 226917393305248712 * q^39 - 239601330320732884 * q^40 - 244508239609665014 * q^41 + 314892317665823000 * q^42 + 385856366764700 * q^43 + 430192194389070091 * q^45 - 213082664571392920 * q^46 + 331698783839659944 * q^47 - 390241619715459200 * q^48 - 86031300471895731 * q^49 - 524959543378906614 * q^50 + 3502866630449780744 * q^51 + 273160775596344396 * q^52 - 5445720140867865548 * q^53 + 1517648899885435100 * q^55 - 6671305974104900320 * q^56 - 6078754084087552432 * q^57 + 453351056336345608 * q^58 + 1043314749558669004 * q^59 - 1532485673787245600 * q^60 - 15873084029629427722 * q^61 + 332798864723209000 * q^62 + 14379833911811983952 * q^63 + 17628506954719635212 * q^65 - 13059206125945465200 * q^66 + 42252724527190558292 * q^67 - 8633006654890054012 * q^68 + 37201878938237402056 * q^69 + 37910475241767033680 * q^70 + 21085396861647733176 * q^71 - 68783419515337210812 * q^72 + 10861316149839693800 * q^73 + 59920185536523166100 * q^75 + 143419349534578281600 * q^76 - 27683470176854305920 * q^77 - 59223834906729351000 * q^78 + 60748537498602752816 * q^79 + 834240646511689616 * q^80 - 434240676489164767305 * q^81 - 407545816973290657784 * q^82 + 22127129825283811956 * q^83 + 3807726934585798852 * q^85 + 252075324417525750280 * q^86 - 127274370545993274312 * q^87 + 49734705082893162400 * q^88 - 68532155109726986662 * q^89 + 327631127666102727126 * q^90 + 546550342335847459408 * q^91 - 1197824558021133628000 * q^92 + 630015601294612529728 * q^93 - 206160482144639460620 * q^95 + 3337884468254168833280 * q^96 - 3122514462629307353952 * q^97 - 1572204607929008916586 * q^98 - 2590340891701498591540 * q^99

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_1(20))\)

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
20.22.a	\(\chi_{20}(1, \cdot)\)	20.22.a.a	3	1
		20.22.a.b	4
20.22.c	\(\chi_{20}(9, \cdot)\)	20.22.c.a	10	1
20.22.e	\(\chi_{20}(3, \cdot)\)	20.22.e.a	2	2
		20.22.e.b	120

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_1(20))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_1(20)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)