Space of modular forms of level 1950 and weight 2

• Label: 1950.2
• Level: 1950
• Weight: 2
• Dimension: 22952
• Nonzero newspaces: 40
• Sturm bound: 403200
• Trace bound: 19

Defining parameters

Level:	\( N \)	=	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 40 \)
Sturm bound:			\(403200\)
Trace bound:			\(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1950))\).

	Total	New	Old
Modular forms	103488	22952	80536
Cusp forms	98113	22952	75161
Eisenstein series	5375	0	5375

Trace form

22952 * q - 6 * q^2 - 14 * q^3 - 6 * q^4 - 20 * q^5 - 14 * q^6 - 56 * q^7 - 12 * q^8 - 10 * q^9 - 4 * q^10 - 32 * q^11 + 14 * q^12 - 58 * q^13 - 8 * q^14 + 8 * q^15 - 14 * q^16 + 38 * q^17 + 40 * q^18 + 48 * q^19 + 16 * q^20 + 36 * q^21 + 120 * q^22 + 88 * q^23 + 26 * q^24 + 172 * q^25 - 2 * q^26 - 50 * q^27 + 32 * q^28 + 46 * q^29 + 40 * q^30 + 8 * q^31 + 14 * q^32 + 52 * q^33 + 56 * q^34 + 16 * q^35 + 18 * q^36 + 42 * q^37 - 24 * q^38 + 98 * q^39 + 12 * q^40 - 18 * q^41 + 52 * q^42 + 120 * q^43 - 40 * q^44 + 140 * q^45 + 48 * q^46 + 40 * q^47 + 18 * q^48 + 118 * q^49 - 12 * q^50 + 228 * q^51 + 32 * q^52 + 360 * q^53 + 238 * q^54 + 336 * q^55 + 152 * q^56 + 456 * q^57 + 262 * q^58 + 440 * q^59 + 32 * q^60 + 142 * q^61 + 408 * q^62 + 440 * q^63 + 36 * q^64 + 310 * q^65 + 240 * q^66 + 448 * q^67 + 30 * q^68 + 264 * q^69 + 192 * q^70 + 288 * q^71 + 130 * q^72 + 276 * q^73 + 286 * q^74 - 88 * q^75 + 144 * q^76 + 240 * q^77 + 110 * q^78 + 112 * q^79 + 4 * q^80 + 174 * q^81 - 178 * q^82 - 112 * q^83 - 164 * q^84 - 68 * q^85 - 88 * q^86 - 148 * q^87 - 40 * q^88 - 128 * q^89 - 108 * q^90 - 104 * q^91 - 96 * q^92 - 280 * q^94 - 32 * q^95 + 18 * q^96 - 204 * q^97 - 198 * q^98 - 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1950))\)

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
1950.2.a	\(\chi_{1950}(1, \cdot)\)	1950.2.a.a	1	1
		1950.2.a.b	1
		1950.2.a.c	1
		1950.2.a.d	1
		1950.2.a.e	1
		1950.2.a.f	1
		1950.2.a.g	1
		1950.2.a.h	1
		1950.2.a.i	1
		1950.2.a.j	1
		1950.2.a.k	1
		1950.2.a.l	1
		1950.2.a.m	1
		1950.2.a.n	1
		1950.2.a.o	1
		1950.2.a.p	1
		1950.2.a.q	1
		1950.2.a.r	1
		1950.2.a.s	1
		1950.2.a.t	1
		1950.2.a.u	1
		1950.2.a.v	1
		1950.2.a.w	1
		1950.2.a.x	1
		1950.2.a.y	1
		1950.2.a.z	1
		1950.2.a.ba	1
		1950.2.a.bb	1
		1950.2.a.bc	2
		1950.2.a.bd	2
		1950.2.a.be	2
		1950.2.a.bf	2
		1950.2.a.bg	2
1950.2.b	\(\chi_{1950}(1351, \cdot)\)	1950.2.b.a	2	1
		1950.2.b.b	2
		1950.2.b.c	2
		1950.2.b.d	2
		1950.2.b.e	2
		1950.2.b.f	2
		1950.2.b.g	2
		1950.2.b.h	4
		1950.2.b.i	4
		1950.2.b.j	4
		1950.2.b.k	4
		1950.2.b.l	6
		1950.2.b.m	6
1950.2.e	\(\chi_{1950}(1249, \cdot)\)	1950.2.e.a	2	1
		1950.2.e.b	2
		1950.2.e.c	2
		1950.2.e.d	2
		1950.2.e.e	2
		1950.2.e.f	2
		1950.2.e.g	2
		1950.2.e.h	2
		1950.2.e.i	2
		1950.2.e.j	2
		1950.2.e.k	2
		1950.2.e.l	2
		1950.2.e.m	2
		1950.2.e.n	2
		1950.2.e.o	4
		1950.2.e.p	4
1950.2.f	\(\chi_{1950}(649, \cdot)\)	1950.2.f.a	2	1
		1950.2.f.b	2
		1950.2.f.c	2
		1950.2.f.d	2
		1950.2.f.e	2
		1950.2.f.f	2
		1950.2.f.g	2
		1950.2.f.h	2
		1950.2.f.i	2
		1950.2.f.j	2
		1950.2.f.k	4
		1950.2.f.l	4
		1950.2.f.m	4
		1950.2.f.n	4
		1950.2.f.o	4
		1950.2.f.p	4
1950.2.i	\(\chi_{1950}(451, \cdot)\)	1950.2.i.a	2	2
		1950.2.i.b	2
		1950.2.i.c	2
		1950.2.i.d	2
		1950.2.i.e	2
		1950.2.i.f	2
		1950.2.i.g	2
		1950.2.i.h	2
		1950.2.i.i	2
		1950.2.i.j	2
		1950.2.i.k	2
		1950.2.i.l	2
		1950.2.i.m	2
		1950.2.i.n	2
		1950.2.i.o	2
		1950.2.i.p	2
		1950.2.i.q	2
		1950.2.i.r	2
		1950.2.i.s	2
		1950.2.i.t	2
		1950.2.i.u	2
		1950.2.i.v	2
		1950.2.i.w	2
		1950.2.i.x	2
		1950.2.i.y	4
		1950.2.i.z	4
		1950.2.i.ba	4
		1950.2.i.bb	4
		1950.2.i.bc	4
		1950.2.i.bd	4
		1950.2.i.be	4
		1950.2.i.bf	4
		1950.2.i.bg	4
		1950.2.i.bh	4
		1950.2.i.bi	4
1950.2.j	\(\chi_{1950}(1243, \cdot)\)	1950.2.j.a	12	2
		1950.2.j.b	12
		1950.2.j.c	12
		1950.2.j.d	16
		1950.2.j.e	16
		1950.2.j.f	16
1950.2.l	\(\chi_{1950}(443, \cdot)\)	n/a	144	2
1950.2.n	\(\chi_{1950}(749, \cdot)\)	n/a	168	2
1950.2.p	\(\chi_{1950}(551, \cdot)\)	n/a	180	2
1950.2.s	\(\chi_{1950}(857, \cdot)\)	n/a	168	2
1950.2.t	\(\chi_{1950}(307, \cdot)\)	1950.2.t.a	12	2
		1950.2.t.b	12
		1950.2.t.c	12
		1950.2.t.d	16
		1950.2.t.e	16
		1950.2.t.f	16
1950.2.v	\(\chi_{1950}(391, \cdot)\)	n/a	240	4
1950.2.y	\(\chi_{1950}(49, \cdot)\)	1950.2.y.a	4	2
		1950.2.y.b	4
		1950.2.y.c	4
		1950.2.y.d	4
		1950.2.y.e	4
		1950.2.y.f	4
		1950.2.y.g	4
		1950.2.y.h	4
		1950.2.y.i	8
		1950.2.y.j	8
		1950.2.y.k	8
		1950.2.y.l	8
		1950.2.y.m	12
		1950.2.y.n	12
1950.2.z	\(\chi_{1950}(1699, \cdot)\)	1950.2.z.a	4	2
		1950.2.z.b	4
		1950.2.z.c	4
		1950.2.z.d	4
		1950.2.z.e	4
		1950.2.z.f	4
		1950.2.z.g	4
		1950.2.z.h	4
		1950.2.z.i	4
		1950.2.z.j	4
		1950.2.z.k	4
		1950.2.z.l	4
		1950.2.z.m	8
		1950.2.z.n	8
		1950.2.z.o	8
		1950.2.z.p	8
1950.2.bc	\(\chi_{1950}(751, \cdot)\)	1950.2.bc.a	4	2
		1950.2.bc.b	4
		1950.2.bc.c	4
		1950.2.bc.d	4
		1950.2.bc.e	8
		1950.2.bc.f	8
		1950.2.bc.g	8
		1950.2.bc.h	12
		1950.2.bc.i	12
		1950.2.bc.j	12
		1950.2.bc.k	12
1950.2.bd	\(\chi_{1950}(79, \cdot)\)	n/a	240	4
1950.2.bg	\(\chi_{1950}(181, \cdot)\)	n/a	288	4
1950.2.bj	\(\chi_{1950}(259, \cdot)\)	n/a	272	4
1950.2.bl	\(\chi_{1950}(7, \cdot)\)	n/a	168	4
1950.2.bm	\(\chi_{1950}(257, \cdot)\)	n/a	336	4
1950.2.bp	\(\chi_{1950}(401, \cdot)\)	n/a	352	4
1950.2.br	\(\chi_{1950}(149, \cdot)\)	n/a	336	4
1950.2.bt	\(\chi_{1950}(107, \cdot)\)	n/a	336	4
1950.2.bv	\(\chi_{1950}(193, \cdot)\)	n/a	168	4
1950.2.bw	\(\chi_{1950}(61, \cdot)\)	n/a	544	8
1950.2.by	\(\chi_{1950}(73, \cdot)\)	n/a	560	8
1950.2.bz	\(\chi_{1950}(77, \cdot)\)	n/a	1120	8
1950.2.cc	\(\chi_{1950}(161, \cdot)\)	n/a	1120	8
1950.2.ce	\(\chi_{1950}(239, \cdot)\)	n/a	1120	8
1950.2.cg	\(\chi_{1950}(53, \cdot)\)	n/a	960	8
1950.2.ci	\(\chi_{1950}(697, \cdot)\)	n/a	560	8
1950.2.cj	\(\chi_{1950}(439, \cdot)\)	n/a	544	8
1950.2.cm	\(\chi_{1950}(121, \cdot)\)	n/a	576	8
1950.2.cp	\(\chi_{1950}(139, \cdot)\)	n/a	576	8
1950.2.cq	\(\chi_{1950}(37, \cdot)\)	n/a	1120	16
1950.2.cs	\(\chi_{1950}(113, \cdot)\)	n/a	2240	16
1950.2.cu	\(\chi_{1950}(59, \cdot)\)	n/a	2240	16
1950.2.cw	\(\chi_{1950}(11, \cdot)\)	n/a	2240	16
1950.2.cz	\(\chi_{1950}(17, \cdot)\)	n/a	2240	16
1950.2.da	\(\chi_{1950}(67, \cdot)\)	n/a	1120	16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1950))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1950)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(195))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(325))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(390))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(650))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(975))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1950))\)\(^{\oplus 1}\)