Space of modular forms of level 1216 and weight 3

• Label: 1216.3
• Level: 1216
• Weight: 3
• Dimension: 51178
• Nonzero newspaces: 24
• Sturm bound: 276480
• Trace bound: 49

Defining parameters

Level:	\( N \)	=	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(276480\)
Trace bound:			\(49\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1216))\).

	Total	New	Old
Modular forms	93456	51926	41530
Cusp forms	90864	51178	39686
Eisenstein series	2592	748	1844

Trace form

51178 * q - 128 * q^2 - 96 * q^3 - 128 * q^4 - 128 * q^5 - 128 * q^6 - 100 * q^7 - 128 * q^8 - 178 * q^9 - 128 * q^10 - 128 * q^11 - 128 * q^12 - 160 * q^13 - 128 * q^14 - 92 * q^15 - 128 * q^16 - 192 * q^17 - 128 * q^18 - 70 * q^19 - 272 * q^20 + 40 * q^21 + 16 * q^22 + 28 * q^23 + 432 * q^24 + 82 * q^25 + 272 * q^26 + 36 * q^27 + 112 * q^28 - 64 * q^29 + 32 * q^30 - 76 * q^31 - 208 * q^32 - 260 * q^33 - 368 * q^34 - 292 * q^35 - 928 * q^36 - 480 * q^37 - 416 * q^38 - 592 * q^39 - 848 * q^40 - 672 * q^41 - 1008 * q^42 - 320 * q^43 - 336 * q^44 - 424 * q^45 - 128 * q^46 - 92 * q^47 - 128 * q^48 - 62 * q^49 - 752 * q^50 + 988 * q^51 - 1184 * q^52 + 160 * q^53 - 1280 * q^54 + 1436 * q^55 - 912 * q^56 + 68 * q^57 - 992 * q^58 + 832 * q^59 - 704 * q^60 + 96 * q^61 - 160 * q^62 - 108 * q^63 + 64 * q^64 - 540 * q^65 + 384 * q^66 - 1184 * q^67 + 352 * q^68 - 536 * q^69 + 1216 * q^70 - 1636 * q^71 + 1168 * q^72 - 672 * q^73 + 1104 * q^74 - 2104 * q^75 + 696 * q^76 + 24 * q^77 + 2128 * q^78 - 1116 * q^79 + 2608 * q^80 + 602 * q^81 + 1952 * q^82 + 544 * q^83 + 2336 * q^84 + 800 * q^85 + 1744 * q^86 + 796 * q^87 + 992 * q^88 + 928 * q^89 + 1312 * q^90 + 284 * q^91 + 784 * q^92 + 592 * q^93 + 64 * q^94 - 92 * q^95 - 544 * q^96 - 512 * q^97 - 944 * q^98 - 688 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1216))\)

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
1216.3.d	\(\chi_{1216}(191, \cdot)\)	1216.3.d.a	4	1
		1216.3.d.b	6
		1216.3.d.c	12
		1216.3.d.d	14
		1216.3.d.e	16
		1216.3.d.f	20
1216.3.e	\(\chi_{1216}(1025, \cdot)\)	1216.3.e.a	1	1
		1216.3.e.b	1
		1216.3.e.c	2
		1216.3.e.d	2
		1216.3.e.e	2
		1216.3.e.f	2
		1216.3.e.g	2
		1216.3.e.h	2
		1216.3.e.i	2
		1216.3.e.j	2
		1216.3.e.k	2
		1216.3.e.l	2
		1216.3.e.m	8
		1216.3.e.n	8
		1216.3.e.o	20
		1216.3.e.p	20
1216.3.f	\(\chi_{1216}(799, \cdot)\)	1216.3.f.a	24	1
		1216.3.f.b	48
1216.3.g	\(\chi_{1216}(417, \cdot)\)	1216.3.g.a	4	1
		1216.3.g.b	4
		1216.3.g.c	8
		1216.3.g.d	16
		1216.3.g.e	48
1216.3.j	\(\chi_{1216}(113, \cdot)\)	n/a	156	2
1216.3.l	\(\chi_{1216}(495, \cdot)\)	n/a	144	2
1216.3.o	\(\chi_{1216}(159, \cdot)\)	n/a	160	2
1216.3.p	\(\chi_{1216}(673, \cdot)\)	n/a	160	2
1216.3.q	\(\chi_{1216}(767, \cdot)\)	n/a	156	2
1216.3.r	\(\chi_{1216}(65, \cdot)\)	n/a	156	2
1216.3.w	\(\chi_{1216}(265, \cdot)\)	None	0	4
1216.3.x	\(\chi_{1216}(39, \cdot)\)	None	0	4
1216.3.ba	\(\chi_{1216}(145, \cdot)\)	n/a	312	4
1216.3.bc	\(\chi_{1216}(239, \cdot)\)	n/a	312	4
1216.3.bf	\(\chi_{1216}(115, \cdot)\)	n/a	2304	8
1216.3.bg	\(\chi_{1216}(37, \cdot)\)	n/a	2544	8
1216.3.bh	\(\chi_{1216}(129, \cdot)\)	n/a	468	6
1216.3.bi	\(\chi_{1216}(33, \cdot)\)	n/a	480	6
1216.3.bk	\(\chi_{1216}(351, \cdot)\)	n/a	480	6
1216.3.bn	\(\chi_{1216}(63, \cdot)\)	n/a	468	6
1216.3.bo	\(\chi_{1216}(7, \cdot)\)	None	0	8
1216.3.bp	\(\chi_{1216}(217, \cdot)\)	None	0	8
1216.3.bt	\(\chi_{1216}(47, \cdot)\)	n/a	936	12
1216.3.bv	\(\chi_{1216}(241, \cdot)\)	n/a	936	12
1216.3.by	\(\chi_{1216}(69, \cdot)\)	n/a	5088	16
1216.3.bz	\(\chi_{1216}(11, \cdot)\)	n/a	5088	16
1216.3.cc	\(\chi_{1216}(23, \cdot)\)	None	0	24
1216.3.cd	\(\chi_{1216}(41, \cdot)\)	None	0	24
1216.3.ce	\(\chi_{1216}(35, \cdot)\)	n/a	15264	48
1216.3.cf	\(\chi_{1216}(13, \cdot)\)	n/a	15264	48

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1216))\) into lower level spaces

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