Space of modular forms of level 1232 and weight 2

• Label: 1232.2
• Level: 1232
• Weight: 2
• Dimension: 24020
• Nonzero newspaces: 32
• Sturm bound: 184320
• Trace bound: 11

Defining parameters

Level:	\( N \)	=	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 32 \)
Sturm bound:			\(184320\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1232))\).

	Total	New	Old
Modular forms	47760	24832	22928
Cusp forms	44401	24020	20381
Eisenstein series	3359	812	2547

Trace form

24020 * q - 64 * q^2 - 50 * q^3 - 56 * q^4 - 78 * q^5 - 40 * q^6 - 57 * q^7 - 136 * q^8 - 14 * q^9 - 56 * q^10 - 47 * q^11 - 152 * q^12 - 72 * q^13 - 84 * q^14 - 98 * q^15 - 88 * q^16 - 142 * q^17 - 48 * q^18 - 6 * q^19 - 40 * q^20 - 58 * q^21 - 176 * q^22 - 66 * q^23 - 56 * q^24 + 34 * q^25 - 40 * q^26 - 32 * q^27 - 60 * q^28 - 142 * q^29 - 72 * q^30 - 58 * q^31 - 24 * q^32 - 97 * q^33 - 120 * q^34 + q^35 - 168 * q^36 + 18 * q^37 - 104 * q^38 + 72 * q^39 - 88 * q^40 + 72 * q^41 - 220 * q^42 - 36 * q^43 - 124 * q^44 - 120 * q^45 - 128 * q^46 + 46 * q^47 - 264 * q^48 - 187 * q^49 - 344 * q^50 + 34 * q^51 - 288 * q^52 - 166 * q^53 - 392 * q^54 - 30 * q^55 - 360 * q^56 - 190 * q^57 - 272 * q^58 - 114 * q^59 - 392 * q^60 - 238 * q^61 - 208 * q^62 - 124 * q^63 - 320 * q^64 - 166 * q^65 - 180 * q^66 - 166 * q^67 - 176 * q^68 - 130 * q^69 - 296 * q^70 - 74 * q^71 - 432 * q^72 - 126 * q^73 - 256 * q^74 - 20 * q^75 - 328 * q^76 - 138 * q^77 - 848 * q^78 - 58 * q^79 - 464 * q^80 - 212 * q^81 - 456 * q^82 - 48 * q^83 - 332 * q^84 - 398 * q^85 - 376 * q^86 - 122 * q^87 - 692 * q^88 - 98 * q^89 - 568 * q^90 - 235 * q^91 - 544 * q^92 - 254 * q^93 - 456 * q^94 - 262 * q^95 - 280 * q^96 - 328 * q^97 - 168 * q^98 - 350 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1232))\)

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
1232.2.a	\(\chi_{1232}(1, \cdot)\)	1232.2.a.a	1	1
		1232.2.a.b	1
		1232.2.a.c	1
		1232.2.a.d	1
		1232.2.a.e	1
		1232.2.a.f	1
		1232.2.a.g	1
		1232.2.a.h	1
		1232.2.a.i	1
		1232.2.a.j	1
		1232.2.a.k	1
		1232.2.a.l	1
		1232.2.a.m	2
		1232.2.a.n	2
		1232.2.a.o	2
		1232.2.a.p	2
		1232.2.a.q	3
		1232.2.a.r	3
		1232.2.a.s	4
1232.2.c	\(\chi_{1232}(617, \cdot)\)	None	0	1
1232.2.e	\(\chi_{1232}(769, \cdot)\)	1232.2.e.a	2	1
		1232.2.e.b	4
		1232.2.e.c	4
		1232.2.e.d	4
		1232.2.e.e	8
		1232.2.e.f	24
1232.2.f	\(\chi_{1232}(351, \cdot)\)	1232.2.f.a	6	1
		1232.2.f.b	6
		1232.2.f.c	12
		1232.2.f.d	12
1232.2.h	\(\chi_{1232}(727, \cdot)\)	None	0	1
1232.2.j	\(\chi_{1232}(111, \cdot)\)	1232.2.j.a	16	1
		1232.2.j.b	24
1232.2.l	\(\chi_{1232}(967, \cdot)\)	None	0	1
1232.2.o	\(\chi_{1232}(153, \cdot)\)	None	0	1
1232.2.q	\(\chi_{1232}(177, \cdot)\)	1232.2.q.a	2	2
		1232.2.q.b	2
		1232.2.q.c	2
		1232.2.q.d	2
		1232.2.q.e	2
		1232.2.q.f	4
		1232.2.q.g	4
		1232.2.q.h	4
		1232.2.q.i	6
		1232.2.q.j	6
		1232.2.q.k	6
		1232.2.q.l	6
		1232.2.q.m	6
		1232.2.q.n	8
		1232.2.q.o	10
		1232.2.q.p	10
1232.2.r	\(\chi_{1232}(43, \cdot)\)	n/a	288	2
1232.2.s	\(\chi_{1232}(419, \cdot)\)	n/a	320	2
1232.2.x	\(\chi_{1232}(461, \cdot)\)	n/a	376	2
1232.2.y	\(\chi_{1232}(309, \cdot)\)	n/a	240	2
1232.2.z	\(\chi_{1232}(113, \cdot)\)	n/a	144	4
1232.2.ba	\(\chi_{1232}(857, \cdot)\)	None	0	2
1232.2.be	\(\chi_{1232}(815, \cdot)\)	1232.2.be.a	24	2
		1232.2.be.b	28
		1232.2.be.c	28
1232.2.bg	\(\chi_{1232}(263, \cdot)\)	None	0	2
1232.2.bi	\(\chi_{1232}(527, \cdot)\)	1232.2.bi.a	32	2
		1232.2.bi.b	32
		1232.2.bi.c	32
1232.2.bk	\(\chi_{1232}(199, \cdot)\)	None	0	2
1232.2.bl	\(\chi_{1232}(793, \cdot)\)	None	0	2
1232.2.bn	\(\chi_{1232}(241, \cdot)\)	1232.2.bn.a	12	2
		1232.2.bn.b	16
		1232.2.bn.c	16
		1232.2.bn.d	48
1232.2.bq	\(\chi_{1232}(41, \cdot)\)	None	0	4
1232.2.bt	\(\chi_{1232}(183, \cdot)\)	None	0	4
1232.2.bv	\(\chi_{1232}(223, \cdot)\)	n/a	192	4
1232.2.bx	\(\chi_{1232}(279, \cdot)\)	None	0	4
1232.2.bz	\(\chi_{1232}(127, \cdot)\)	n/a	144	4
1232.2.ca	\(\chi_{1232}(321, \cdot)\)	n/a	184	4
1232.2.cc	\(\chi_{1232}(169, \cdot)\)	None	0	4
1232.2.cg	\(\chi_{1232}(243, \cdot)\)	n/a	640	4
1232.2.ch	\(\chi_{1232}(219, \cdot)\)	n/a	752	4
1232.2.ci	\(\chi_{1232}(221, \cdot)\)	n/a	640	4
1232.2.cj	\(\chi_{1232}(285, \cdot)\)	n/a	752	4
1232.2.cm	\(\chi_{1232}(81, \cdot)\)	n/a	368	8
1232.2.cn	\(\chi_{1232}(141, \cdot)\)	n/a	1152	8
1232.2.co	\(\chi_{1232}(13, \cdot)\)	n/a	1504	8
1232.2.ct	\(\chi_{1232}(27, \cdot)\)	n/a	1504	8
1232.2.cu	\(\chi_{1232}(211, \cdot)\)	n/a	1152	8
1232.2.cw	\(\chi_{1232}(17, \cdot)\)	n/a	368	8
1232.2.cy	\(\chi_{1232}(9, \cdot)\)	None	0	8
1232.2.cz	\(\chi_{1232}(103, \cdot)\)	None	0	8
1232.2.db	\(\chi_{1232}(79, \cdot)\)	n/a	384	8
1232.2.dd	\(\chi_{1232}(39, \cdot)\)	None	0	8
1232.2.df	\(\chi_{1232}(31, \cdot)\)	n/a	384	8
1232.2.dj	\(\chi_{1232}(73, \cdot)\)	None	0	8
1232.2.dm	\(\chi_{1232}(61, \cdot)\)	n/a	3008	16
1232.2.dn	\(\chi_{1232}(37, \cdot)\)	n/a	3008	16
1232.2.do	\(\chi_{1232}(51, \cdot)\)	n/a	3008	16
1232.2.dp	\(\chi_{1232}(3, \cdot)\)	n/a	3008	16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1232))\) into lower level spaces

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