Space of modular forms of level 1216 and weight 2

• Label: 1216.2
• Level: 1216
• Weight: 2
• Dimension: 25402
• Nonzero newspaces: 24
• Sturm bound: 184320
• Trace bound: 49

Defining parameters

Level:	\( N \)	=	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(184320\)
Trace bound:			\(49\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1216))\).

	Total	New	Old
Modular forms	47376	26150	21226
Cusp forms	44785	25402	19383
Eisenstein series	2591	748	1843

Trace form

25402 * q - 128 * q^2 - 96 * q^3 - 128 * q^4 - 128 * q^5 - 128 * q^6 - 92 * q^7 - 128 * q^8 - 154 * q^9 - 128 * q^10 - 88 * q^11 - 128 * q^12 - 112 * q^13 - 128 * q^14 - 84 * q^15 - 128 * q^16 - 208 * q^17 - 128 * q^18 - 94 * q^19 - 272 * q^20 - 136 * q^21 - 144 * q^22 - 92 * q^23 - 208 * q^24 - 182 * q^25 - 208 * q^26 - 108 * q^27 - 208 * q^28 - 160 * q^29 - 288 * q^30 - 140 * q^31 - 208 * q^32 - 148 * q^33 - 208 * q^34 - 100 * q^35 - 288 * q^36 - 144 * q^37 - 176 * q^38 - 200 * q^39 - 208 * q^40 - 160 * q^41 - 208 * q^42 - 72 * q^43 - 144 * q^44 - 120 * q^45 - 128 * q^46 - 60 * q^47 - 128 * q^48 - 206 * q^49 - 80 * q^50 - 148 * q^51 - 32 * q^52 - 80 * q^53 - 220 * q^55 - 16 * q^56 - 164 * q^57 - 128 * q^58 - 232 * q^59 + 64 * q^60 - 112 * q^61 - 64 * q^62 - 228 * q^63 + 64 * q^64 - 348 * q^65 + 32 * q^66 - 272 * q^67 - 32 * q^68 - 104 * q^69 + 64 * q^70 - 220 * q^71 + 16 * q^72 - 160 * q^73 - 16 * q^74 - 208 * q^75 - 72 * q^76 - 280 * q^77 - 80 * q^78 - 156 * q^79 - 208 * q^80 - 230 * q^81 - 288 * q^82 - 96 * q^83 - 352 * q^84 - 144 * q^85 - 336 * q^86 - 92 * q^87 - 288 * q^88 - 256 * q^89 - 416 * q^90 - 84 * q^91 - 432 * q^92 - 208 * q^93 - 320 * q^94 - 120 * q^95 - 544 * q^96 - 176 * q^97 - 400 * q^98 - 144 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1216))\)

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
1216.2.a	\(\chi_{1216}(1, \cdot)\)	1216.2.a.a	1	1
		1216.2.a.b	1
		1216.2.a.c	1
		1216.2.a.d	1
		1216.2.a.e	1
		1216.2.a.f	1
		1216.2.a.g	1
		1216.2.a.h	1
		1216.2.a.i	1
		1216.2.a.j	1
		1216.2.a.k	1
		1216.2.a.l	1
		1216.2.a.m	1
		1216.2.a.n	1
		1216.2.a.o	1
		1216.2.a.p	1
		1216.2.a.q	1
		1216.2.a.r	1
		1216.2.a.s	2
		1216.2.a.t	2
		1216.2.a.u	3
		1216.2.a.v	3
		1216.2.a.w	4
		1216.2.a.x	4
1216.2.b	\(\chi_{1216}(607, \cdot)\)	1216.2.b.a	4	1
		1216.2.b.b	4
		1216.2.b.c	4
		1216.2.b.d	8
		1216.2.b.e	8
		1216.2.b.f	12
1216.2.c	\(\chi_{1216}(609, \cdot)\)	1216.2.c.a	2	1
		1216.2.c.b	2
		1216.2.c.c	2
		1216.2.c.d	2
		1216.2.c.e	4
		1216.2.c.f	4
		1216.2.c.g	4
		1216.2.c.h	8
		1216.2.c.i	8
1216.2.h	\(\chi_{1216}(1215, \cdot)\)	1216.2.h.a	2	1
		1216.2.h.b	4
		1216.2.h.c	4
		1216.2.h.d	8
		1216.2.h.e	20
1216.2.i	\(\chi_{1216}(577, \cdot)\)	1216.2.i.a	2	2
		1216.2.i.b	2
		1216.2.i.c	2
		1216.2.i.d	2
		1216.2.i.e	2
		1216.2.i.f	2
		1216.2.i.g	2
		1216.2.i.h	2
		1216.2.i.i	2
		1216.2.i.j	2
		1216.2.i.k	4
		1216.2.i.l	4
		1216.2.i.m	6
		1216.2.i.n	6
		1216.2.i.o	8
		1216.2.i.p	8
		1216.2.i.q	8
		1216.2.i.r	12
1216.2.k	\(\chi_{1216}(305, \cdot)\)	1216.2.k.a	4	2
		1216.2.k.b	68
1216.2.m	\(\chi_{1216}(303, \cdot)\)	1216.2.m.a	76	2
1216.2.n	\(\chi_{1216}(255, \cdot)\)	1216.2.n.a	2	2
		1216.2.n.b	2
		1216.2.n.c	4
		1216.2.n.d	6
		1216.2.n.e	6
		1216.2.n.f	16
		1216.2.n.g	40
1216.2.s	\(\chi_{1216}(31, \cdot)\)	1216.2.s.a	4	2
		1216.2.s.b	4
		1216.2.s.c	4
		1216.2.s.d	4
		1216.2.s.e	4
		1216.2.s.f	4
		1216.2.s.g	12
		1216.2.s.h	12
		1216.2.s.i	32
1216.2.t	\(\chi_{1216}(353, \cdot)\)	1216.2.t.a	8	2
		1216.2.t.b	8
		1216.2.t.c	16
		1216.2.t.d	24
		1216.2.t.e	24
1216.2.u	\(\chi_{1216}(151, \cdot)\)	None	0	4
1216.2.v	\(\chi_{1216}(153, \cdot)\)	None	0	4
1216.2.y	\(\chi_{1216}(321, \cdot)\)	n/a	228	6
1216.2.z	\(\chi_{1216}(49, \cdot)\)	n/a	152	4
1216.2.bb	\(\chi_{1216}(335, \cdot)\)	n/a	152	4
1216.2.bd	\(\chi_{1216}(77, \cdot)\)	n/a	1152	8
1216.2.be	\(\chi_{1216}(75, \cdot)\)	n/a	1264	8
1216.2.bj	\(\chi_{1216}(161, \cdot)\)	n/a	240	6
1216.2.bl	\(\chi_{1216}(223, \cdot)\)	n/a	240	6
1216.2.bm	\(\chi_{1216}(127, \cdot)\)	n/a	228	6
1216.2.bq	\(\chi_{1216}(121, \cdot)\)	None	0	8
1216.2.br	\(\chi_{1216}(103, \cdot)\)	None	0	8
1216.2.bs	\(\chi_{1216}(15, \cdot)\)	n/a	456	12
1216.2.bu	\(\chi_{1216}(17, \cdot)\)	n/a	456	12
1216.2.bw	\(\chi_{1216}(27, \cdot)\)	n/a	2528	16
1216.2.bx	\(\chi_{1216}(45, \cdot)\)	n/a	2528	16
1216.2.ca	\(\chi_{1216}(9, \cdot)\)	None	0	24
1216.2.cb	\(\chi_{1216}(71, \cdot)\)	None	0	24
1216.2.cg	\(\chi_{1216}(5, \cdot)\)	n/a	7584	48
1216.2.ch	\(\chi_{1216}(3, \cdot)\)	n/a	7584	48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1216))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1216)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(304))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(608))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1216))\)\(^{\oplus 1}\)