Space of modular forms of level 18 and weight 21

• Label: 18.21
• Level: 18
• Weight: 21
• Dimension: 48
• Nonzero newspaces: 2
• Newform subspaces: 3
• Sturm bound: 378
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	=	\( 21 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 3 \)
Sturm bound:			\(378\)
Trace bound:			\(1\)

Dimensions

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

	Total	New	Old
Modular forms	188	48	140
Cusp forms	172	48	124
Eisenstein series	16	0	16

Trace form

48 * q - 18846 * q^3 + 6291456 * q^4 + 29763918 * q^5 + 102690816 * q^6 + 732904026 * q^7 + 967310598 * q^9 - 13746831360 * q^10 - 35793208728 * q^11 + 26559381504 * q^12 - 218681439210 * q^13 + 187564400640 * q^14 - 965812538286 * q^15 - 3298534883328 * q^16 - 481837940736 * q^18 - 28974045669972 * q^19 + 15604865040384 * q^20 - 64715095872294 * q^21 + 11776658018304 * q^22 - 95164852839678 * q^23 + 18380312543232 * q^24 - 95868942555306 * q^25 - 312810773554224 * q^27 - 174307110027264 * q^28 + 487337329131246 * q^29 - 1016412645851136 * q^30 - 3387318959927130 * q^31 + 2417458230482544 * q^33 - 5012844973252608 * q^34 + 440007640743936 * q^36 + 8961330563051472 * q^37 - 27431157167935488 * q^38 + 21847743729103830 * q^39 + 7207298720071680 * q^40 - 76546903885431012 * q^41 - 27408162766282752 * q^42 + 88834673705479788 * q^43 - 151711625857797018 * q^45 + 88705110087647232 * q^46 + 220882065588142506 * q^47 + 19105114044235776 * q^48 - 223738088614870362 * q^49 + 84434006357065728 * q^50 - 112944490440784866 * q^51 + 114652054400532480 * q^52 - 907744599291211776 * q^54 - 1313369885954700036 * q^55 + 98337764482744320 * q^56 + 524175567253271298 * q^57 - 693770756844871680 * q^58 - 4671324023815652220 * q^59 + 999198431835586560 * q^60 - 1235078483136027666 * q^61 - 6762387225153657666 * q^63 - 6917529027641081856 * q^64 + 4959300225343873626 * q^65 + 7794266473078972416 * q^66 - 5798101914559833864 * q^67 - 5171455594224156672 * q^68 - 715869785458553814 * q^69 + 10371282942106411008 * q^70 - 3996696553325592576 * q^72 + 21379363412572789764 * q^73 + 7089371473773993984 * q^74 + 10151951406704814570 * q^75 + 6885378036681670656 * q^76 - 30865724759591472834 * q^77 + 14351578809049718784 * q^78 + 36670370747771122002 * q^79 - 14205809545514203338 * q^81 - 20359653083337818112 * q^82 + 54829678294093455594 * q^83 - 34962890419605602304 * q^84 - 74993065101186050772 * q^85 + 47393791396458614784 * q^86 + 23116374920781444150 * q^87 - 6174360479100567552 * q^88 + 122957322600559583232 * q^90 - 91108967900667512532 * q^91 - 49893790365609099264 * q^92 + 30021582829442833806 * q^93 + 197246804631615774720 * q^94 + 332020921293200455200 * q^95 - 18590859261785407488 * q^96 - 553231212204258686736 * q^97 + 525216922205664004722 * q^99

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

We only show spaces with odd 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
18.21.b	\(\chi_{18}(17, \cdot)\)	18.21.b.a	4	1
		18.21.b.b	4
18.21.d	\(\chi_{18}(5, \cdot)\)	18.21.d.a	40	2

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

\( S_{21}^{\mathrm{old}}(\Gamma_1(18)) \cong \) \(S_{21}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 1}\)