Space of modular forms of level 1127 and weight 4

• Label: 1127.4
• Level: 1127
• Weight: 4
• Dimension: 147379
• Nonzero newspaces: 16
• Sturm bound: 413952
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 1127 = 7^{2} \cdot 23 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(413952\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1127))\).

	Total	New	Old
Modular forms	156552	149415	7137
Cusp forms	153912	147379	6533
Eisenstein series	2640	2036	604

Trace form

147379 * q - 311 * q^2 - 335 * q^3 - 311 * q^4 - 263 * q^5 - 179 * q^6 - 312 * q^7 - 659 * q^8 - 479 * q^9 - 419 * q^10 - 311 * q^11 - 131 * q^12 - 299 * q^13 - 312 * q^14 - 637 * q^15 - 511 * q^16 - 87 * q^17 - 295 * q^18 - 825 * q^19 - 267 * q^20 - 816 * q^21 - 102 * q^22 + 578 * q^23 + 1232 * q^24 + 881 * q^25 - 79 * q^26 - 113 * q^27 + 24 * q^28 - 723 * q^29 - 2059 * q^30 - 1389 * q^31 - 3079 * q^32 - 1063 * q^33 - 2765 * q^34 - 480 * q^35 + 826 * q^36 + 1357 * q^37 + 4352 * q^38 + 4117 * q^39 + 8701 * q^40 + 4451 * q^41 - 606 * q^42 - 803 * q^43 - 3988 * q^44 - 6988 * q^45 - 1112 * q^46 - 3416 * q^47 - 12921 * q^48 - 8124 * q^49 - 8490 * q^50 - 6539 * q^51 - 12065 * q^52 - 4753 * q^53 - 10455 * q^54 - 6839 * q^55 + 108 * q^56 - 827 * q^57 - 1220 * q^58 + 4587 * q^59 + 18479 * q^60 + 10513 * q^61 + 14977 * q^62 + 9348 * q^63 + 15829 * q^64 + 6197 * q^65 + 5076 * q^66 + 469 * q^67 + 6818 * q^68 - 1224 * q^69 - 1506 * q^70 - 3645 * q^71 + 7528 * q^72 + 2401 * q^73 - 88 * q^74 - 5181 * q^75 - 5926 * q^76 + 108 * q^77 - 5557 * q^78 - 2835 * q^79 + 18008 * q^80 + 27761 * q^81 + 21253 * q^82 + 18363 * q^83 + 38328 * q^84 + 12567 * q^85 + 11945 * q^86 + 12697 * q^87 + 1755 * q^88 + 5347 * q^89 - 10568 * q^90 - 10770 * q^91 + 466 * q^92 - 31912 * q^93 - 29598 * q^94 - 35261 * q^95 - 66882 * q^96 - 24743 * q^97 - 55332 * q^98 - 35321 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1127))\)

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
1127.4.a	\(\chi_{1127}(1, \cdot)\)	1127.4.a.a	1	1
		1127.4.a.b	2
		1127.4.a.c	4
		1127.4.a.d	5
		1127.4.a.e	8
		1127.4.a.f	9
		1127.4.a.g	12
		1127.4.a.h	12
		1127.4.a.i	20
		1127.4.a.j	22
		1127.4.a.k	22
		1127.4.a.l	22
		1127.4.a.m	22
		1127.4.a.n	26
		1127.4.a.o	38
1127.4.c	\(\chi_{1127}(1126, \cdot)\)	n/a	236	1
1127.4.e	\(\chi_{1127}(116, \cdot)\)	n/a	440	2
1127.4.g	\(\chi_{1127}(68, \cdot)\)	n/a	472	2
1127.4.i	\(\chi_{1127}(162, \cdot)\)	n/a	1848	6
1127.4.j	\(\chi_{1127}(50, \cdot)\)	n/a	2410	10
1127.4.l	\(\chi_{1127}(160, \cdot)\)	n/a	2004	6
1127.4.n	\(\chi_{1127}(93, \cdot)\)	n/a	3696	12
1127.4.p	\(\chi_{1127}(97, \cdot)\)	n/a	2360	10
1127.4.r	\(\chi_{1127}(18, \cdot)\)	n/a	4720	20
1127.4.t	\(\chi_{1127}(45, \cdot)\)	n/a	4008	12
1127.4.w	\(\chi_{1127}(19, \cdot)\)	n/a	4720	20
1127.4.y	\(\chi_{1127}(8, \cdot)\)	n/a	20040	60
1127.4.ba	\(\chi_{1127}(20, \cdot)\)	n/a	20040	60
1127.4.bc	\(\chi_{1127}(2, \cdot)\)	n/a	40080	120
1127.4.be	\(\chi_{1127}(5, \cdot)\)	n/a	40080	120

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1127))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1127)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 2}\)