Space of modular forms of level 1232 and weight 4

• Label: 1232.4
• Level: 1232
• Weight: 4
• Dimension: 72872
• Nonzero newspaces: 32
• Sturm bound: 368640
• Trace bound: 11

Defining parameters

Level:	\( N \)	=	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 32 \)
Sturm bound:			\(368640\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1232))\).

	Total	New	Old
Modular forms	139920	73684	66236
Cusp forms	136560	72872	63688
Eisenstein series	3360	812	2548

Trace form

72872 * q - 64 * q^2 - 34 * q^3 - 24 * q^4 - 86 * q^5 - 184 * q^6 - 105 * q^7 - 328 * q^8 - 58 * q^9 - 328 * q^10 + 73 * q^11 + 264 * q^12 + 16 * q^13 + 300 * q^14 - 642 * q^15 + 1064 * q^16 + 58 * q^17 + 640 * q^18 + 218 * q^19 - 840 * q^20 + 182 * q^21 - 1352 * q^22 - 130 * q^23 - 3448 * q^24 - 1506 * q^25 - 1112 * q^26 - 1216 * q^27 + 484 * q^28 - 806 * q^29 + 4888 * q^30 + 1350 * q^31 + 3816 * q^32 + 2943 * q^33 + 1608 * q^34 + 2905 * q^35 - 2536 * q^36 + 714 * q^37 - 4984 * q^38 - 1352 * q^39 - 5400 * q^40 - 3760 * q^41 - 6620 * q^42 - 7476 * q^43 - 2028 * q^44 - 9344 * q^45 + 272 * q^46 - 8402 * q^47 + 6776 * q^48 + 7385 * q^49 + 6952 * q^50 - 1582 * q^51 + 8288 * q^52 + 4034 * q^53 + 12248 * q^54 + 6418 * q^55 + 8088 * q^56 + 14994 * q^57 + 8208 * q^58 + 11518 * q^59 + 10936 * q^60 + 8170 * q^61 + 2432 * q^62 + 5532 * q^63 - 960 * q^64 - 4870 * q^65 - 7524 * q^66 + 6410 * q^67 - 15696 * q^68 - 2674 * q^69 - 21496 * q^70 - 3690 * q^71 - 38576 * q^72 - 17782 * q^73 - 20864 * q^74 - 21252 * q^75 - 19368 * q^76 - 5242 * q^77 - 4880 * q^78 - 18874 * q^79 + 2992 * q^80 + 4128 * q^81 + 19928 * q^82 - 13504 * q^83 + 21844 * q^84 + 17506 * q^85 + 42200 * q^86 + 5686 * q^87 + 58668 * q^88 + 11334 * q^89 + 64552 * q^90 - 2507 * q^91 + 30272 * q^92 + 7090 * q^93 + 36632 * q^94 + 7322 * q^95 + 19176 * q^96 + 1984 * q^97 + 6048 * q^98 + 3218 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1232))\)

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
1232.4.a	\(\chi_{1232}(1, \cdot)\)	1232.4.a.a	1	1
		1232.4.a.b	1
		1232.4.a.c	1
		1232.4.a.d	1
		1232.4.a.e	1
		1232.4.a.f	1
		1232.4.a.g	1
		1232.4.a.h	1
		1232.4.a.i	1
		1232.4.a.j	2
		1232.4.a.k	2
		1232.4.a.l	2
		1232.4.a.m	2
		1232.4.a.n	2
		1232.4.a.o	2
		1232.4.a.p	2
		1232.4.a.q	3
		1232.4.a.r	3
		1232.4.a.s	4
		1232.4.a.t	4
		1232.4.a.u	4
		1232.4.a.v	4
		1232.4.a.w	4
		1232.4.a.x	5
		1232.4.a.y	5
		1232.4.a.z	5
		1232.4.a.ba	6
		1232.4.a.bb	6
		1232.4.a.bc	7
		1232.4.a.bd	7
1232.4.c	\(\chi_{1232}(617, \cdot)\)	None	0	1
1232.4.e	\(\chi_{1232}(769, \cdot)\)	n/a	142	1
1232.4.f	\(\chi_{1232}(351, \cdot)\)	n/a	108	1
1232.4.h	\(\chi_{1232}(727, \cdot)\)	None	0	1
1232.4.j	\(\chi_{1232}(111, \cdot)\)	n/a	120	1
1232.4.l	\(\chi_{1232}(967, \cdot)\)	None	0	1
1232.4.o	\(\chi_{1232}(153, \cdot)\)	None	0	1
1232.4.q	\(\chi_{1232}(177, \cdot)\)	n/a	240	2
1232.4.r	\(\chi_{1232}(43, \cdot)\)	n/a	864	2
1232.4.s	\(\chi_{1232}(419, \cdot)\)	n/a	960	2
1232.4.x	\(\chi_{1232}(461, \cdot)\)	n/a	1144	2
1232.4.y	\(\chi_{1232}(309, \cdot)\)	n/a	720	2
1232.4.z	\(\chi_{1232}(113, \cdot)\)	n/a	432	4
1232.4.ba	\(\chi_{1232}(857, \cdot)\)	None	0	2
1232.4.be	\(\chi_{1232}(815, \cdot)\)	n/a	240	2
1232.4.bg	\(\chi_{1232}(263, \cdot)\)	None	0	2
1232.4.bi	\(\chi_{1232}(527, \cdot)\)	n/a	288	2
1232.4.bk	\(\chi_{1232}(199, \cdot)\)	None	0	2
1232.4.bl	\(\chi_{1232}(793, \cdot)\)	None	0	2
1232.4.bn	\(\chi_{1232}(241, \cdot)\)	n/a	284	2
1232.4.bq	\(\chi_{1232}(41, \cdot)\)	None	0	4
1232.4.bt	\(\chi_{1232}(183, \cdot)\)	None	0	4
1232.4.bv	\(\chi_{1232}(223, \cdot)\)	n/a	576	4
1232.4.bx	\(\chi_{1232}(279, \cdot)\)	None	0	4
1232.4.bz	\(\chi_{1232}(127, \cdot)\)	n/a	432	4
1232.4.ca	\(\chi_{1232}(321, \cdot)\)	n/a	568	4
1232.4.cc	\(\chi_{1232}(169, \cdot)\)	None	0	4
1232.4.cg	\(\chi_{1232}(243, \cdot)\)	n/a	1920	4
1232.4.ch	\(\chi_{1232}(219, \cdot)\)	n/a	2288	4
1232.4.ci	\(\chi_{1232}(221, \cdot)\)	n/a	1920	4
1232.4.cj	\(\chi_{1232}(285, \cdot)\)	n/a	2288	4
1232.4.cm	\(\chi_{1232}(81, \cdot)\)	n/a	1136	8
1232.4.cn	\(\chi_{1232}(141, \cdot)\)	n/a	3456	8
1232.4.co	\(\chi_{1232}(13, \cdot)\)	n/a	4576	8
1232.4.ct	\(\chi_{1232}(27, \cdot)\)	n/a	4576	8
1232.4.cu	\(\chi_{1232}(211, \cdot)\)	n/a	3456	8
1232.4.cw	\(\chi_{1232}(17, \cdot)\)	n/a	1136	8
1232.4.cy	\(\chi_{1232}(9, \cdot)\)	None	0	8
1232.4.cz	\(\chi_{1232}(103, \cdot)\)	None	0	8
1232.4.db	\(\chi_{1232}(79, \cdot)\)	n/a	1152	8
1232.4.dd	\(\chi_{1232}(39, \cdot)\)	None	0	8
1232.4.df	\(\chi_{1232}(31, \cdot)\)	n/a	1152	8
1232.4.dj	\(\chi_{1232}(73, \cdot)\)	None	0	8
1232.4.dm	\(\chi_{1232}(61, \cdot)\)	n/a	9152	16
1232.4.dn	\(\chi_{1232}(37, \cdot)\)	n/a	9152	16
1232.4.do	\(\chi_{1232}(51, \cdot)\)	n/a	9152	16
1232.4.dp	\(\chi_{1232}(3, \cdot)\)	n/a	9152	16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1232))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1232)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(308))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(616))\)\(^{\oplus 2}\)