Space of modular forms of level 1150 and weight 4

• Label: 1150.4
• Level: 1150
• Weight: 4
• Dimension: 36360
• Nonzero newspaces: 12
• Sturm bound: 316800
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(316800\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1150))\).

	Total	New	Old
Modular forms	120032	36360	83672
Cusp forms	117568	36360	81208
Eisenstein series	2464	0	2464

Trace form

36360 * q + 8 * q^2 - 32 * q^3 - 16 * q^4 - 10 * q^5 - 32 * q^6 - 16 * q^7 + 32 * q^8 + 332 * q^9 + 100 * q^10 - 176 * q^11 - 128 * q^12 - 232 * q^13 - 448 * q^14 - 160 * q^15 + 192 * q^16 - 840 * q^17 - 692 * q^18 - 620 * q^19 + 160 * q^20 + 184 * q^21 + 1052 * q^22 + 176 * q^23 + 576 * q^24 + 2630 * q^25 + 388 * q^26 + 1708 * q^27 + 592 * q^28 - 320 * q^29 - 720 * q^30 - 756 * q^31 - 192 * q^32 - 2288 * q^33 - 1748 * q^34 - 2440 * q^35 - 144 * q^36 - 18 * q^37 - 800 * q^38 - 3348 * q^39 - 240 * q^40 - 1286 * q^41 + 256 * q^42 - 1028 * q^43 + 1088 * q^44 + 4550 * q^45 + 64 * q^46 + 732 * q^47 - 512 * q^48 - 1740 * q^49 - 700 * q^50 + 1844 * q^51 - 928 * q^52 + 4460 * q^53 + 4084 * q^54 + 2200 * q^55 + 3472 * q^56 + 10132 * q^57 + 1128 * q^58 - 3130 * q^59 - 5440 * q^60 - 5072 * q^61 - 10340 * q^62 - 27012 * q^63 - 256 * q^64 - 6170 * q^65 - 6880 * q^66 - 4120 * q^67 + 1904 * q^68 - 2968 * q^69 + 9600 * q^70 - 4196 * q^71 - 1280 * q^72 + 10856 * q^73 + 7408 * q^74 + 24080 * q^75 + 2240 * q^76 + 22008 * q^77 + 17564 * q^78 + 18886 * q^79 - 160 * q^80 + 15632 * q^81 + 4392 * q^82 + 2882 * q^83 + 712 * q^84 - 13210 * q^85 + 4324 * q^86 - 22766 * q^87 + 384 * q^88 - 22020 * q^89 - 17340 * q^90 - 14260 * q^91 - 3584 * q^92 - 11024 * q^93 - 5248 * q^94 - 19288 * q^95 - 512 * q^96 - 81902 * q^97 - 51280 * q^98 - 90826 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1150))\)

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
1150.4.a	\(\chi_{1150}(1, \cdot)\)	1150.4.a.a	1	1
		1150.4.a.b	1
		1150.4.a.c	1
		1150.4.a.d	1
		1150.4.a.e	1
		1150.4.a.f	1
		1150.4.a.g	1
		1150.4.a.h	1
		1150.4.a.i	1
		1150.4.a.j	2
		1150.4.a.k	2
		1150.4.a.l	2
		1150.4.a.m	3
		1150.4.a.n	4
		1150.4.a.o	4
		1150.4.a.p	4
		1150.4.a.q	5
		1150.4.a.r	5
		1150.4.a.s	5
		1150.4.a.t	5
		1150.4.a.u	5
		1150.4.a.v	5
		1150.4.a.w	6
		1150.4.a.x	6
		1150.4.a.y	7
		1150.4.a.z	7
		1150.4.a.ba	9
		1150.4.a.bb	9
1150.4.b	\(\chi_{1150}(599, \cdot)\)	1150.4.b.a	2	1
		1150.4.b.b	2
		1150.4.b.c	2
		1150.4.b.d	2
		1150.4.b.e	2
		1150.4.b.f	2
		1150.4.b.g	2
		1150.4.b.h	2
		1150.4.b.i	4
		1150.4.b.j	4
		1150.4.b.k	4
		1150.4.b.l	6
		1150.4.b.m	8
		1150.4.b.n	8
		1150.4.b.o	8
		1150.4.b.p	10
		1150.4.b.q	10
		1150.4.b.r	10
		1150.4.b.s	12
1150.4.e	\(\chi_{1150}(643, \cdot)\)	n/a	216	2
1150.4.g	\(\chi_{1150}(231, \cdot)\)	n/a	664	4
1150.4.i	\(\chi_{1150}(139, \cdot)\)	n/a	656	4
1150.4.k	\(\chi_{1150}(101, \cdot)\)	n/a	1140	10
1150.4.m	\(\chi_{1150}(137, \cdot)\)	n/a	1440	8
1150.4.p	\(\chi_{1150}(49, \cdot)\)	n/a	1080	10
1150.4.r	\(\chi_{1150}(7, \cdot)\)	n/a	2160	20
1150.4.s	\(\chi_{1150}(31, \cdot)\)	n/a	7200	40
1150.4.u	\(\chi_{1150}(9, \cdot)\)	n/a	7200	40
1150.4.w	\(\chi_{1150}(17, \cdot)\)	n/a	14400	80

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1150))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1150)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(575))\)\(^{\oplus 2}\)