Space of modular forms of level 63 and weight 18

• Label: 63.18
• Level: 63
• Weight: 18
• Dimension: 1835
• Nonzero newspaces: 10
• Sturm bound: 5184
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 18 \)
Nonzero newspaces:			\( 10 \)
Sturm bound:			\(5184\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_1(63))\).

	Total	New	Old
Modular forms	2496	1879	617
Cusp forms	2400	1835	565
Eisenstein series	96	44	52

Trace form

1835 * q + 21 * q^2 + 4548 * q^3 + 1758801 * q^4 - 1198806 * q^5 + 23947782 * q^6 + 22774527 * q^7 + 385854783 * q^8 - 722836056 * q^9 + 815312550 * q^10 - 3021924282 * q^11 + 2085977580 * q^12 - 7981267576 * q^13 - 43779459717 * q^14 + 65112235260 * q^15 - 79198340083 * q^16 + 53284955142 * q^17 - 139911765108 * q^18 - 213483142984 * q^19 + 992352629022 * q^20 - 198889154700 * q^21 + 900585561210 * q^22 - 546389014254 * q^23 + 4088294151306 * q^24 + 2308330604171 * q^25 + 6849922721574 * q^26 - 3565630711434 * q^27 - 6200969128303 * q^28 - 4791703517502 * q^29 + 22588660813890 * q^30 + 13005045233186 * q^31 - 20002261697961 * q^32 - 59438982574788 * q^33 - 20343952640922 * q^34 - 88521282143232 * q^35 + 131765899729518 * q^36 + 125993599609056 * q^37 - 360853633647516 * q^38 + 93975117194592 * q^39 + 185135804638674 * q^40 + 232786960761324 * q^41 - 355651496134416 * q^42 - 756945093044328 * q^43 + 534043079969694 * q^44 + 770690638020600 * q^45 + 994519668087102 * q^46 - 1155380250160842 * q^47 + 928029009661866 * q^48 - 2683056919535683 * q^49 + 206560789831479 * q^50 + 630876715648980 * q^51 + 942783558611498 * q^52 - 1201389051747192 * q^53 + 11697873652777404 * q^54 - 5721173586700056 * q^55 - 6048976597520625 * q^56 - 400083899741772 * q^57 - 518669799342396 * q^58 + 2441365548710472 * q^59 + 9316824138681150 * q^60 - 134186180897380 * q^61 + 5044456098985044 * q^62 - 12695728466324796 * q^63 - 6420052187151795 * q^64 + 20631167616769644 * q^65 - 3744973850645358 * q^66 + 306061766273188 * q^67 + 18828585328823610 * q^68 - 24031519550266464 * q^69 - 106221997918870350 * q^70 + 3334332449625396 * q^71 + 97402382562362064 * q^72 + 57775750258420904 * q^73 - 120959729120367990 * q^74 - 90010584241645296 * q^75 - 16744798761947230 * q^76 + 113408028034245156 * q^77 + 65309792366773272 * q^78 - 31828528015082384 * q^79 - 315676697359579986 * q^80 - 132575457655687860 * q^81 + 16594588275273978 * q^82 + 212736668571572946 * q^83 + 63148790613352638 * q^84 - 145398302375813484 * q^85 - 283683169280031384 * q^86 + 18647414617262478 * q^87 - 26684639236637772 * q^88 - 243817156854000858 * q^89 + 894962386590165114 * q^90 + 296391815862470678 * q^91 + 501712410065247552 * q^92 - 620478730954113258 * q^93 - 749693684527408548 * q^94 - 120833599152625722 * q^95 + 883473561876636168 * q^96 + 355604273783733296 * q^97 - 266372508549358737 * q^98 - 608883641823678696 * q^99

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_1(63))\)

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
63.18.a	\(\chi_{63}(1, \cdot)\)	63.18.a.a	3	1
		63.18.a.b	4
		63.18.a.c	4
		63.18.a.d	4
		63.18.a.e	5
		63.18.a.f	5
		63.18.a.g	8
		63.18.a.h	10
63.18.c	\(\chi_{63}(62, \cdot)\)	63.18.c.a	4	1
		63.18.c.b	40
63.18.e	\(\chi_{63}(37, \cdot)\)	n/a	112	2
63.18.f	\(\chi_{63}(22, \cdot)\)	n/a	204	2
63.18.g	\(\chi_{63}(4, \cdot)\)	n/a	268	2
63.18.h	\(\chi_{63}(25, \cdot)\)	n/a	268	2
63.18.i	\(\chi_{63}(5, \cdot)\)	n/a	268	2
63.18.o	\(\chi_{63}(20, \cdot)\)	n/a	268	2
63.18.p	\(\chi_{63}(17, \cdot)\)	63.18.p.a	92	2
63.18.s	\(\chi_{63}(47, \cdot)\)	n/a	268	2

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_1(63))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_1(63)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)