Space of modular forms of level 1176 and weight 3

• Label: 1176.3
• Level: 1176
• Weight: 3
• Dimension: 30276
• Nonzero newspaces: 24
• Sturm bound: 225792
• Trace bound: 8

Defining parameters

Level:	\( N \)	=	\( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(225792\)
Trace bound:			\(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1176))\).

	Total	New	Old
Modular forms	76704	30664	46040
Cusp forms	73824	30276	43548
Eisenstein series	2880	388	2492

Trace form

30276 * q + 2 * q^2 - 28 * q^3 - 72 * q^4 - 44 * q^6 - 72 * q^7 - 4 * q^8 - 16 * q^9 - 72 * q^10 + 16 * q^11 - 14 * q^12 + 20 * q^13 - 90 * q^15 - 28 * q^16 - 104 * q^17 + 32 * q^18 - 360 * q^19 - 432 * q^20 - 84 * q^21 - 660 * q^22 - 288 * q^23 - 298 * q^24 - 336 * q^25 - 216 * q^26 - 88 * q^27 + 24 * q^28 + 86 * q^30 + 340 * q^31 + 512 * q^32 - 16 * q^33 + 880 * q^34 + 288 * q^35 + 270 * q^36 + 228 * q^37 + 832 * q^38 + 66 * q^39 + 788 * q^40 + 40 * q^41 + 180 * q^42 - 488 * q^43 + 1120 * q^44 - 104 * q^45 + 1172 * q^46 - 1152 * q^47 + 738 * q^48 - 360 * q^49 + 722 * q^50 - 374 * q^51 + 428 * q^52 - 144 * q^53 - 16 * q^54 + 4 * q^55 - 84 * q^56 + 336 * q^57 - 464 * q^58 + 1120 * q^59 - 714 * q^60 + 836 * q^61 - 1308 * q^62 + 480 * q^63 - 1380 * q^64 + 1104 * q^65 - 702 * q^66 + 1608 * q^67 - 1448 * q^68 + 944 * q^69 - 792 * q^70 + 672 * q^71 + 530 * q^72 - 64 * q^73 - 120 * q^74 + 1024 * q^75 - 132 * q^76 - 288 * q^77 + 626 * q^78 - 620 * q^79 - 96 * q^80 - 840 * q^81 - 408 * q^82 - 2192 * q^83 - 144 * q^84 - 1376 * q^85 + 88 * q^86 - 1278 * q^87 - 108 * q^88 - 1160 * q^89 - 1582 * q^90 - 348 * q^91 + 552 * q^92 - 1700 * q^93 + 2220 * q^94 + 1824 * q^95 - 454 * q^96 - 3184 * q^97 + 1092 * q^98 - 560 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1176))\)

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
1176.3.d	\(\chi_{1176}(785, \cdot)\)	1176.3.d.a	2	1
		1176.3.d.b	2
		1176.3.d.c	2
		1176.3.d.d	8
		1176.3.d.e	12
		1176.3.d.f	16
		1176.3.d.g	16
		1176.3.d.h	24
1176.3.e	\(\chi_{1176}(587, \cdot)\)	n/a	312	1
1176.3.f	\(\chi_{1176}(97, \cdot)\)	1176.3.f.a	8	1
		1176.3.f.b	8
		1176.3.f.c	8
		1176.3.f.d	16
1176.3.g	\(\chi_{1176}(883, \cdot)\)	n/a	164	1
1176.3.l	\(\chi_{1176}(685, \cdot)\)	n/a	160	1
1176.3.m	\(\chi_{1176}(295, \cdot)\)	None	0	1
1176.3.n	\(\chi_{1176}(197, \cdot)\)	n/a	318	1
1176.3.o	\(\chi_{1176}(1175, \cdot)\)	None	0	1
1176.3.r	\(\chi_{1176}(215, \cdot)\)	None	0	2
1176.3.s	\(\chi_{1176}(557, \cdot)\)	n/a	624	2
1176.3.w	\(\chi_{1176}(79, \cdot)\)	None	0	2
1176.3.x	\(\chi_{1176}(325, \cdot)\)	n/a	320	2
1176.3.y	\(\chi_{1176}(67, \cdot)\)	n/a	320	2
1176.3.z	\(\chi_{1176}(313, \cdot)\)	1176.3.z.a	8	2
		1176.3.z.b	8
		1176.3.z.c	8
		1176.3.z.d	8
		1176.3.z.e	8
		1176.3.z.f	8
		1176.3.z.g	16
		1176.3.z.h	16
1176.3.be	\(\chi_{1176}(227, \cdot)\)	n/a	624	2
1176.3.bf	\(\chi_{1176}(569, \cdot)\)	n/a	160	2
1176.3.bi	\(\chi_{1176}(167, \cdot)\)	None	0	6
1176.3.bj	\(\chi_{1176}(29, \cdot)\)	n/a	2664	6
1176.3.bk	\(\chi_{1176}(127, \cdot)\)	None	0	6
1176.3.bl	\(\chi_{1176}(13, \cdot)\)	n/a	1344	6
1176.3.bq	\(\chi_{1176}(43, \cdot)\)	n/a	1344	6
1176.3.br	\(\chi_{1176}(265, \cdot)\)	n/a	336	6
1176.3.bs	\(\chi_{1176}(83, \cdot)\)	n/a	2664	6
1176.3.bt	\(\chi_{1176}(113, \cdot)\)	n/a	672	6
1176.3.bx	\(\chi_{1176}(65, \cdot)\)	n/a	1344	12
1176.3.by	\(\chi_{1176}(59, \cdot)\)	n/a	5328	12
1176.3.cd	\(\chi_{1176}(73, \cdot)\)	n/a	672	12
1176.3.ce	\(\chi_{1176}(163, \cdot)\)	n/a	2688	12
1176.3.cf	\(\chi_{1176}(61, \cdot)\)	n/a	2688	12
1176.3.cg	\(\chi_{1176}(151, \cdot)\)	None	0	12
1176.3.ck	\(\chi_{1176}(53, \cdot)\)	n/a	5328	12
1176.3.cl	\(\chi_{1176}(47, \cdot)\)	None	0	12

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1176))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(1176)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(588))\)\(^{\oplus 2}\)