Space of modular forms of level 3276 and weight 2

• Label: 3276.2
• Level: 3276
• Weight: 2
• Dimension: 125962
• Nonzero newspaces: 168
• Sturm bound: 1161216
• Trace bound: 40

Defining parameters

Level:	$N$	=	$3276 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 13$
Weight:	$k$	=	$2$
Nonzero newspaces:			$168$
Sturm bound:			$1161216$
Trace bound:			$40$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_1(3276))$.

	Total	New	Old
Modular forms	296064	127938	168126
Cusp forms	284545	125962	158583
Eisenstein series	11519	1976	9543

Trace form

125962 * q - 66 * q^2 - 74 * q^4 - 138 * q^5 - 84 * q^6 + 4 * q^7 - 150 * q^8 - 192 * q^9 - 196 * q^10 - 6 * q^11 - 48 * q^12 - 130 * q^13 - 162 * q^14 + 12 * q^15 - 50 * q^16 - 120 * q^17 - 66 * q^19 - 12 * q^20 - 234 * q^21 - 168 * q^22 - 78 * q^23 - 60 * q^24 - 270 * q^25 - 90 * q^26 - 36 * q^27 - 222 * q^28 - 450 * q^29 - 84 * q^30 - 118 * q^31 - 126 * q^32 - 108 * q^33 - 16 * q^34 - 204 * q^36 - 384 * q^37 + 72 * q^38 - 66 * q^39 + 140 * q^40 - 30 * q^41 + 32 * q^43 + 228 * q^44 - 108 * q^45 + 216 * q^46 + 30 * q^47 + 132 * q^48 - 156 * q^49 + 342 * q^50 + 96 * q^51 + 178 * q^52 - 162 * q^53 + 120 * q^54 + 96 * q^55 + 162 * q^56 - 264 * q^57 + 176 * q^58 + 102 * q^59 + 84 * q^60 - 224 * q^61 + 96 * q^62 + 210 * q^63 - 146 * q^64 + 168 * q^65 - 60 * q^66 + 58 * q^67 + 228 * q^68 + 36 * q^69 - 48 * q^70 + 360 * q^71 + 24 * q^72 - 58 * q^73 + 12 * q^74 + 384 * q^75 + 180 * q^77 + 132 * q^78 + 78 * q^79 + 216 * q^80 + 264 * q^81 - 16 * q^82 + 420 * q^83 - 84 * q^84 + 106 * q^85 + 192 * q^86 + 192 * q^87 + 24 * q^88 + 402 * q^89 + 36 * q^90 - 48 * q^91 - 132 * q^92 + 240 * q^93 - 48 * q^94 + 42 * q^95 - 120 * q^96 + 28 * q^97 - 258 * q^98 + 132 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_1(3276))$

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
3276.2.a	$\chi_{3276}(1, \cdot)$	3276.2.a.a	1	1
		3276.2.a.b	1
		3276.2.a.c	1
		3276.2.a.d	1
		3276.2.a.e	1
		3276.2.a.f	1
		3276.2.a.g	1
		3276.2.a.h	1
		3276.2.a.i	1
		3276.2.a.j	1
		3276.2.a.k	1
		3276.2.a.l	2
		3276.2.a.m	2
		3276.2.a.n	2
		3276.2.a.o	2
		3276.2.a.p	2
		3276.2.a.q	2
		3276.2.a.r	3
		3276.2.a.s	4
3276.2.c	$\chi_{3276}(2575, \cdot)$	n/a	240	1
3276.2.e	$\chi_{3276}(2521, \cdot)$	3276.2.e.a	2	1
		3276.2.e.b	2
		3276.2.e.c	2
		3276.2.e.d	2
		3276.2.e.e	4
		3276.2.e.f	8
		3276.2.e.g	16
3276.2.f	$\chi_{3276}(3095, \cdot)$	n/a	144	1
3276.2.h	$\chi_{3276}(1637, \cdot)$	3276.2.h.a	8	1
		3276.2.h.b	16
		3276.2.h.c	16
3276.2.j	$\chi_{3276}(2339, \cdot)$	n/a	168	1
3276.2.l	$\chi_{3276}(2393, \cdot)$	3276.2.l.a	8	1
		3276.2.l.b	24
3276.2.o	$\chi_{3276}(1819, \cdot)$	n/a	276	1
3276.2.q	$\chi_{3276}(625, \cdot)$	n/a	192	2
3276.2.r	$\chi_{3276}(1873, \cdot)$	3276.2.r.a	2	2
		3276.2.r.b	2
		3276.2.r.c	2
		3276.2.r.d	2
		3276.2.r.e	4
		3276.2.r.f	4
		3276.2.r.g	6
		3276.2.r.h	6
		3276.2.r.i	6
		3276.2.r.j	8
		3276.2.r.k	10
		3276.2.r.l	12
		3276.2.r.m	16
3276.2.s	$\chi_{3276}(1849, \cdot)$	n/a	168	2
3276.2.t	$\chi_{3276}(373, \cdot)$	n/a	224	2
3276.2.u	$\chi_{3276}(289, \cdot)$	3276.2.u.a	2	2
		3276.2.u.b	2
		3276.2.u.c	2
		3276.2.u.d	2
		3276.2.u.e	2
		3276.2.u.f	2
		3276.2.u.g	2
		3276.2.u.h	4
		3276.2.u.i	4
		3276.2.u.j	12
		3276.2.u.k	18
		3276.2.u.l	18
		3276.2.u.m	24
3276.2.v	$\chi_{3276}(1093, \cdot)$	n/a	144	2
3276.2.w	$\chi_{3276}(841, \cdot)$	n/a	168	2
3276.2.x	$\chi_{3276}(2557, \cdot)$	3276.2.x.a	2	2
		3276.2.x.b	2
		3276.2.x.c	2
		3276.2.x.d	2
		3276.2.x.e	2
		3276.2.x.f	2
		3276.2.x.g	2
		3276.2.x.h	4
		3276.2.x.i	4
		3276.2.x.j	12
		3276.2.x.k	18
		3276.2.x.l	18
		3276.2.x.m	24
3276.2.y	$\chi_{3276}(529, \cdot)$	n/a	224	2
3276.2.z	$\chi_{3276}(757, \cdot)$	3276.2.z.a	2	2
		3276.2.z.b	2
		3276.2.z.c	2
		3276.2.z.d	4
		3276.2.z.e	4
		3276.2.z.f	6
		3276.2.z.g	8
		3276.2.z.h	8
		3276.2.z.i	8
		3276.2.z.j	12
		3276.2.z.k	12
3276.2.ba	$\chi_{3276}(445, \cdot)$	n/a	224	2
3276.2.bb	$\chi_{3276}(2473, \cdot)$	n/a	224	2
3276.2.bc	$\chi_{3276}(1717, \cdot)$	n/a	192	2
3276.2.bd	$\chi_{3276}(1763, \cdot)$	n/a	448	2
3276.2.bg	$\chi_{3276}(2647, \cdot)$	n/a	420	2
3276.2.bi	$\chi_{3276}(1945, \cdot)$	3276.2.bi.a	4	2
		3276.2.bi.b	4
		3276.2.bi.c	16
		3276.2.bi.d	20
		3276.2.bi.e	20
		3276.2.bi.f	32
3276.2.bj	$\chi_{3276}(2465, \cdot)$	3276.2.bj.a	28	2
		3276.2.bj.b	28
3276.2.bl	$\chi_{3276}(961, \cdot)$	n/a	224	2
3276.2.bn	$\chi_{3276}(1795, \cdot)$	n/a	1152	2
3276.2.bp	$\chi_{3276}(347, \cdot)$	n/a	1328	2
3276.2.bs	$\chi_{3276}(881, \cdot)$	3276.2.bs.a	72	2
3276.2.bu	$\chi_{3276}(173, \cdot)$	n/a	224	2
3276.2.bw	$\chi_{3276}(191, \cdot)$	n/a	1328	2
3276.2.by	$\chi_{3276}(575, \cdot)$	n/a	336	2
3276.2.bz	$\chi_{3276}(2201, \cdot)$	n/a	224	2
3276.2.cc	$\chi_{3276}(1543, \cdot)$	n/a	1328	2
3276.2.cd	$\chi_{3276}(1213, \cdot)$	n/a	224	2
3276.2.cf	$\chi_{3276}(1765, \cdot)$	3276.2.cf.a	12	2
		3276.2.cf.b	12
		3276.2.cf.c	16
		3276.2.cf.d	32
3276.2.ch	$\chi_{3276}(55, \cdot)$	n/a	552	2
3276.2.cj	$\chi_{3276}(1699, \cdot)$	n/a	1328	2
3276.2.cm	$\chi_{3276}(205, \cdot)$	n/a	224	2
3276.2.co	$\chi_{3276}(1949, \cdot)$	n/a	224	2
3276.2.cq	$\chi_{3276}(443, \cdot)$	n/a	1152	2
3276.2.cs	$\chi_{3276}(23, \cdot)$	n/a	1328	2
3276.2.cu	$\chi_{3276}(1277, \cdot)$	3276.2.cu.a	76	2
3276.2.cv	$\chi_{3276}(965, \cdot)$	n/a	224	2
3276.2.cx	$\chi_{3276}(1499, \cdot)$	n/a	1008	2
3276.2.da	$\chi_{3276}(179, \cdot)$	n/a	448	2
3276.2.dc	$\chi_{3276}(1361, \cdot)$	n/a	224	2
3276.2.dd	$\chi_{3276}(727, \cdot)$	n/a	1328	2
3276.2.df	$\chi_{3276}(199, \cdot)$	n/a	552	2
3276.2.dm	$\chi_{3276}(355, \cdot)$	n/a	1328	2
3276.2.dn	$\chi_{3276}(979, \cdot)$	n/a	1328	2
3276.2.dq	$\chi_{3276}(103, \cdot)$	n/a	1328	2
3276.2.ds	$\chi_{3276}(2287, \cdot)$	n/a	552	2
3276.2.dw	$\chi_{3276}(1115, \cdot)$	n/a	448	2
3276.2.dy	$\chi_{3276}(155, \cdot)$	n/a	1008	2
3276.2.dz	$\chi_{3276}(1517, \cdot)$	n/a	224	2
3276.2.ec	$\chi_{3276}(2057, \cdot)$	n/a	224	2
3276.2.ed	$\chi_{3276}(521, \cdot)$	3276.2.ed.a	64	2
3276.2.ef	$\chi_{3276}(1613, \cdot)$	n/a	192	2
3276.2.eh	$\chi_{3276}(935, \cdot)$	n/a	448	2
3276.2.ej	$\chi_{3276}(779, \cdot)$	n/a	1328	2
3276.2.em	$\chi_{3276}(407, \cdot)$	n/a	1008	2
3276.2.en	$\chi_{3276}(1031, \cdot)$	n/a	1328	2
3276.2.eq	$\chi_{3276}(209, \cdot)$	n/a	192	2
3276.2.es	$\chi_{3276}(269, \cdot)$	3276.2.es.a	76	2
3276.2.et	$\chi_{3276}(2383, \cdot)$	n/a	1328	2
3276.2.ex	$\chi_{3276}(2467, \cdot)$	n/a	552	2
3276.2.fa	$\chi_{3276}(3163, \cdot)$	n/a	1328	2
3276.2.fc	$\chi_{3276}(1615, \cdot)$	n/a	1328	2
3276.2.fe	$\chi_{3276}(361, \cdot)$	3276.2.fe.a	2	2
		3276.2.fe.b	2
		3276.2.fe.c	2
		3276.2.fe.d	2
		3276.2.fe.e	2
		3276.2.fe.f	4
		3276.2.fe.g	14
		3276.2.fe.h	16
		3276.2.fe.i	18
		3276.2.fe.j	32
3276.2.fh	$\chi_{3276}(589, \cdot)$	n/a	168	2
3276.2.fj	$\chi_{3276}(139, \cdot)$	n/a	1328	2
3276.2.fk	$\chi_{3276}(1459, \cdot)$	n/a	552	2
3276.2.fm	$\chi_{3276}(277, \cdot)$	n/a	224	2
3276.2.fp	$\chi_{3276}(911, \cdot)$	n/a	864	2
3276.2.fr	$\chi_{3276}(107, \cdot)$	n/a	448	2
3276.2.ft	$\chi_{3276}(2981, \cdot)$	n/a	224	2
3276.2.fu	$\chi_{3276}(2105, \cdot)$	3276.2.fu.a	72	2
3276.2.fw	$\chi_{3276}(857, \cdot)$	n/a	224	2
3276.2.fy	$\chi_{3276}(101, \cdot)$	n/a	224	2
3276.2.ga	$\chi_{3276}(263, \cdot)$	n/a	1328	2
3276.2.gc	$\chi_{3276}(1691, \cdot)$	n/a	384	2
3276.2.ge	$\chi_{3276}(1535, \cdot)$	n/a	1152	2
3276.2.gh	$\chi_{3276}(659, \cdot)$	n/a	1008	2
3276.2.gj	$\chi_{3276}(17, \cdot)$	3276.2.gj.a	4	2
		3276.2.gj.b	4
		3276.2.gj.c	68
3276.2.gl	$\chi_{3276}(545, \cdot)$	n/a	224	2
3276.2.gm	$\chi_{3276}(451, \cdot)$	n/a	552	2
3276.2.go	$\chi_{3276}(391, \cdot)$	n/a	1152	2
3276.2.gr	$\chi_{3276}(121, \cdot)$	n/a	224	2
3276.2.gt	$\chi_{3276}(25, \cdot)$	n/a	224	2
3276.2.gv	$\chi_{3276}(1117, \cdot)$	3276.2.gv.a	2	2
		3276.2.gv.b	2
		3276.2.gv.c	4
		3276.2.gv.d	8
		3276.2.gv.e	12
		3276.2.gv.f	12
		3276.2.gv.g	20
		3276.2.gv.h	32
3276.2.gw	$\chi_{3276}(1681, \cdot)$	n/a	168	2
3276.2.gy	$\chi_{3276}(1147, \cdot)$	n/a	1328	2
3276.2.hb	$\chi_{3276}(859, \cdot)$	n/a	1152	2
3276.2.hd	$\chi_{3276}(703, \cdot)$	n/a	480	2
3276.2.hf	$\chi_{3276}(367, \cdot)$	n/a	1328	2
3276.2.hg	$\chi_{3276}(337, \cdot)$	n/a	168	2
3276.2.hi	$\chi_{3276}(1297, \cdot)$	3276.2.hi.a	2	2
		3276.2.hi.b	2
		3276.2.hi.c	2
		3276.2.hi.d	2
		3276.2.hi.e	2
		3276.2.hi.f	4
		3276.2.hi.g	14
		3276.2.hi.h	16
		3276.2.hi.i	18
		3276.2.hi.j	32
3276.2.hl	$\chi_{3276}(2291, \cdot)$	n/a	1328	2
3276.2.hm	$\chi_{3276}(797, \cdot)$	n/a	224	2
3276.2.hp	$\chi_{3276}(2285, \cdot)$	3276.2.hp.a	4	2
		3276.2.hp.b	4
		3276.2.hp.c	68
3276.2.hr	$\chi_{3276}(2375, \cdot)$	n/a	448	2
3276.2.hs	$\chi_{3276}(1667, \cdot)$	n/a	1008	2
3276.2.hv	$\chi_{3276}(257, \cdot)$	n/a	224	2
3276.2.hx	$\chi_{3276}(677, \cdot)$	n/a	192	2
3276.2.hz	$\chi_{3276}(2963, \cdot)$	n/a	1328	2
3276.2.ib	$\chi_{3276}(439, \cdot)$	n/a	1328	2
3276.2.ie	$\chi_{3276}(283, \cdot)$	n/a	1328	2
3276.2.ig	$\chi_{3276}(1063, \cdot)$	n/a	552	2
3276.2.ij	$\chi_{3276}(95, \cdot)$	n/a	1328	2
3276.2.im	$\chi_{3276}(185, \cdot)$	n/a	224	2
3276.2.io	$\chi_{3276}(2141, \cdot)$	3276.2.io.a	4	2
		3276.2.io.b	4
		3276.2.io.c	64
3276.2.iq	$\chi_{3276}(1583, \cdot)$	n/a	336	2
3276.2.is	$\chi_{3276}(2363, \cdot)$	n/a	1328	2
3276.2.it	$\chi_{3276}(1433, \cdot)$	n/a	224	2
3276.2.iw	$\chi_{3276}(1039, \cdot)$	n/a	1328	2
3276.2.iz	$\chi_{3276}(1151, \cdot)$	n/a	896	4
3276.2.jb	$\chi_{3276}(319, \cdot)$	n/a	2656	4
3276.2.jc	$\chi_{3276}(463, \cdot)$	n/a	2016	4
3276.2.jd	$\chi_{3276}(1003, \cdot)$	n/a	2656	4
3276.2.jg	$\chi_{3276}(59, \cdot)$	n/a	2656	4
3276.2.jk	$\chi_{3276}(83, \cdot)$	n/a	2656	4
3276.2.jl	$\chi_{3276}(227, \cdot)$	n/a	2656	4
3276.2.jm	$\chi_{3276}(487, \cdot)$	n/a	1104	4
3276.2.jo	$\chi_{3276}(1165, \cdot)$	n/a	448	4
3276.2.jr	$\chi_{3276}(97, \cdot)$	n/a	448	4
3276.2.jt	$\chi_{3276}(1489, \cdot)$	n/a	448	4
3276.2.jw	$\chi_{3276}(977, \cdot)$	n/a	448	4
3276.2.jx	$\chi_{3276}(197, \cdot)$	n/a	112	4
3276.2.jy	$\chi_{3276}(1061, \cdot)$	n/a	144	4
3276.2.jz	$\chi_{3276}(617, \cdot)$	n/a	336	4
3276.2.kc	$\chi_{3276}(557, \cdot)$	n/a	152	4
3276.2.kd	$\chi_{3276}(905, \cdot)$	n/a	448	4
3276.2.kg	$\chi_{3276}(565, \cdot)$	n/a	448	4
3276.2.kh	$\chi_{3276}(1189, \cdot)$	n/a	184	4
3276.2.km	$\chi_{3276}(229, \cdot)$	n/a	448	4
3276.2.kn	$\chi_{3276}(397, \cdot)$	n/a	188	4
3276.2.kq	$\chi_{3276}(73, \cdot)$	n/a	184	4
3276.2.kr	$\chi_{3276}(349, \cdot)$	n/a	448	4
3276.2.kt	$\chi_{3276}(317, \cdot)$	n/a	448	4
3276.2.ku	$\chi_{3276}(149, \cdot)$	n/a	448	4
3276.2.kw	$\chi_{3276}(869, \cdot)$	n/a	336	4
3276.2.kz	$\chi_{3276}(47, \cdot)$	n/a	2656	4
3276.2.la	$\chi_{3276}(383, \cdot)$	n/a	2656	4
3276.2.lc	$\chi_{3276}(167, \cdot)$	n/a	2656	4
3276.2.le	$\chi_{3276}(379, \cdot)$	n/a	840	4
3276.2.lf	$\chi_{3276}(67, \cdot)$	n/a	2656	4
3276.2.lk	$\chi_{3276}(151, \cdot)$	n/a	2656	4
3276.2.ll	$\chi_{3276}(163, \cdot)$	n/a	1104	4
3276.2.lo	$\chi_{3276}(1051, \cdot)$	n/a	2016	4
3276.2.lp	$\chi_{3276}(1243, \cdot)$	n/a	1104	4
3276.2.ls	$\chi_{3276}(1007, \cdot)$	n/a	896	4
3276.2.lt	$\chi_{3276}(1307, \cdot)$	n/a	2656	4
3276.2.lu	$\chi_{3276}(587, \cdot)$	n/a	2656	4
3276.2.lv	$\chi_{3276}(395, \cdot)$	n/a	896	4
3276.2.ly	$\chi_{3276}(215, \cdot)$	n/a	896	4
3276.2.lz	$\chi_{3276}(983, \cdot)$	n/a	2656	4
3276.2.mc	$\chi_{3276}(1087, \cdot)$	n/a	2656	4
3276.2.mf	$\chi_{3276}(799, \cdot)$	n/a	2016	4
3276.2.mh	$\chi_{3276}(1159, \cdot)$	n/a	2656	4
3276.2.mi	$\chi_{3276}(145, \cdot)$	n/a	188	4
3276.2.mk	$\chi_{3276}(821, \cdot)$	n/a	448	4
3276.2.mo	$\chi_{3276}(137, \cdot)$	n/a	448	4
3276.2.mp	$\chi_{3276}(281, \cdot)$	n/a	336	4
3276.2.mr	$\chi_{3276}(409, \cdot)$	n/a	448	4
3276.2.ms	$\chi_{3276}(241, \cdot)$	n/a	448	4
3276.2.mt	$\chi_{3276}(265, \cdot)$	n/a	448	4
3276.2.mx	$\chi_{3276}(305, \cdot)$	n/a	152	4

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

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_1(3276))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_1(3276)) \cong$ $S_{2}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 36}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$^{\oplus 24}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$^{\oplus 24}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$^{\oplus 16}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$^{\oplus 18}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$^{\oplus 18}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(52))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(78))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(84))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(91))$$^{\oplus 9}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(117))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(126))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(156))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(182))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(234))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(252))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(273))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(364))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(468))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(546))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(819))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(1092))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(1638))$$^{\oplus 2}$