Space of modular forms of level 1950 and weight 4

• Label: 1950.4
• Level: 1950
• Weight: 4
• Dimension: 68848
• Nonzero newspaces: 40
• Sturm bound: 806400
• Trace bound: 18

Defining parameters

Level:	\( N \)	=	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 40 \)
Sturm bound:			\(806400\)
Trace bound:			\(18\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1950))\).

	Total	New	Old
Modular forms	305088	68848	236240
Cusp forms	299712	68848	230864
Eisenstein series	5376	0	5376

Trace form

68848 * q - 12 * q^2 + 38 * q^3 + 24 * q^4 + 20 * q^5 + 20 * q^6 - 80 * q^7 - 96 * q^8 + 54 * q^9 - 104 * q^10 + 440 * q^11 - 56 * q^12 + 386 * q^13 + 176 * q^14 - 512 * q^15 - 416 * q^16 + 1042 * q^17 + 80 * q^18 - 224 * q^19 - 64 * q^20 + 1448 * q^21 - 1680 * q^22 - 1768 * q^23 - 624 * q^24 - 5548 * q^25 - 532 * q^26 - 1870 * q^27 - 704 * q^28 - 934 * q^29 + 720 * q^30 + 2040 * q^31 + 448 * q^32 + 4448 * q^33 + 7216 * q^34 + 7136 * q^35 + 1496 * q^36 + 5294 * q^37 + 1488 * q^38 + 310 * q^39 - 288 * q^40 + 234 * q^41 - 5864 * q^42 - 12696 * q^43 - 3680 * q^44 - 7260 * q^45 - 7648 * q^46 - 7288 * q^47 - 416 * q^48 - 4854 * q^49 + 4008 * q^50 + 21196 * q^51 + 5024 * q^52 + 19128 * q^53 + 12348 * q^54 + 8176 * q^55 + 832 * q^56 + 2124 * q^57 + 2076 * q^58 - 8096 * q^59 - 7488 * q^60 - 12990 * q^61 - 24144 * q^62 - 29332 * q^63 - 2304 * q^64 - 21430 * q^65 - 19456 * q^66 - 36560 * q^67 - 6360 * q^68 - 18292 * q^69 - 15168 * q^70 - 9552 * q^71 - 1520 * q^72 + 5404 * q^73 + 2732 * q^74 + 33552 * q^75 + 5248 * q^76 + 31680 * q^77 + 27308 * q^78 + 33616 * q^79 + 4544 * q^80 + 21462 * q^81 + 16764 * q^82 + 8728 * q^83 + 1728 * q^84 + 8372 * q^85 + 9808 * q^86 + 10932 * q^87 + 4800 * q^88 + 16592 * q^89 - 9368 * q^90 + 10912 * q^91 + 9408 * q^92 - 812 * q^93 + 20240 * q^94 - 14752 * q^95 - 704 * q^96 - 21548 * q^97 - 5388 * q^98 - 1440 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1950))\)

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
1950.4.a	\(\chi_{1950}(1, \cdot)\)	1950.4.a.a	1	1
		1950.4.a.b	1
		1950.4.a.c	1
		1950.4.a.d	1
		1950.4.a.e	1
		1950.4.a.f	1
		1950.4.a.g	1
		1950.4.a.h	1
		1950.4.a.i	1
		1950.4.a.j	1
		1950.4.a.k	1
		1950.4.a.l	1
		1950.4.a.m	1
		1950.4.a.n	1
		1950.4.a.o	1
		1950.4.a.p	1
		1950.4.a.q	1
		1950.4.a.r	2
		1950.4.a.s	2
		1950.4.a.t	2
		1950.4.a.u	2
		1950.4.a.v	2
		1950.4.a.w	2
		1950.4.a.x	2
		1950.4.a.y	2
		1950.4.a.z	2
		1950.4.a.ba	3
		1950.4.a.bb	3
		1950.4.a.bc	3
		1950.4.a.bd	3
		1950.4.a.be	3
		1950.4.a.bf	3
		1950.4.a.bg	3
		1950.4.a.bh	3
		1950.4.a.bi	3
		1950.4.a.bj	4
		1950.4.a.bk	4
		1950.4.a.bl	4
		1950.4.a.bm	4
		1950.4.a.bn	4
		1950.4.a.bo	4
		1950.4.a.bp	4
		1950.4.a.bq	4
		1950.4.a.br	5
		1950.4.a.bs	5
		1950.4.a.bt	5
		1950.4.a.bu	5
1950.4.b	\(\chi_{1950}(1351, \cdot)\)	n/a	134	1
1950.4.e	\(\chi_{1950}(1249, \cdot)\)	n/a	108	1
1950.4.f	\(\chi_{1950}(649, \cdot)\)	n/a	124	1
1950.4.i	\(\chi_{1950}(451, \cdot)\)	n/a	264	2
1950.4.j	\(\chi_{1950}(1243, \cdot)\)	n/a	252	2
1950.4.l	\(\chi_{1950}(443, \cdot)\)	n/a	432	2
1950.4.n	\(\chi_{1950}(749, \cdot)\)	n/a	504	2
1950.4.p	\(\chi_{1950}(551, \cdot)\)	n/a	532	2
1950.4.s	\(\chi_{1950}(857, \cdot)\)	n/a	504	2
1950.4.t	\(\chi_{1950}(307, \cdot)\)	n/a	252	2
1950.4.v	\(\chi_{1950}(391, \cdot)\)	n/a	720	4
1950.4.y	\(\chi_{1950}(49, \cdot)\)	n/a	248	2
1950.4.z	\(\chi_{1950}(1699, \cdot)\)	n/a	256	2
1950.4.bc	\(\chi_{1950}(751, \cdot)\)	n/a	268	2
1950.4.bd	\(\chi_{1950}(79, \cdot)\)	n/a	720	4
1950.4.bg	\(\chi_{1950}(181, \cdot)\)	n/a	832	4
1950.4.bj	\(\chi_{1950}(259, \cdot)\)	n/a	848	4
1950.4.bl	\(\chi_{1950}(7, \cdot)\)	n/a	504	4
1950.4.bm	\(\chi_{1950}(257, \cdot)\)	n/a	1008	4
1950.4.bp	\(\chi_{1950}(401, \cdot)\)	n/a	1064	4
1950.4.br	\(\chi_{1950}(149, \cdot)\)	n/a	1008	4
1950.4.bt	\(\chi_{1950}(107, \cdot)\)	n/a	1008	4
1950.4.bv	\(\chi_{1950}(193, \cdot)\)	n/a	504	4
1950.4.bw	\(\chi_{1950}(61, \cdot)\)	n/a	1696	8
1950.4.by	\(\chi_{1950}(73, \cdot)\)	n/a	1680	8
1950.4.bz	\(\chi_{1950}(77, \cdot)\)	n/a	3360	8
1950.4.cc	\(\chi_{1950}(161, \cdot)\)	n/a	3360	8
1950.4.ce	\(\chi_{1950}(239, \cdot)\)	n/a	3360	8
1950.4.cg	\(\chi_{1950}(53, \cdot)\)	n/a	2880	8
1950.4.ci	\(\chi_{1950}(697, \cdot)\)	n/a	1680	8
1950.4.cj	\(\chi_{1950}(439, \cdot)\)	n/a	1696	8
1950.4.cm	\(\chi_{1950}(121, \cdot)\)	n/a	1664	8
1950.4.cp	\(\chi_{1950}(139, \cdot)\)	n/a	1664	8
1950.4.cq	\(\chi_{1950}(37, \cdot)\)	n/a	3360	16
1950.4.cs	\(\chi_{1950}(113, \cdot)\)	n/a	6720	16
1950.4.cu	\(\chi_{1950}(59, \cdot)\)	n/a	6720	16
1950.4.cw	\(\chi_{1950}(11, \cdot)\)	n/a	6720	16
1950.4.cz	\(\chi_{1950}(17, \cdot)\)	n/a	6720	16
1950.4.da	\(\chi_{1950}(67, \cdot)\)	n/a	3360	16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1950))\) into lower level spaces

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