Space of modular forms of level 1872 and weight 2

• Label: 1872.2
• Level: 1872
• Weight: 2
• Dimension: 42134
• Nonzero newspaces: 70
• Sturm bound: 387072
• Trace bound: 77

Defining parameters

Level:	\( N \)	=	\( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 70 \)
Sturm bound:			\(387072\)
Trace bound:			\(77\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1872))\).

	Total	New	Old
Modular forms	99456	43024	56432
Cusp forms	94081	42134	51947
Eisenstein series	5375	890	4485

Trace form

42134 * q - 60 * q^2 - 60 * q^3 - 64 * q^4 - 80 * q^5 - 80 * q^6 - 56 * q^7 - 72 * q^8 - 28 * q^9 - 184 * q^10 - 72 * q^11 - 80 * q^12 - 91 * q^13 - 96 * q^14 - 66 * q^15 - 16 * q^16 - 118 * q^17 - 40 * q^18 - 142 * q^19 + 40 * q^20 - 74 * q^21 + 32 * q^22 - 4 * q^23 - 16 * q^24 + 32 * q^25 - 8 * q^26 - 96 * q^27 - 104 * q^28 - 16 * q^29 - 40 * q^30 - 20 * q^31 - 138 * q^33 - 40 * q^34 + 102 * q^35 - 72 * q^36 - 242 * q^37 - 152 * q^38 - 9 * q^39 - 248 * q^40 - 12 * q^41 - 160 * q^42 + 24 * q^43 - 232 * q^44 - 54 * q^45 - 304 * q^46 + 60 * q^47 - 184 * q^48 - 250 * q^49 - 228 * q^50 + 4 * q^51 - 128 * q^52 - 196 * q^53 - 168 * q^54 - 78 * q^55 - 264 * q^56 - 64 * q^57 - 136 * q^58 - 32 * q^59 - 296 * q^60 - 88 * q^61 - 264 * q^62 - 66 * q^63 - 40 * q^64 - 267 * q^65 - 416 * q^66 - 80 * q^67 - 232 * q^68 - 250 * q^69 + 16 * q^70 - 182 * q^71 - 304 * q^72 - 14 * q^73 - 176 * q^74 - 164 * q^75 + 8 * q^76 - 146 * q^77 - 196 * q^78 - 190 * q^79 - 328 * q^80 - 332 * q^81 - 200 * q^82 - 252 * q^83 - 368 * q^84 + 10 * q^85 - 256 * q^86 - 198 * q^87 - 88 * q^88 + 42 * q^89 - 368 * q^90 - 184 * q^91 - 184 * q^92 - 18 * q^93 - 64 * q^94 - 194 * q^95 - 216 * q^96 - 16 * q^97 - 28 * q^98 - 90 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1872))\)

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
1872.2.a	\(\chi_{1872}(1, \cdot)\)	1872.2.a.a	1	1
		1872.2.a.b	1
		1872.2.a.c	1
		1872.2.a.d	1
		1872.2.a.e	1
		1872.2.a.f	1
		1872.2.a.g	1
		1872.2.a.h	1
		1872.2.a.i	1
		1872.2.a.j	1
		1872.2.a.k	1
		1872.2.a.l	1
		1872.2.a.m	1
		1872.2.a.n	1
		1872.2.a.o	1
		1872.2.a.p	1
		1872.2.a.q	1
		1872.2.a.r	1
		1872.2.a.s	1
		1872.2.a.t	1
		1872.2.a.u	2
		1872.2.a.v	2
		1872.2.a.w	2
		1872.2.a.x	2
		1872.2.a.y	2
1872.2.c	\(\chi_{1872}(1585, \cdot)\)	1872.2.c.a	2	1
		1872.2.c.b	2
		1872.2.c.c	2
		1872.2.c.d	2
		1872.2.c.e	2
		1872.2.c.f	2
		1872.2.c.g	2
		1872.2.c.h	2
		1872.2.c.i	2
		1872.2.c.j	4
		1872.2.c.k	4
		1872.2.c.l	8
1872.2.d	\(\chi_{1872}(287, \cdot)\)	1872.2.d.a	4	1
		1872.2.d.b	4
		1872.2.d.c	8
		1872.2.d.d	8
1872.2.g	\(\chi_{1872}(937, \cdot)\)	None	0	1
1872.2.h	\(\chi_{1872}(935, \cdot)\)	None	0	1
1872.2.j	\(\chi_{1872}(1223, \cdot)\)	None	0	1
1872.2.m	\(\chi_{1872}(649, \cdot)\)	None	0	1
1872.2.n	\(\chi_{1872}(1871, \cdot)\)	1872.2.n.a	4	1
		1872.2.n.b	4
		1872.2.n.c	4
		1872.2.n.d	8
		1872.2.n.e	8
1872.2.q	\(\chi_{1872}(625, \cdot)\)	n/a	144	2
1872.2.r	\(\chi_{1872}(1537, \cdot)\)	n/a	164	2
1872.2.s	\(\chi_{1872}(529, \cdot)\)	n/a	164	2
1872.2.t	\(\chi_{1872}(289, \cdot)\)	1872.2.t.a	2	2
		1872.2.t.b	2
		1872.2.t.c	2
		1872.2.t.d	2
		1872.2.t.e	2
		1872.2.t.f	2
		1872.2.t.g	2
		1872.2.t.h	2
		1872.2.t.i	2
		1872.2.t.j	2
		1872.2.t.k	2
		1872.2.t.l	2
		1872.2.t.m	2
		1872.2.t.n	4
		1872.2.t.o	4
		1872.2.t.p	4
		1872.2.t.q	4
		1872.2.t.r	4
		1872.2.t.s	4
		1872.2.t.t	6
		1872.2.t.u	6
		1872.2.t.v	6
1872.2.u	\(\chi_{1872}(1243, \cdot)\)	n/a	276	2
1872.2.x	\(\chi_{1872}(125, \cdot)\)	n/a	224	2
1872.2.y	\(\chi_{1872}(467, \cdot)\)	n/a	224	2
1872.2.ba	\(\chi_{1872}(469, \cdot)\)	n/a	240	2
1872.2.be	\(\chi_{1872}(343, \cdot)\)	None	0	2
1872.2.bf	\(\chi_{1872}(1279, \cdot)\)	1872.2.bf.a	2	2
		1872.2.bf.b	2
		1872.2.bf.c	2
		1872.2.bf.d	2
		1872.2.bf.e	2
		1872.2.bf.f	4
		1872.2.bf.g	4
		1872.2.bf.h	4
		1872.2.bf.i	4
		1872.2.bf.j	4
		1872.2.bf.k	4
		1872.2.bf.l	8
		1872.2.bf.m	8
		1872.2.bf.n	8
		1872.2.bf.o	12
1872.2.bi	\(\chi_{1872}(161, \cdot)\)	1872.2.bi.a	4	2
		1872.2.bi.b	4
		1872.2.bi.c	12
		1872.2.bi.d	12
		1872.2.bi.e	12
		1872.2.bi.f	12
1872.2.bj	\(\chi_{1872}(1097, \cdot)\)	None	0	2
1872.2.bk	\(\chi_{1872}(755, \cdot)\)	n/a	192	2
1872.2.bm	\(\chi_{1872}(181, \cdot)\)	n/a	276	2
1872.2.bp	\(\chi_{1872}(1061, \cdot)\)	n/a	224	2
1872.2.bq	\(\chi_{1872}(307, \cdot)\)	n/a	276	2
1872.2.bt	\(\chi_{1872}(647, \cdot)\)	None	0	2
1872.2.bu	\(\chi_{1872}(217, \cdot)\)	None	0	2
1872.2.bx	\(\chi_{1872}(575, \cdot)\)	1872.2.bx.a	8	2
		1872.2.bx.b	8
		1872.2.bx.c	20
		1872.2.bx.d	20
1872.2.by	\(\chi_{1872}(433, \cdot)\)	1872.2.by.a	2	2
		1872.2.by.b	2
		1872.2.by.c	2
		1872.2.by.d	2
		1872.2.by.e	2
		1872.2.by.f	2
		1872.2.by.g	4
		1872.2.by.h	4
		1872.2.by.i	4
		1872.2.by.j	4
		1872.2.by.k	4
		1872.2.by.l	4
		1872.2.by.m	8
		1872.2.by.n	8
		1872.2.by.o	16
1872.2.ca	\(\chi_{1872}(745, \cdot)\)	None	0	2
1872.2.cd	\(\chi_{1872}(887, \cdot)\)	None	0	2
1872.2.cf	\(\chi_{1872}(95, \cdot)\)	n/a	168	2
1872.2.ch	\(\chi_{1872}(623, \cdot)\)	n/a	168	2
1872.2.cl	\(\chi_{1872}(263, \cdot)\)	None	0	2
1872.2.cn	\(\chi_{1872}(25, \cdot)\)	None	0	2
1872.2.co	\(\chi_{1872}(599, \cdot)\)	None	0	2
1872.2.cq	\(\chi_{1872}(121, \cdot)\)	None	0	2
1872.2.cu	\(\chi_{1872}(959, \cdot)\)	n/a	168	2
1872.2.cw	\(\chi_{1872}(191, \cdot)\)	n/a	168	2
1872.2.cx	\(\chi_{1872}(49, \cdot)\)	n/a	164	2
1872.2.cz	\(\chi_{1872}(601, \cdot)\)	None	0	2
1872.2.db	\(\chi_{1872}(311, \cdot)\)	None	0	2
1872.2.de	\(\chi_{1872}(313, \cdot)\)	None	0	2
1872.2.dg	\(\chi_{1872}(1031, \cdot)\)	None	0	2
1872.2.dh	\(\chi_{1872}(673, \cdot)\)	n/a	164	2
1872.2.dj	\(\chi_{1872}(911, \cdot)\)	n/a	144	2
1872.2.dm	\(\chi_{1872}(337, \cdot)\)	n/a	164	2
1872.2.do	\(\chi_{1872}(815, \cdot)\)	n/a	168	2
1872.2.dq	\(\chi_{1872}(23, \cdot)\)	None	0	2
1872.2.dr	\(\chi_{1872}(1465, \cdot)\)	None	0	2
1872.2.dv	\(\chi_{1872}(719, \cdot)\)	1872.2.dv.a	4	2
		1872.2.dv.b	4
		1872.2.dv.c	8
		1872.2.dv.d	20
		1872.2.dv.e	20
1872.2.dw	\(\chi_{1872}(361, \cdot)\)	None	0	2
1872.2.dz	\(\chi_{1872}(503, \cdot)\)	None	0	2
1872.2.ea	\(\chi_{1872}(197, \cdot)\)	n/a	448	4
1872.2.ed	\(\chi_{1872}(19, \cdot)\)	n/a	552	4
1872.2.ee	\(\chi_{1872}(245, \cdot)\)	n/a	1328	4
1872.2.eg	\(\chi_{1872}(187, \cdot)\)	n/a	1328	4
1872.2.ei	\(\chi_{1872}(331, \cdot)\)	n/a	1328	4
1872.2.el	\(\chi_{1872}(461, \cdot)\)	n/a	1328	4
1872.2.en	\(\chi_{1872}(317, \cdot)\)	n/a	1328	4
1872.2.ep	\(\chi_{1872}(115, \cdot)\)	n/a	1328	4
1872.2.eq	\(\chi_{1872}(61, \cdot)\)	n/a	1328	4
1872.2.es	\(\chi_{1872}(491, \cdot)\)	n/a	1328	4
1872.2.ev	\(\chi_{1872}(131, \cdot)\)	n/a	1152	4
1872.2.ey	\(\chi_{1872}(829, \cdot)\)	n/a	552	4
1872.2.ez	\(\chi_{1872}(205, \cdot)\)	n/a	1328	4
1872.2.fc	\(\chi_{1872}(35, \cdot)\)	n/a	448	4
1872.2.fd	\(\chi_{1872}(347, \cdot)\)	n/a	1328	4
1872.2.ff	\(\chi_{1872}(493, \cdot)\)	n/a	1328	4
1872.2.fg	\(\chi_{1872}(31, \cdot)\)	n/a	336	4
1872.2.fh	\(\chi_{1872}(151, \cdot)\)	None	0	4
1872.2.fm	\(\chi_{1872}(89, \cdot)\)	None	0	4
1872.2.fn	\(\chi_{1872}(305, \cdot)\)	n/a	112	4
1872.2.fo	\(\chi_{1872}(353, \cdot)\)	n/a	328	4
1872.2.fp	\(\chi_{1872}(617, \cdot)\)	None	0	4
1872.2.fu	\(\chi_{1872}(41, \cdot)\)	None	0	4
1872.2.fv	\(\chi_{1872}(401, \cdot)\)	n/a	328	4
1872.2.fy	\(\chi_{1872}(271, \cdot)\)	n/a	140	4
1872.2.fz	\(\chi_{1872}(487, \cdot)\)	None	0	4
1872.2.ga	\(\chi_{1872}(583, \cdot)\)	None	0	4
1872.2.gb	\(\chi_{1872}(175, \cdot)\)	n/a	336	4
1872.2.gg	\(\chi_{1872}(799, \cdot)\)	n/a	336	4
1872.2.gh	\(\chi_{1872}(7, \cdot)\)	None	0	4
1872.2.gi	\(\chi_{1872}(281, \cdot)\)	None	0	4
1872.2.gj	\(\chi_{1872}(785, \cdot)\)	n/a	328	4
1872.2.gn	\(\chi_{1872}(155, \cdot)\)	n/a	1328	4
1872.2.gq	\(\chi_{1872}(685, \cdot)\)	n/a	552	4
1872.2.gr	\(\chi_{1872}(133, \cdot)\)	n/a	1328	4
1872.2.gu	\(\chi_{1872}(179, \cdot)\)	n/a	448	4
1872.2.gv	\(\chi_{1872}(563, \cdot)\)	n/a	1328	4
1872.2.gx	\(\chi_{1872}(157, \cdot)\)	n/a	1152	4
1872.2.gy	\(\chi_{1872}(277, \cdot)\)	n/a	1328	4
1872.2.ha	\(\chi_{1872}(419, \cdot)\)	n/a	1328	4
1872.2.hd	\(\chi_{1872}(643, \cdot)\)	n/a	1328	4
1872.2.hf	\(\chi_{1872}(605, \cdot)\)	n/a	1328	4
1872.2.hh	\(\chi_{1872}(5, \cdot)\)	n/a	1328	4
1872.2.hi	\(\chi_{1872}(499, \cdot)\)	n/a	1328	4
1872.2.hk	\(\chi_{1872}(67, \cdot)\)	n/a	1328	4
1872.2.hm	\(\chi_{1872}(149, \cdot)\)	n/a	1328	4
1872.2.hp	\(\chi_{1872}(163, \cdot)\)	n/a	552	4
1872.2.hq	\(\chi_{1872}(917, \cdot)\)	n/a	448	4

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1872))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1872)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(234))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(312))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(468))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(624))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(936))\)\(^{\oplus 2}\)