Space of modular forms of level 912 and weight 6

• Label: 912.6
• Level: 912
• Weight: 6
• Dimension: 48176
• Nonzero newspaces: 24
• Sturm bound: 276480
• Trace bound: 13

Defining parameters

Level:	\( N \)	=	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(276480\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(912))\).

	Total	New	Old
Modular forms	116208	48484	67724
Cusp forms	114192	48176	66016
Eisenstein series	2016	308	1708

Trace form

48176 * q - 41 * q^3 - 152 * q^4 - 76 * q^5 + 196 * q^6 + 282 * q^7 + 984 * q^8 - 951 * q^9 - 1800 * q^10 - 3624 * q^11 - 20 * q^12 + 394 * q^13 - 648 * q^14 + 4473 * q^15 - 8424 * q^16 - 404 * q^17 + 8764 * q^18 - 9734 * q^19 + 15200 * q^20 - 3989 * q^21 - 2488 * q^22 + 9328 * q^23 - 15612 * q^24 + 3892 * q^25 + 25960 * q^26 + 5983 * q^27 + 3768 * q^28 + 16708 * q^29 + 1444 * q^30 - 40726 * q^31 - 88320 * q^32 - 15265 * q^33 - 62296 * q^34 + 38352 * q^35 + 64700 * q^36 + 25420 * q^37 + 72088 * q^38 + 80294 * q^39 + 180776 * q^40 + 21756 * q^41 + 5892 * q^42 - 44406 * q^43 - 87536 * q^44 - 65121 * q^45 - 244040 * q^46 - 70272 * q^47 - 71268 * q^48 - 162112 * q^49 - 212424 * q^50 - 59007 * q^51 + 329688 * q^52 + 223636 * q^53 + 68084 * q^54 + 198026 * q^55 + 317184 * q^56 + 42591 * q^57 + 70624 * q^58 + 61064 * q^59 + 71852 * q^60 + 337074 * q^61 - 382200 * q^62 - 82809 * q^63 - 715976 * q^64 - 820152 * q^65 - 310460 * q^66 - 1327614 * q^67 + 244672 * q^68 - 304061 * q^69 + 747912 * q^70 + 143228 * q^71 + 90388 * q^72 + 694970 * q^73 + 189992 * q^74 + 865856 * q^75 - 242296 * q^76 + 1014488 * q^77 - 426324 * q^78 + 1096422 * q^79 - 1246736 * q^80 + 997001 * q^81 + 333704 * q^82 - 244908 * q^83 + 10156 * q^84 - 376898 * q^85 + 1162336 * q^86 - 1252995 * q^87 + 1179960 * q^88 - 673716 * q^89 + 127340 * q^90 - 259878 * q^91 + 25504 * q^92 - 155609 * q^93 - 1021912 * q^94 - 119624 * q^95 + 19624 * q^96 - 1038990 * q^97 - 955472 * q^98 + 282149 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(912))\)

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
912.6.a	\(\chi_{912}(1, \cdot)\)	912.6.a.a	1	1
		912.6.a.b	1
		912.6.a.c	1
		912.6.a.d	1
		912.6.a.e	1
		912.6.a.f	1
		912.6.a.g	2
		912.6.a.h	2
		912.6.a.i	2
		912.6.a.j	2
		912.6.a.k	3
		912.6.a.l	3
		912.6.a.m	3
		912.6.a.n	3
		912.6.a.o	3
		912.6.a.p	4
		912.6.a.q	4
		912.6.a.r	4
		912.6.a.s	4
		912.6.a.t	5
		912.6.a.u	5
		912.6.a.v	5
		912.6.a.w	5
		912.6.a.x	5
		912.6.a.y	6
		912.6.a.z	7
		912.6.a.ba	7
912.6.d	\(\chi_{912}(191, \cdot)\)	n/a	180	1
912.6.e	\(\chi_{912}(151, \cdot)\)	None	0	1
912.6.f	\(\chi_{912}(113, \cdot)\)	n/a	198	1
912.6.g	\(\chi_{912}(457, \cdot)\)	None	0	1
912.6.j	\(\chi_{912}(647, \cdot)\)	None	0	1
912.6.k	\(\chi_{912}(607, \cdot)\)	912.6.k.a	16	1
		912.6.k.b	16
		912.6.k.c	34
		912.6.k.d	34
912.6.p	\(\chi_{912}(569, \cdot)\)	None	0	1
912.6.q	\(\chi_{912}(49, \cdot)\)	n/a	200	2
912.6.r	\(\chi_{912}(341, \cdot)\)	n/a	1592	2
912.6.u	\(\chi_{912}(229, \cdot)\)	n/a	720	2
912.6.v	\(\chi_{912}(419, \cdot)\)	n/a	1440	2
912.6.y	\(\chi_{912}(379, \cdot)\)	n/a	800	2
912.6.bb	\(\chi_{912}(31, \cdot)\)	n/a	200	2
912.6.bc	\(\chi_{912}(311, \cdot)\)	None	0	2
912.6.bd	\(\chi_{912}(521, \cdot)\)	None	0	2
912.6.bg	\(\chi_{912}(103, \cdot)\)	None	0	2
912.6.bh	\(\chi_{912}(239, \cdot)\)	n/a	400	2
912.6.bm	\(\chi_{912}(121, \cdot)\)	None	0	2
912.6.bn	\(\chi_{912}(65, \cdot)\)	n/a	396	2
912.6.bo	\(\chi_{912}(289, \cdot)\)	n/a	600	6
912.6.bq	\(\chi_{912}(277, \cdot)\)	n/a	1600	4
912.6.br	\(\chi_{912}(221, \cdot)\)	n/a	3184	4
912.6.bu	\(\chi_{912}(259, \cdot)\)	n/a	1600	4
912.6.bv	\(\chi_{912}(11, \cdot)\)	n/a	3184	4
912.6.bz	\(\chi_{912}(41, \cdot)\)	None	0	6
912.6.ca	\(\chi_{912}(25, \cdot)\)	None	0	6
912.6.cc	\(\chi_{912}(257, \cdot)\)	n/a	1188	6
912.6.cf	\(\chi_{912}(295, \cdot)\)	None	0	6
912.6.ch	\(\chi_{912}(47, \cdot)\)	n/a	1200	6
912.6.ci	\(\chi_{912}(79, \cdot)\)	n/a	600	6
912.6.ck	\(\chi_{912}(23, \cdot)\)	None	0	6
912.6.cn	\(\chi_{912}(67, \cdot)\)	n/a	4800	12
912.6.cp	\(\chi_{912}(35, \cdot)\)	n/a	9552	12
912.6.cq	\(\chi_{912}(61, \cdot)\)	n/a	4800	12
912.6.cs	\(\chi_{912}(29, \cdot)\)	n/a	9552	12

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(912))\) into lower level spaces

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