Space of modular forms of level 1050 and weight 6

• Label: 1050.6
• Level: 1050
• Weight: 6
• Dimension: 31798
• Nonzero newspaces: 24
• Sturm bound: 345600
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(345600\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(1050))\).

	Total	New	Old
Modular forms	145344	31798	113546
Cusp forms	142656	31798	110858
Eisenstein series	2688	0	2688

Trace form

31798 * q + 24 * q^2 - 16 * q^3 - 96 * q^4 - 340 * q^5 + 176 * q^6 + 608 * q^7 + 384 * q^8 - 78 * q^9 - 1264 * q^10 + 848 * q^11 + 256 * q^12 + 4124 * q^13 - 704 * q^14 + 7048 * q^15 - 10752 * q^16 + 3472 * q^17 - 12136 * q^18 - 54104 * q^19 - 4864 * q^20 + 4558 * q^21 + 23136 * q^22 + 57092 * q^23 + 13056 * q^24 + 144460 * q^25 - 6176 * q^26 - 54592 * q^27 - 74304 * q^28 - 187204 * q^29 - 80448 * q^30 - 5400 * q^31 - 14336 * q^32 + 170708 * q^33 + 203840 * q^34 + 235672 * q^35 + 96608 * q^36 - 79480 * q^37 - 21072 * q^38 - 161800 * q^39 - 768 * q^40 - 232548 * q^41 - 194776 * q^42 - 231704 * q^43 - 24320 * q^44 + 113172 * q^45 + 412640 * q^46 + 730796 * q^47 + 4096 * q^48 + 73330 * q^49 - 57456 * q^50 - 574112 * q^51 - 233920 * q^52 - 114972 * q^53 - 101232 * q^54 - 28064 * q^55 + 87296 * q^56 + 37044 * q^57 + 275072 * q^58 - 756152 * q^59 - 205824 * q^60 - 326468 * q^61 - 156000 * q^62 + 334756 * q^63 - 122880 * q^64 + 399436 * q^65 + 142592 * q^66 + 668048 * q^67 - 188928 * q^68 - 117040 * q^69 - 135168 * q^70 + 753672 * q^71 + 152704 * q^72 + 1994320 * q^73 + 755264 * q^74 - 879432 * q^75 + 104320 * q^76 - 1035420 * q^77 - 502352 * q^78 - 2511464 * q^79 - 87040 * q^80 - 533766 * q^81 - 426224 * q^82 + 547264 * q^83 + 470880 * q^84 + 116668 * q^85 + 24400 * q^86 + 854304 * q^87 - 119552 * q^88 - 367216 * q^89 - 183824 * q^90 - 455712 * q^91 - 504960 * q^92 + 48304 * q^93 - 319104 * q^94 + 563168 * q^95 + 151552 * q^96 + 332856 * q^97 - 115848 * q^98 - 1406472 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(1050))\)

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
1050.6.a	\(\chi_{1050}(1, \cdot)\)	1050.6.a.a	1	1
		1050.6.a.b	1
		1050.6.a.c	1
		1050.6.a.d	1
		1050.6.a.e	1
		1050.6.a.f	1
		1050.6.a.g	1
		1050.6.a.h	1
		1050.6.a.i	1
		1050.6.a.j	1
		1050.6.a.k	1
		1050.6.a.l	1
		1050.6.a.m	1
		1050.6.a.n	1
		1050.6.a.o	1
		1050.6.a.p	1
		1050.6.a.q	2
		1050.6.a.r	2
		1050.6.a.s	2
		1050.6.a.t	2
		1050.6.a.u	2
		1050.6.a.v	2
		1050.6.a.w	2
		1050.6.a.x	2
		1050.6.a.y	2
		1050.6.a.z	2
		1050.6.a.ba	2
		1050.6.a.bb	2
		1050.6.a.bc	2
		1050.6.a.bd	3
		1050.6.a.be	3
		1050.6.a.bf	3
		1050.6.a.bg	3
		1050.6.a.bh	3
		1050.6.a.bi	3
		1050.6.a.bj	3
		1050.6.a.bk	3
		1050.6.a.bl	3
		1050.6.a.bm	3
		1050.6.a.bn	3
		1050.6.a.bo	3
		1050.6.a.bp	4
		1050.6.a.bq	4
		1050.6.a.br	4
		1050.6.a.bs	4
1050.6.b	\(\chi_{1050}(251, \cdot)\)	n/a	252	1
1050.6.d	\(\chi_{1050}(1049, \cdot)\)	n/a	240	1
1050.6.g	\(\chi_{1050}(799, \cdot)\)	1050.6.g.a	2	1
		1050.6.g.b	2
		1050.6.g.c	2
		1050.6.g.d	2
		1050.6.g.e	2
		1050.6.g.f	2
		1050.6.g.g	2
		1050.6.g.h	2
		1050.6.g.i	2
		1050.6.g.j	2
		1050.6.g.k	2
		1050.6.g.l	2
		1050.6.g.m	2
		1050.6.g.n	2
		1050.6.g.o	2
		1050.6.g.p	2
		1050.6.g.q	4
		1050.6.g.r	4
		1050.6.g.s	4
		1050.6.g.t	4
		1050.6.g.u	4
		1050.6.g.v	4
		1050.6.g.w	4
		1050.6.g.x	4
		1050.6.g.y	4
		1050.6.g.z	6
		1050.6.g.ba	6
		1050.6.g.bb	6
		1050.6.g.bc	6
1050.6.i	\(\chi_{1050}(151, \cdot)\)	n/a	252	2
1050.6.j	\(\chi_{1050}(407, \cdot)\)	n/a	360	2
1050.6.m	\(\chi_{1050}(307, \cdot)\)	n/a	240	2
1050.6.n	\(\chi_{1050}(211, \cdot)\)	n/a	608	4
1050.6.o	\(\chi_{1050}(499, \cdot)\)	n/a	240	2
1050.6.s	\(\chi_{1050}(101, \cdot)\)	n/a	508	2
1050.6.u	\(\chi_{1050}(299, \cdot)\)	n/a	480	2
1050.6.w	\(\chi_{1050}(169, \cdot)\)	n/a	592	4
1050.6.z	\(\chi_{1050}(209, \cdot)\)	n/a	1600	4
1050.6.bb	\(\chi_{1050}(41, \cdot)\)	n/a	1600	4
1050.6.bc	\(\chi_{1050}(157, \cdot)\)	n/a	480	4
1050.6.bf	\(\chi_{1050}(107, \cdot)\)	n/a	960	4
1050.6.bg	\(\chi_{1050}(121, \cdot)\)	n/a	1600	8
1050.6.bh	\(\chi_{1050}(13, \cdot)\)	n/a	1600	8
1050.6.bk	\(\chi_{1050}(113, \cdot)\)	n/a	2400	8
1050.6.bl	\(\chi_{1050}(59, \cdot)\)	n/a	3200	8
1050.6.bn	\(\chi_{1050}(131, \cdot)\)	n/a	3200	8
1050.6.br	\(\chi_{1050}(79, \cdot)\)	n/a	1600	8
1050.6.bs	\(\chi_{1050}(23, \cdot)\)	n/a	6400	16
1050.6.bv	\(\chi_{1050}(73, \cdot)\)	n/a	3200	16

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(1050))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(1050)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 16}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(350))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(525))\)\(^{\oplus 2}\)