Space of modular forms of level 1150 and weight 2

• Label: 1150.2
• Level: 1150
• Weight: 2
• Dimension: 12118
• Nonzero newspaces: 12
• Sturm bound: 158400
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(158400\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1150))\).

	Total	New	Old
Modular forms	40832	12118	28714
Cusp forms	38369	12118	26251
Eisenstein series	2463	0	2463

Trace form

12118 * q + 2 * q^2 + 8 * q^3 + 2 * q^4 + 10 * q^5 + 8 * q^6 + 16 * q^7 + 2 * q^8 + 26 * q^9 + 10 * q^10 + 24 * q^11 + 8 * q^12 + 28 * q^13 + 16 * q^14 + 40 * q^15 + 2 * q^16 + 18 * q^17 + 20 * q^18 - 18 * q^19 + 50 * q^21 - 34 * q^22 + 28 * q^23 - 32 * q^24 - 70 * q^25 + 10 * q^26 + 26 * q^27 - 2 * q^28 + 2 * q^29 - 40 * q^30 + 6 * q^31 - 8 * q^32 + 38 * q^33 - 14 * q^34 + 40 * q^35 + 26 * q^36 + 110 * q^37 + 40 * q^38 + 76 * q^39 + 10 * q^40 + 66 * q^41 + 64 * q^42 + 52 * q^43 + 24 * q^44 - 30 * q^45 + 24 * q^46 + 60 * q^47 + 8 * q^48 + 90 * q^49 + 50 * q^50 + 68 * q^51 + 28 * q^52 + 40 * q^53 + 102 * q^54 + 40 * q^55 + 38 * q^56 + 110 * q^57 + 104 * q^58 + 110 * q^59 + 92 * q^61 + 10 * q^62 + 38 * q^63 + 2 * q^64 - 70 * q^65 + 64 * q^66 + 20 * q^67 - 40 * q^68 + 66 * q^69 - 80 * q^70 + 94 * q^71 + 70 * q^72 + 32 * q^73 - 36 * q^74 - 120 * q^75 - 40 * q^76 - 18 * q^77 - 22 * q^78 + 110 * q^79 + 10 * q^80 + 214 * q^81 - 32 * q^82 - 64 * q^83 - 34 * q^84 - 30 * q^85 - 10 * q^86 + 26 * q^87 + 24 * q^88 - 8 * q^89 + 10 * q^90 + 108 * q^91 + 4 * q^92 + 136 * q^93 + 96 * q^94 + 32 * q^95 + 8 * q^96 - 284 * q^97 - 194 * q^98 - 512 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1150))\)

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
1150.2.a	\(\chi_{1150}(1, \cdot)\)	1150.2.a.a	1	1
		1150.2.a.b	1
		1150.2.a.c	1
		1150.2.a.d	1
		1150.2.a.e	1
		1150.2.a.f	1
		1150.2.a.g	1
		1150.2.a.h	1
		1150.2.a.i	1
		1150.2.a.j	2
		1150.2.a.k	2
		1150.2.a.l	2
		1150.2.a.m	2
		1150.2.a.n	2
		1150.2.a.o	2
		1150.2.a.p	2
		1150.2.a.q	3
		1150.2.a.r	4
		1150.2.a.s	4
1150.2.b	\(\chi_{1150}(599, \cdot)\)	1150.2.b.a	2	1
		1150.2.b.b	2
		1150.2.b.c	2
		1150.2.b.d	2
		1150.2.b.e	2
		1150.2.b.f	4
		1150.2.b.g	4
		1150.2.b.h	4
		1150.2.b.i	4
		1150.2.b.j	6
1150.2.e	\(\chi_{1150}(643, \cdot)\)	1150.2.e.a	8	2
		1150.2.e.b	8
		1150.2.e.c	8
		1150.2.e.d	16
		1150.2.e.e	16
		1150.2.e.f	16
1150.2.g	\(\chi_{1150}(231, \cdot)\)	n/a	216	4
1150.2.i	\(\chi_{1150}(139, \cdot)\)	n/a	224	4
1150.2.k	\(\chi_{1150}(101, \cdot)\)	n/a	380	10
1150.2.m	\(\chi_{1150}(137, \cdot)\)	n/a	480	8
1150.2.p	\(\chi_{1150}(49, \cdot)\)	n/a	360	10
1150.2.r	\(\chi_{1150}(7, \cdot)\)	n/a	720	20
1150.2.s	\(\chi_{1150}(31, \cdot)\)	n/a	2400	40
1150.2.u	\(\chi_{1150}(9, \cdot)\)	n/a	2400	40
1150.2.w	\(\chi_{1150}(17, \cdot)\)	n/a	4800	80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1150))\) into lower level spaces

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