Space of modular forms of level 1122 and weight 2

• Label: 1122.2
• Level: 1122
• Weight: 2
• Dimension: 8433
• Nonzero newspaces: 20
• Sturm bound: 138240
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 1122 = 2 \cdot 3 \cdot 11 \cdot 17 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 20 \)
Sturm bound:			\(138240\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1122))\).

	Total	New	Old
Modular forms	35840	8433	27407
Cusp forms	33281	8433	24848
Eisenstein series	2559	0	2559

Trace form

8433 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 18 * q^5 + 7 * q^6 + 16 * q^7 - 3 * q^8 + 37 * q^9 + 38 * q^10 + 49 * q^11 + 33 * q^12 + 62 * q^13 + 80 * q^14 + 138 * q^15 + 13 * q^16 + 69 * q^17 + 71 * q^18 + 64 * q^19 - 2 * q^20 + 112 * q^21 + 9 * q^22 + 32 * q^23 + 3 * q^24 + 131 * q^25 - 26 * q^26 - 63 * q^27 - 24 * q^28 + 30 * q^29 - 78 * q^30 + 72 * q^31 - 3 * q^32 - 81 * q^33 - 35 * q^34 + 24 * q^35 - 13 * q^36 + 14 * q^37 - 60 * q^38 - 62 * q^39 - 18 * q^40 - 6 * q^41 - 140 * q^42 + 84 * q^43 + 17 * q^44 - 130 * q^45 + 8 * q^46 + 16 * q^47 - 3 * q^48 + 69 * q^49 - 13 * q^50 - 108 * q^51 + 38 * q^52 - 26 * q^53 - 95 * q^54 + 94 * q^55 - 24 * q^56 - 194 * q^57 + 70 * q^58 + 4 * q^59 - 42 * q^60 + 78 * q^61 + 24 * q^62 - 4 * q^63 - 3 * q^64 + 4 * q^65 + 89 * q^66 + 60 * q^67 + 21 * q^68 + 116 * q^69 + 144 * q^70 + 136 * q^71 + 53 * q^72 + 274 * q^73 + 110 * q^74 + 221 * q^75 - 20 * q^76 + 136 * q^77 + 166 * q^78 + 200 * q^79 + 86 * q^80 + 93 * q^81 + 166 * q^82 + 124 * q^83 + 40 * q^84 + 250 * q^85 + 116 * q^86 + 6 * q^87 + 81 * q^88 + 42 * q^89 - 22 * q^90 - 32 * q^91 - 8 * q^92 - 36 * q^93 + 32 * q^94 + 16 * q^95 - 3 * q^96 + 22 * q^97 - 27 * q^98 - 91 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1122))\)

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
1122.2.a	\(\chi_{1122}(1, \cdot)\)	1122.2.a.a	1	1
		1122.2.a.b	1
		1122.2.a.c	1
		1122.2.a.d	1
		1122.2.a.e	1
		1122.2.a.f	1
		1122.2.a.g	1
		1122.2.a.h	1
		1122.2.a.i	1
		1122.2.a.j	1
		1122.2.a.k	1
		1122.2.a.l	1
		1122.2.a.m	1
		1122.2.a.n	1
		1122.2.a.o	2
		1122.2.a.p	2
		1122.2.a.q	2
		1122.2.a.r	2
		1122.2.a.s	3
1122.2.b	\(\chi_{1122}(1055, \cdot)\)	1122.2.b.a	16	1
		1122.2.b.b	16
		1122.2.b.c	16
		1122.2.b.d	16
1122.2.c	\(\chi_{1122}(67, \cdot)\)	1122.2.c.a	2	1
		1122.2.c.b	2
		1122.2.c.c	2
		1122.2.c.d	2
		1122.2.c.e	4
		1122.2.c.f	4
		1122.2.c.g	6
		1122.2.c.h	10
1122.2.h	\(\chi_{1122}(1121, \cdot)\)	1122.2.h.a	2	1
		1122.2.h.b	2
		1122.2.h.c	2
		1122.2.h.d	2
		1122.2.h.e	4
		1122.2.h.f	4
		1122.2.h.g	28
		1122.2.h.h	28
1122.2.j	\(\chi_{1122}(395, \cdot)\)	n/a	144	2
1122.2.l	\(\chi_{1122}(463, \cdot)\)	1122.2.l.a	4	2
		1122.2.l.b	4
		1122.2.l.c	4
		1122.2.l.d	4
		1122.2.l.e	12
		1122.2.l.f	16
		1122.2.l.g	20
1122.2.m	\(\chi_{1122}(103, \cdot)\)	n/a	128	4
1122.2.o	\(\chi_{1122}(331, \cdot)\)	n/a	112	4
1122.2.q	\(\chi_{1122}(263, \cdot)\)	n/a	288	4
1122.2.r	\(\chi_{1122}(101, \cdot)\)	n/a	288	4
1122.2.w	\(\chi_{1122}(169, \cdot)\)	n/a	144	4
1122.2.x	\(\chi_{1122}(35, \cdot)\)	n/a	256	4
1122.2.y	\(\chi_{1122}(23, \cdot)\)	n/a	480	8
1122.2.z	\(\chi_{1122}(109, \cdot)\)	n/a	288	8
1122.2.bc	\(\chi_{1122}(115, \cdot)\)	n/a	288	8
1122.2.be	\(\chi_{1122}(149, \cdot)\)	n/a	576	8
1122.2.bg	\(\chi_{1122}(83, \cdot)\)	n/a	1152	16
1122.2.bi	\(\chi_{1122}(25, \cdot)\)	n/a	576	16
1122.2.bm	\(\chi_{1122}(7, \cdot)\)	n/a	1152	32
1122.2.bn	\(\chi_{1122}(5, \cdot)\)	n/a	2304	32

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1122))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1122)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(187))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(374))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(561))\)\(^{\oplus 2}\)