Space of modular forms of level 21 and weight 18

• Label: 21.18
• Level: 21
• Weight: 18
• Dimension: 192
• Nonzero newspaces: 4
• Newform subspaces: 9
• Sturm bound: 576
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	=	\( 18 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 9 \)
Sturm bound:			\(576\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_1(21))\).

	Total	New	Old
Modular forms	284	204	80
Cusp forms	260	192	68
Eisenstein series	24	12	12

Trace form

192 * q - 1596 * q^2 - 6564 * q^3 - 698414 * q^4 - 2289906 * q^5 + 4960116 * q^6 - 50397326 * q^7 + 238954278 * q^8 + 40710972 * q^9 + 1551745296 * q^10 + 899235402 * q^11 - 6841812504 * q^12 + 8579855326 * q^13 - 18546627336 * q^14 - 31918630932 * q^15 + 1376577906 * q^16 + 92537967936 * q^17 - 41658733566 * q^18 + 158068860934 * q^19 - 347663688252 * q^20 + 574153249530 * q^21 - 2897544867408 * q^22 + 1879866803016 * q^23 - 2518413020424 * q^24 - 5442858860946 * q^25 - 1229764048758 * q^26 + 564859072962 * q^27 - 7627257622710 * q^28 - 13287442796904 * q^29 + 13260409171758 * q^30 + 19525108250182 * q^31 - 60163635248610 * q^32 - 24322945283316 * q^33 + 88602982181988 * q^34 + 43393479582042 * q^35 + 63082180607514 * q^36 - 44566001605576 * q^37 + 35028492016134 * q^38 + 139421918568018 * q^39 + 230096646721848 * q^40 - 12772817827956 * q^41 - 30041464591242 * q^42 + 403655922998672 * q^43 - 26343937391400 * q^44 - 562401660279384 * q^45 + 62308971574596 * q^46 + 272415532415838 * q^47 - 10746919049760 * q^48 + 1039199566947558 * q^49 + 264496561033650 * q^50 - 953655301944216 * q^51 - 2578834368433064 * q^52 - 67752032107020 * q^53 + 308658355044498 * q^54 + 2735403368059752 * q^55 - 1167461701543182 * q^56 - 6261665680744416 * q^57 + 4393158380689224 * q^58 + 772973750641020 * q^59 + 9749669672471724 * q^60 - 12569326167673358 * q^61 + 7010620740846180 * q^62 - 12538343098286166 * q^63 - 42296973632666 * q^64 + 2732152051359438 * q^65 + 14114237895237474 * q^66 - 11290024713175590 * q^67 - 14156069919985200 * q^68 - 815780679672024 * q^69 + 97102979468807184 * q^70 + 16025133414488748 * q^71 - 48981177778082202 * q^72 - 41901650391813764 * q^73 - 15595716763797402 * q^74 + 30732588573327786 * q^75 + 80188675647544072 * q^76 + 31709653602330336 * q^77 - 66569962539519216 * q^78 - 85324054504458882 * q^79 - 171235752958626936 * q^80 + 62369906860411488 * q^81 + 99355012862918472 * q^82 - 9163852298684244 * q^83 + 16647703590959436 * q^84 + 121929280951532040 * q^85 - 282364021302156330 * q^86 - 186199777341478476 * q^87 + 100721600726251692 * q^88 + 225256537946264856 * q^89 + 124211092701914712 * q^90 + 38632159994016712 * q^91 - 713661965132685408 * q^92 + 124898432283238314 * q^93 + 26111187649430136 * q^94 - 338714470554036198 * q^95 - 408868794401377788 * q^96 + 486807172162037908 * q^97 + 1378136444637480870 * q^98 + 238305712437160596 * q^99

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_1(21))\)

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
21.18.a	\(\chi_{21}(1, \cdot)\)	21.18.a.a	3	1
		21.18.a.b	4
		21.18.a.c	4
		21.18.a.d	5
21.18.c	\(\chi_{21}(20, \cdot)\)	21.18.c.a	44	1
21.18.e	\(\chi_{21}(4, \cdot)\)	21.18.e.a	22	2
		21.18.e.b	24
21.18.g	\(\chi_{21}(5, \cdot)\)	21.18.g.a	2	2
		21.18.g.b	84

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)