Space of modular forms of level 1216 and weight 4

• Label: 1216.4
• Level: 1216
• Weight: 4
• Dimension: 76954
• Nonzero newspaces: 24
• Sturm bound: 368640
• Trace bound: 49

Defining parameters

Level:	\( N \)	=	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(368640\)
Trace bound:			\(49\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1216))\).

	Total	New	Old
Modular forms	139536	77702	61834
Cusp forms	136944	76954	59990
Eisenstein series	2592	748	1844

Trace form

76954 * q - 128 * q^2 - 96 * q^3 - 128 * q^4 - 128 * q^5 - 128 * q^6 - 92 * q^7 - 128 * q^8 - 106 * q^9 - 128 * q^10 - 56 * q^11 - 128 * q^12 - 272 * q^13 - 128 * q^14 - 340 * q^15 - 128 * q^16 - 432 * q^17 - 128 * q^18 - 126 * q^19 - 272 * q^20 - 104 * q^21 - 1072 * q^22 - 92 * q^23 - 2128 * q^24 - 262 * q^25 - 48 * q^26 + 276 * q^27 + 1392 * q^28 + 672 * q^29 + 4512 * q^30 + 628 * q^31 + 2352 * q^32 + 1868 * q^33 + 1872 * q^34 + 860 * q^35 + 1632 * q^36 + 912 * q^37 - 576 * q^38 - 200 * q^39 - 3408 * q^40 - 2208 * q^41 - 6448 * q^42 - 1768 * q^43 - 2128 * q^44 - 3096 * q^45 - 128 * q^46 - 1980 * q^47 - 128 * q^48 - 2350 * q^49 + 5584 * q^50 - 9044 * q^51 + 6496 * q^52 - 944 * q^53 + 3328 * q^54 - 1244 * q^55 - 912 * q^56 + 908 * q^57 - 5024 * q^58 + 8824 * q^59 - 9920 * q^60 + 2032 * q^61 - 6112 * q^62 + 15260 * q^63 - 12224 * q^64 + 4196 * q^65 - 11200 * q^66 + 11952 * q^67 - 4256 * q^68 + 1144 * q^69 - 4160 * q^70 + 804 * q^71 + 1168 * q^72 - 2208 * q^73 + 5136 * q^74 - 14832 * q^75 + 5816 * q^76 - 6520 * q^77 + 3856 * q^78 - 20252 * q^79 - 8656 * q^80 - 13862 * q^81 - 14048 * q^82 - 5216 * q^83 - 8416 * q^84 - 3440 * q^85 + 912 * q^86 - 92 * q^87 + 6112 * q^88 + 6976 * q^89 + 18592 * q^90 + 6572 * q^91 + 25104 * q^92 + 16624 * q^93 + 17728 * q^94 + 6792 * q^95 + 25568 * q^96 + 18608 * q^97 + 24080 * q^98 + 9392 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1216))\)

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
1216.4.a	\(\chi_{1216}(1, \cdot)\)	1216.4.a.a	1	1
		1216.4.a.b	1
		1216.4.a.c	1
		1216.4.a.d	1
		1216.4.a.e	1
		1216.4.a.f	1
		1216.4.a.g	2
		1216.4.a.h	2
		1216.4.a.i	2
		1216.4.a.j	2
		1216.4.a.k	2
		1216.4.a.l	2
		1216.4.a.m	2
		1216.4.a.n	2
		1216.4.a.o	2
		1216.4.a.p	2
		1216.4.a.q	3
		1216.4.a.r	3
		1216.4.a.s	3
		1216.4.a.t	3
		1216.4.a.u	3
		1216.4.a.v	3
		1216.4.a.w	3
		1216.4.a.x	3
		1216.4.a.y	5
		1216.4.a.z	5
		1216.4.a.ba	5
		1216.4.a.bb	5
		1216.4.a.bc	5
		1216.4.a.bd	5
		1216.4.a.be	7
		1216.4.a.bf	7
		1216.4.a.bg	7
		1216.4.a.bh	7
1216.4.b	\(\chi_{1216}(607, \cdot)\)	n/a	120	1
1216.4.c	\(\chi_{1216}(609, \cdot)\)	n/a	108	1
1216.4.h	\(\chi_{1216}(1215, \cdot)\)	n/a	118	1
1216.4.i	\(\chi_{1216}(577, \cdot)\)	n/a	236	2
1216.4.k	\(\chi_{1216}(305, \cdot)\)	n/a	216	2
1216.4.m	\(\chi_{1216}(303, \cdot)\)	n/a	236	2
1216.4.n	\(\chi_{1216}(255, \cdot)\)	n/a	236	2
1216.4.s	\(\chi_{1216}(31, \cdot)\)	n/a	240	2
1216.4.t	\(\chi_{1216}(353, \cdot)\)	n/a	240	2
1216.4.u	\(\chi_{1216}(151, \cdot)\)	None	0	4
1216.4.v	\(\chi_{1216}(153, \cdot)\)	None	0	4
1216.4.y	\(\chi_{1216}(321, \cdot)\)	n/a	708	6
1216.4.z	\(\chi_{1216}(49, \cdot)\)	n/a	472	4
1216.4.bb	\(\chi_{1216}(335, \cdot)\)	n/a	472	4
1216.4.bd	\(\chi_{1216}(77, \cdot)\)	n/a	3456	8
1216.4.be	\(\chi_{1216}(75, \cdot)\)	n/a	3824	8
1216.4.bj	\(\chi_{1216}(161, \cdot)\)	n/a	720	6
1216.4.bl	\(\chi_{1216}(223, \cdot)\)	n/a	720	6
1216.4.bm	\(\chi_{1216}(127, \cdot)\)	n/a	708	6
1216.4.bq	\(\chi_{1216}(121, \cdot)\)	None	0	8
1216.4.br	\(\chi_{1216}(103, \cdot)\)	None	0	8
1216.4.bs	\(\chi_{1216}(15, \cdot)\)	n/a	1416	12
1216.4.bu	\(\chi_{1216}(17, \cdot)\)	n/a	1416	12
1216.4.bw	\(\chi_{1216}(27, \cdot)\)	n/a	7648	16
1216.4.bx	\(\chi_{1216}(45, \cdot)\)	n/a	7648	16
1216.4.ca	\(\chi_{1216}(9, \cdot)\)	None	0	24
1216.4.cb	\(\chi_{1216}(71, \cdot)\)	None	0	24
1216.4.cg	\(\chi_{1216}(5, \cdot)\)	n/a	22944	48
1216.4.ch	\(\chi_{1216}(3, \cdot)\)	n/a	22944	48

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1216))\) into lower level spaces

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