Space of modular forms of level 1050 and weight 3

• Label: 1050.3
• Level: 1050
• Weight: 3
• Dimension: 12720
• Nonzero newspaces: 24
• Sturm bound: 172800
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(172800\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1050))\).

	Total	New	Old
Modular forms	58944	12720	46224
Cusp forms	56256	12720	43536
Eisenstein series	2688	0	2688

Trace form

12720 * q + 16 * q^2 + 22 * q^3 + 8 * q^4 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 142 * q^9 - 24 * q^10 - 100 * q^11 - 44 * q^12 - 140 * q^13 + 8 * q^15 + 64 * q^16 - 432 * q^17 + 32 * q^18 - 520 * q^19 - 64 * q^20 - 10 * q^21 - 192 * q^22 - 176 * q^23 + 24 * q^24 - 120 * q^25 - 416 * q^26 - 644 * q^27 - 312 * q^28 - 40 * q^29 + 192 * q^30 - 152 * q^31 + 96 * q^32 + 282 * q^33 + 360 * q^34 + 472 * q^35 + 24 * q^36 - 132 * q^37 + 536 * q^38 + 156 * q^39 - 48 * q^40 + 832 * q^41 + 920 * q^42 + 1248 * q^43 + 888 * q^44 + 32 * q^45 + 1400 * q^46 + 1180 * q^47 + 64 * q^48 + 348 * q^49 + 184 * q^50 + 758 * q^51 + 280 * q^52 + 1024 * q^53 + 816 * q^54 + 1216 * q^55 + 32 * q^56 + 676 * q^57 - 128 * q^58 - 344 * q^59 + 416 * q^60 - 2256 * q^61 - 320 * q^62 + 1046 * q^63 - 64 * q^64 - 664 * q^65 + 16 * q^66 - 1592 * q^67 - 256 * q^68 + 852 * q^69 - 48 * q^70 + 832 * q^71 - 112 * q^72 + 1964 * q^73 + 240 * q^74 - 232 * q^75 + 8 * q^76 + 2192 * q^77 + 32 * q^78 + 2384 * q^79 - 442 * q^81 + 1136 * q^82 + 2176 * q^83 - 132 * q^84 + 48 * q^85 + 120 * q^86 + 196 * q^87 - 400 * q^88 - 272 * q^89 - 504 * q^90 - 672 * q^91 - 176 * q^92 + 1654 * q^93 - 1736 * q^94 - 512 * q^95 + 208 * q^96 + 1104 * q^97 - 48 * q^98 + 2324 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1050))\)

We only show spaces with odd 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
1050.3.c	\(\chi_{1050}(449, \cdot)\)	1050.3.c.a	8	1
		1050.3.c.b	32
		1050.3.c.c	32
1050.3.e	\(\chi_{1050}(701, \cdot)\)	1050.3.e.a	4	1
		1050.3.e.b	16
		1050.3.e.c	16
		1050.3.e.d	16
		1050.3.e.e	24
1050.3.f	\(\chi_{1050}(601, \cdot)\)	1050.3.f.a	4	1
		1050.3.f.b	8
		1050.3.f.c	12
		1050.3.f.d	12
		1050.3.f.e	16
1050.3.h	\(\chi_{1050}(349, \cdot)\)	1050.3.h.a	8	1
		1050.3.h.b	16
		1050.3.h.c	24
1050.3.k	\(\chi_{1050}(293, \cdot)\)	n/a	192	2
1050.3.l	\(\chi_{1050}(43, \cdot)\)	1050.3.l.a	8	2
		1050.3.l.b	8
		1050.3.l.c	8
		1050.3.l.d	8
		1050.3.l.e	8
		1050.3.l.f	8
		1050.3.l.g	8
		1050.3.l.h	16
1050.3.p	\(\chi_{1050}(451, \cdot)\)	1050.3.p.a	4	2
		1050.3.p.b	8
		1050.3.p.c	8
		1050.3.p.d	8
		1050.3.p.e	12
		1050.3.p.f	12
		1050.3.p.g	16
		1050.3.p.h	16
		1050.3.p.i	16
1050.3.q	\(\chi_{1050}(199, \cdot)\)	1050.3.q.a	8	2
		1050.3.q.b	16
		1050.3.q.c	16
		1050.3.q.d	24
		1050.3.q.e	32
1050.3.r	\(\chi_{1050}(149, \cdot)\)	n/a	192	2
1050.3.t	\(\chi_{1050}(401, \cdot)\)	n/a	204	2
1050.3.v	\(\chi_{1050}(139, \cdot)\)	n/a	320	4
1050.3.x	\(\chi_{1050}(181, \cdot)\)	n/a	320	4
1050.3.y	\(\chi_{1050}(71, \cdot)\)	n/a	480	4
1050.3.ba	\(\chi_{1050}(29, \cdot)\)	n/a	480	4
1050.3.bd	\(\chi_{1050}(193, \cdot)\)	n/a	192	4
1050.3.be	\(\chi_{1050}(143, \cdot)\)	n/a	384	4
1050.3.bi	\(\chi_{1050}(127, \cdot)\)	n/a	480	8
1050.3.bj	\(\chi_{1050}(83, \cdot)\)	n/a	1280	8
1050.3.bm	\(\chi_{1050}(11, \cdot)\)	n/a	1280	8
1050.3.bo	\(\chi_{1050}(179, \cdot)\)	n/a	1280	8
1050.3.bp	\(\chi_{1050}(19, \cdot)\)	n/a	640	8
1050.3.bq	\(\chi_{1050}(31, \cdot)\)	n/a	640	8
1050.3.bt	\(\chi_{1050}(17, \cdot)\)	n/a	2560	16
1050.3.bu	\(\chi_{1050}(37, \cdot)\)	n/a	1280	16

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1050))\) into lower level spaces

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