Space of modular forms of level 912 and weight 2

• Label: 912.2
• Level: 912
• Weight: 2
• Dimension: 9512
• Nonzero newspaces: 24
• Newform subspaces: 126
• Sturm bound: 92160
• Trace bound: 13

Defining parameters

Level:	\( N \)	=	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Newform subspaces:			\( 126 \)
Sturm bound:			\(92160\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(912))\).

	Total	New	Old
Modular forms	24048	9820	14228
Cusp forms	22033	9512	12521
Eisenstein series	2015	308	1707

Trace form

9512 * q - 25 * q^3 - 56 * q^4 + 4 * q^5 - 20 * q^6 - 38 * q^7 + 24 * q^8 + q^9 - 56 * q^10 + 24 * q^11 - 36 * q^12 - 70 * q^13 - 24 * q^14 - 7 * q^15 - 104 * q^16 - 4 * q^17 - 52 * q^18 - 38 * q^19 - 32 * q^20 - 53 * q^21 - 104 * q^22 - 16 * q^23 - 92 * q^24 - 36 * q^25 - 40 * q^26 - 49 * q^27 - 72 * q^28 + 20 * q^29 - 76 * q^30 - 86 * q^31 - 65 * q^33 - 56 * q^34 - 48 * q^35 - 68 * q^36 - 4 * q^37 + 8 * q^38 - 90 * q^39 - 24 * q^40 + 12 * q^41 + 52 * q^42 - 54 * q^43 + 80 * q^44 - 17 * q^45 + 24 * q^46 + 92 * q^48 - 72 * q^49 + 72 * q^50 - 95 * q^51 - 8 * q^52 - 28 * q^53 + 60 * q^54 - 118 * q^55 - q^57 - 176 * q^58 - 56 * q^59 - 52 * q^60 - 126 * q^61 + 24 * q^62 - 25 * q^63 - 200 * q^64 + 168 * q^65 - 140 * q^66 + 130 * q^67 - 64 * q^68 - 29 * q^69 - 216 * q^70 + 124 * q^71 - 108 * q^72 + 138 * q^73 - 104 * q^74 + 128 * q^75 - 136 * q^76 + 184 * q^77 - 132 * q^78 + 230 * q^79 - 16 * q^80 - 95 * q^81 - 120 * q^82 + 180 * q^83 - 20 * q^84 + 30 * q^85 + 32 * q^86 + 189 * q^87 - 8 * q^88 + 156 * q^89 + 12 * q^90 + 218 * q^91 + 32 * q^92 + 23 * q^93 + 8 * q^94 + 56 * q^95 + 40 * q^96 - 94 * q^97 + 80 * q^98 + 101 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(912))\)

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
912.2.a	\(\chi_{912}(1, \cdot)\)	912.2.a.a	1	1
		912.2.a.b	1
		912.2.a.c	1
		912.2.a.d	1
		912.2.a.e	1
		912.2.a.f	1
		912.2.a.g	1
		912.2.a.h	1
		912.2.a.i	1
		912.2.a.j	1
		912.2.a.k	1
		912.2.a.l	1
		912.2.a.m	2
		912.2.a.n	2
		912.2.a.o	2
912.2.d	\(\chi_{912}(191, \cdot)\)	912.2.d.a	12	1
		912.2.d.b	24
912.2.e	\(\chi_{912}(151, \cdot)\)	None	0	1
912.2.f	\(\chi_{912}(113, \cdot)\)	912.2.f.a	2	1
		912.2.f.b	2
		912.2.f.c	2
		912.2.f.d	2
		912.2.f.e	2
		912.2.f.f	4
		912.2.f.g	4
		912.2.f.h	10
		912.2.f.i	10
912.2.g	\(\chi_{912}(457, \cdot)\)	None	0	1
912.2.j	\(\chi_{912}(647, \cdot)\)	None	0	1
912.2.k	\(\chi_{912}(607, \cdot)\)	912.2.k.a	2	1
		912.2.k.b	2
		912.2.k.c	2
		912.2.k.d	2
		912.2.k.e	2
		912.2.k.f	2
		912.2.k.g	4
		912.2.k.h	4
912.2.p	\(\chi_{912}(569, \cdot)\)	None	0	1
912.2.q	\(\chi_{912}(49, \cdot)\)	912.2.q.a	2	2
		912.2.q.b	2
		912.2.q.c	2
		912.2.q.d	2
		912.2.q.e	2
		912.2.q.f	2
		912.2.q.g	4
		912.2.q.h	4
		912.2.q.i	4
		912.2.q.j	4
		912.2.q.k	6
		912.2.q.l	6
912.2.r	\(\chi_{912}(341, \cdot)\)	912.2.r.a	312	2
912.2.u	\(\chi_{912}(229, \cdot)\)	912.2.u.a	72	2
		912.2.u.b	72
912.2.v	\(\chi_{912}(419, \cdot)\)	912.2.v.a	288	2
912.2.y	\(\chi_{912}(379, \cdot)\)	912.2.y.a	160	2
912.2.bb	\(\chi_{912}(31, \cdot)\)	912.2.bb.a	2	2
		912.2.bb.b	2
		912.2.bb.c	4
		912.2.bb.d	4
		912.2.bb.e	6
		912.2.bb.f	6
		912.2.bb.g	8
		912.2.bb.h	8
912.2.bc	\(\chi_{912}(311, \cdot)\)	None	0	2
912.2.bd	\(\chi_{912}(521, \cdot)\)	None	0	2
912.2.bg	\(\chi_{912}(103, \cdot)\)	None	0	2
912.2.bh	\(\chi_{912}(239, \cdot)\)	912.2.bh.a	2	2
		912.2.bh.b	2
		912.2.bh.c	2
		912.2.bh.d	2
		912.2.bh.e	24
		912.2.bh.f	24
		912.2.bh.g	24
912.2.bm	\(\chi_{912}(121, \cdot)\)	None	0	2
912.2.bn	\(\chi_{912}(65, \cdot)\)	912.2.bn.a	2	2
		912.2.bn.b	2
		912.2.bn.c	2
		912.2.bn.d	2
		912.2.bn.e	2
		912.2.bn.f	2
		912.2.bn.g	4
		912.2.bn.h	4
		912.2.bn.i	4
		912.2.bn.j	4
		912.2.bn.k	4
		912.2.bn.l	4
		912.2.bn.m	8
		912.2.bn.n	16
		912.2.bn.o	16
912.2.bo	\(\chi_{912}(289, \cdot)\)	912.2.bo.a	6	6
		912.2.bo.b	6
		912.2.bo.c	6
		912.2.bo.d	6
		912.2.bo.e	6
		912.2.bo.f	6
		912.2.bo.g	12
		912.2.bo.h	12
		912.2.bo.i	12
		912.2.bo.j	12
		912.2.bo.k	18
		912.2.bo.l	18
912.2.bq	\(\chi_{912}(277, \cdot)\)	912.2.bq.a	320	4
912.2.br	\(\chi_{912}(221, \cdot)\)	912.2.br.a	624	4
912.2.bu	\(\chi_{912}(259, \cdot)\)	912.2.bu.a	320	4
912.2.bv	\(\chi_{912}(11, \cdot)\)	912.2.bv.a	8	4
		912.2.bv.b	8
		912.2.bv.c	608
912.2.bz	\(\chi_{912}(41, \cdot)\)	None	0	6
912.2.ca	\(\chi_{912}(25, \cdot)\)	None	0	6
912.2.cc	\(\chi_{912}(257, \cdot)\)	912.2.cc.a	6	6
		912.2.cc.b	6
		912.2.cc.c	18
		912.2.cc.d	18
		912.2.cc.e	24
		912.2.cc.f	36
		912.2.cc.g	60
		912.2.cc.h	60
912.2.cf	\(\chi_{912}(295, \cdot)\)	None	0	6
912.2.ch	\(\chi_{912}(47, \cdot)\)	912.2.ch.a	6	6
		912.2.ch.b	6
		912.2.ch.c	6
		912.2.ch.d	6
		912.2.ch.e	72
		912.2.ch.f	72
		912.2.ch.g	72
912.2.ci	\(\chi_{912}(79, \cdot)\)	912.2.ci.a	6	6
		912.2.ci.b	6
		912.2.ci.c	12
		912.2.ci.d	12
		912.2.ci.e	18
		912.2.ci.f	18
		912.2.ci.g	24
		912.2.ci.h	24
912.2.ck	\(\chi_{912}(23, \cdot)\)	None	0	6
912.2.cn	\(\chi_{912}(67, \cdot)\)	912.2.cn.a	960	12
912.2.cp	\(\chi_{912}(35, \cdot)\)	912.2.cp.a	1872	12
912.2.cq	\(\chi_{912}(61, \cdot)\)	912.2.cq.a	960	12
912.2.cs	\(\chi_{912}(29, \cdot)\)	912.2.cs.a	1872	12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(912))\) into lower level spaces

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