Space of modular forms of level 1134 and weight 2

• Label: 1134.2
• Level: 1134
• Weight: 2
• Dimension: 8832
• Nonzero newspaces: 22
• Sturm bound: 139968
• Trace bound: 23

Defining parameters

Level:	\( N \)	=	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 22 \)
Sturm bound:			\(139968\)
Trace bound:			\(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1134))\).

	Total	New	Old
Modular forms	36288	8832	27456
Cusp forms	33697	8832	24865
Eisenstein series	2591	0	2591

Trace form

8832 * q - 12 * q^5 - 6 * q^7 - 6 * q^8 - 12 * q^10 - 30 * q^11 - 24 * q^13 - 6 * q^14 - 24 * q^17 + 18 * q^18 + 36 * q^19 + 60 * q^20 + 54 * q^21 + 42 * q^22 + 156 * q^23 + 72 * q^25 + 180 * q^26 + 108 * q^27 + 24 * q^28 + 168 * q^29 + 108 * q^30 + 72 * q^31 + 108 * q^33 + 30 * q^34 + 60 * q^35 + 36 * q^36 + 12 * q^37 - 6 * q^38 - 12 * q^40 + 6 * q^41 - 18 * q^43 - 12 * q^44 + 108 * q^45 - 24 * q^46 + 108 * q^47 + 48 * q^49 + 126 * q^51 + 12 * q^52 + 240 * q^53 + 216 * q^55 - 6 * q^56 + 108 * q^57 + 60 * q^58 + 318 * q^59 + 144 * q^61 + 96 * q^62 + 54 * q^63 - 6 * q^64 + 228 * q^65 - 144 * q^66 + 198 * q^67 + 48 * q^68 - 252 * q^69 + 132 * q^70 - 96 * q^71 - 144 * q^72 + 60 * q^73 - 120 * q^74 - 360 * q^75 + 66 * q^76 - 138 * q^77 - 288 * q^78 + 156 * q^79 - 48 * q^80 - 288 * q^81 - 12 * q^82 - 288 * q^83 - 36 * q^84 + 72 * q^85 - 234 * q^86 - 576 * q^87 + 42 * q^88 - 348 * q^89 - 288 * q^90 - 30 * q^91 - 132 * q^92 - 252 * q^93 + 36 * q^94 - 168 * q^95 - 36 * q^96 + 30 * q^97 - 66 * q^98 - 36 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1134))\)

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
1134.2.a	\(\chi_{1134}(1, \cdot)\)	1134.2.a.a	1	1
		1134.2.a.b	1
		1134.2.a.c	1
		1134.2.a.d	1
		1134.2.a.e	1
		1134.2.a.f	1
		1134.2.a.g	1
		1134.2.a.h	1
		1134.2.a.i	2
		1134.2.a.j	2
		1134.2.a.k	2
		1134.2.a.l	2
		1134.2.a.m	2
		1134.2.a.n	2
		1134.2.a.o	2
		1134.2.a.p	2
1134.2.d	\(\chi_{1134}(1133, \cdot)\)	1134.2.d.a	16	1
		1134.2.d.b	16
1134.2.e	\(\chi_{1134}(865, \cdot)\)	1134.2.e.a	2	2
		1134.2.e.b	2
		1134.2.e.c	2
		1134.2.e.d	2
		1134.2.e.e	2
		1134.2.e.f	2
		1134.2.e.g	2
		1134.2.e.h	2
		1134.2.e.i	2
		1134.2.e.j	2
		1134.2.e.k	2
		1134.2.e.l	2
		1134.2.e.m	2
		1134.2.e.n	2
		1134.2.e.o	2
		1134.2.e.p	2
		1134.2.e.q	4
		1134.2.e.r	4
		1134.2.e.s	4
		1134.2.e.t	4
		1134.2.e.u	8
		1134.2.e.v	8
1134.2.f	\(\chi_{1134}(379, \cdot)\)	1134.2.f.a	2	2
		1134.2.f.b	2
		1134.2.f.c	2
		1134.2.f.d	2
		1134.2.f.e	2
		1134.2.f.f	2
		1134.2.f.g	2
		1134.2.f.h	2
		1134.2.f.i	2
		1134.2.f.j	2
		1134.2.f.k	2
		1134.2.f.l	2
		1134.2.f.m	2
		1134.2.f.n	2
		1134.2.f.o	2
		1134.2.f.p	2
		1134.2.f.q	4
		1134.2.f.r	4
		1134.2.f.s	4
		1134.2.f.t	4
1134.2.g	\(\chi_{1134}(163, \cdot)\)	1134.2.g.a	2	2
		1134.2.g.b	2
		1134.2.g.c	2
		1134.2.g.d	2
		1134.2.g.e	2
		1134.2.g.f	2
		1134.2.g.g	2
		1134.2.g.h	2
		1134.2.g.i	4
		1134.2.g.j	4
		1134.2.g.k	6
		1134.2.g.l	6
		1134.2.g.m	6
		1134.2.g.n	6
		1134.2.g.o	8
		1134.2.g.p	8
1134.2.h	\(\chi_{1134}(109, \cdot)\)	1134.2.h.a	2	2
		1134.2.h.b	2
		1134.2.h.c	2
		1134.2.h.d	2
		1134.2.h.e	2
		1134.2.h.f	2
		1134.2.h.g	2
		1134.2.h.h	2
		1134.2.h.i	2
		1134.2.h.j	2
		1134.2.h.k	2
		1134.2.h.l	2
		1134.2.h.m	2
		1134.2.h.n	2
		1134.2.h.o	2
		1134.2.h.p	2
		1134.2.h.q	4
		1134.2.h.r	4
		1134.2.h.s	4
		1134.2.h.t	4
		1134.2.h.u	8
		1134.2.h.v	8
1134.2.k	\(\chi_{1134}(647, \cdot)\)	1134.2.k.a	16	2
		1134.2.k.b	16
		1134.2.k.c	16
		1134.2.k.d	16
1134.2.l	\(\chi_{1134}(215, \cdot)\)	1134.2.l.a	4	2
		1134.2.l.b	4
		1134.2.l.c	4
		1134.2.l.d	4
		1134.2.l.e	8
		1134.2.l.f	8
		1134.2.l.g	16
		1134.2.l.h	16
1134.2.m	\(\chi_{1134}(377, \cdot)\)	1134.2.m.a	4	2
		1134.2.m.b	4
		1134.2.m.c	4
		1134.2.m.d	4
		1134.2.m.e	4
		1134.2.m.f	4
		1134.2.m.g	8
		1134.2.m.h	16
		1134.2.m.i	16
1134.2.t	\(\chi_{1134}(593, \cdot)\)	1134.2.t.a	4	2
		1134.2.t.b	4
		1134.2.t.c	4
		1134.2.t.d	4
		1134.2.t.e	8
		1134.2.t.f	8
		1134.2.t.g	16
		1134.2.t.h	16
1134.2.u	\(\chi_{1134}(127, \cdot)\)	n/a	108	6
1134.2.v	\(\chi_{1134}(289, \cdot)\)	n/a	144	6
1134.2.w	\(\chi_{1134}(37, \cdot)\)	n/a	144	6
1134.2.z	\(\chi_{1134}(125, \cdot)\)	n/a	144	6
1134.2.ba	\(\chi_{1134}(17, \cdot)\)	n/a	144	6
1134.2.bf	\(\chi_{1134}(143, \cdot)\)	n/a	144	6
1134.2.bg	\(\chi_{1134}(67, \cdot)\)	n/a	1296	18
1134.2.bh	\(\chi_{1134}(43, \cdot)\)	n/a	972	18
1134.2.bi	\(\chi_{1134}(25, \cdot)\)	n/a	1296	18
1134.2.bk	\(\chi_{1134}(5, \cdot)\)	n/a	1296	18
1134.2.bp	\(\chi_{1134}(47, \cdot)\)	n/a	1296	18
1134.2.bq	\(\chi_{1134}(41, \cdot)\)	n/a	1296	18

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1134))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1134)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(189))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(378))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(567))\)\(^{\oplus 2}\)