Space of modular forms of level 912 and weight 3

• Label: 912.3
• Level: 912
• Weight: 3
• Dimension: 19180
• Nonzero newspaces: 24
• Sturm bound: 138240
• Trace bound: 13

Defining parameters

Level:	\( N \)	=	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(138240\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(912))\).

	Total	New	Old
Modular forms	47088	19484	27604
Cusp forms	45072	19180	25892
Eisenstein series	2016	304	1712

Trace form

19180 * q - 25 * q^3 - 88 * q^4 - 24 * q^5 - 44 * q^6 - 74 * q^7 + 24 * q^8 + 13 * q^9 + 88 * q^10 - 64 * q^11 + 76 * q^12 - 22 * q^13 + 88 * q^14 + 45 * q^15 - 104 * q^16 + 24 * q^17 + 60 * q^18 + 44 * q^19 - 160 * q^20 + 7 * q^21 - 216 * q^22 + 256 * q^23 + 4 * q^24 - 84 * q^25 + 200 * q^26 - 73 * q^27 - 72 * q^28 - 184 * q^29 - 348 * q^30 - 218 * q^31 - 320 * q^32 - 281 * q^33 - 536 * q^34 - 192 * q^35 - 452 * q^36 - 40 * q^37 - 168 * q^38 + 118 * q^39 - 344 * q^40 + 216 * q^41 - 476 * q^42 + 46 * q^43 - 176 * q^44 + 3 * q^45 + 56 * q^46 + 28 * q^48 - 176 * q^49 + 472 * q^50 - 283 * q^51 + 664 * q^52 + 392 * q^53 + 292 * q^54 + 330 * q^55 + 448 * q^56 + 41 * q^57 + 704 * q^58 + 256 * q^59 + 1260 * q^60 - 486 * q^61 + 552 * q^62 - 423 * q^63 + 1208 * q^64 - 1040 * q^65 + 964 * q^66 - 2418 * q^67 + 896 * q^68 - 501 * q^69 + 72 * q^70 - 1456 * q^71 + 468 * q^72 - 1014 * q^73 - 696 * q^74 - 936 * q^75 - 920 * q^76 - 592 * q^77 - 1300 * q^78 + 214 * q^79 - 1104 * q^80 - 51 * q^81 - 1464 * q^82 + 1184 * q^83 - 1940 * q^84 + 790 * q^85 - 1056 * q^86 + 1461 * q^87 - 1736 * q^88 + 1560 * q^89 - 2004 * q^90 + 2306 * q^91 - 992 * q^92 + 695 * q^93 - 24 * q^94 - 88 * q^96 + 90 * q^97 + 880 * q^98 + 493 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(912))\)

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
912.3.b	\(\chi_{912}(911, \cdot)\)	912.3.b.a	2	1
		912.3.b.b	2
		912.3.b.c	2
		912.3.b.d	2
		912.3.b.e	4
		912.3.b.f	4
		912.3.b.g	16
		912.3.b.h	48
912.3.c	\(\chi_{912}(343, \cdot)\)	None	0	1
912.3.h	\(\chi_{912}(305, \cdot)\)	912.3.h.a	12	1
		912.3.h.b	12
		912.3.h.c	12
		912.3.h.d	36
912.3.i	\(\chi_{912}(265, \cdot)\)	None	0	1
912.3.l	\(\chi_{912}(455, \cdot)\)	None	0	1
912.3.m	\(\chi_{912}(799, \cdot)\)	912.3.m.a	12	1
		912.3.m.b	12
		912.3.m.c	12
912.3.n	\(\chi_{912}(761, \cdot)\)	None	0	1
912.3.o	\(\chi_{912}(721, \cdot)\)	912.3.o.a	2	1
		912.3.o.b	4
		912.3.o.c	6
		912.3.o.d	8
		912.3.o.e	20
912.3.s	\(\chi_{912}(77, \cdot)\)	n/a	576	2
912.3.t	\(\chi_{912}(37, \cdot)\)	n/a	320	2
912.3.w	\(\chi_{912}(227, \cdot)\)	n/a	632	2
912.3.x	\(\chi_{912}(115, \cdot)\)	n/a	288	2
912.3.z	\(\chi_{912}(463, \cdot)\)	912.3.z.a	12	2
		912.3.z.b	12
		912.3.z.c	12
		912.3.z.d	12
		912.3.z.e	16
		912.3.z.f	16
912.3.ba	\(\chi_{912}(407, \cdot)\)	None	0	2
912.3.be	\(\chi_{912}(145, \cdot)\)	912.3.be.a	2	2
		912.3.be.b	2
		912.3.be.c	2
		912.3.be.d	6
		912.3.be.e	6
		912.3.be.f	6
		912.3.be.g	8
		912.3.be.h	8
		912.3.be.i	20
		912.3.be.j	20
912.3.bf	\(\chi_{912}(425, \cdot)\)	None	0	2
912.3.bi	\(\chi_{912}(7, \cdot)\)	None	0	2
912.3.bj	\(\chi_{912}(335, \cdot)\)	n/a	160	2
912.3.bk	\(\chi_{912}(217, \cdot)\)	None	0	2
912.3.bl	\(\chi_{912}(353, \cdot)\)	n/a	156	2
912.3.bp	\(\chi_{912}(373, \cdot)\)	n/a	640	4
912.3.bs	\(\chi_{912}(125, \cdot)\)	n/a	1264	4
912.3.bt	\(\chi_{912}(163, \cdot)\)	n/a	640	4
912.3.bw	\(\chi_{912}(107, \cdot)\)	n/a	1264	4
912.3.bx	\(\chi_{912}(137, \cdot)\)	None	0	6
912.3.by	\(\chi_{912}(97, \cdot)\)	n/a	240	6
912.3.cb	\(\chi_{912}(17, \cdot)\)	n/a	468	6
912.3.cd	\(\chi_{912}(409, \cdot)\)	None	0	6
912.3.ce	\(\chi_{912}(143, \cdot)\)	n/a	480	6
912.3.cg	\(\chi_{912}(55, \cdot)\)	None	0	6
912.3.cj	\(\chi_{912}(71, \cdot)\)	None	0	6
912.3.cl	\(\chi_{912}(175, \cdot)\)	n/a	240	6
912.3.cm	\(\chi_{912}(59, \cdot)\)	n/a	3792	12
912.3.co	\(\chi_{912}(43, \cdot)\)	n/a	1920	12
912.3.cr	\(\chi_{912}(5, \cdot)\)	n/a	3792	12
912.3.ct	\(\chi_{912}(13, \cdot)\)	n/a	1920	12

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(912))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(912)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(304))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(456))\)\(^{\oplus 2}\)