Space of modular forms of level 1650 and weight 4

• Label: 1650.4
• Level: 1650
• Weight: 4
• Dimension: 48940
• Nonzero newspaces: 42
• Sturm bound: 576000
• Trace bound: 13

Defining parameters

Level:	\( N \)	=	\( 1650 = 2 \cdot 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 42 \)
Sturm bound:			\(576000\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1650))\).

	Total	New	Old
Modular forms	218240	48940	169300
Cusp forms	213760	48940	164820
Eisenstein series	4480	0	4480

Trace form

48940 * q - 12 * q^2 + 38 * q^3 + 24 * q^4 + 20 * q^5 - 30 * q^6 + 24 * q^7 - 48 * q^8 + 214 * q^9 - 104 * q^10 + 300 * q^11 - 24 * q^12 - 300 * q^13 - 104 * q^14 - 512 * q^15 - 416 * q^16 + 896 * q^17 - 42 * q^18 + 1594 * q^19 - 64 * q^20 + 1988 * q^21 - 840 * q^22 - 1844 * q^23 - 424 * q^24 - 5548 * q^25 - 1064 * q^26 - 2758 * q^27 - 704 * q^28 - 2024 * q^29 + 720 * q^30 + 780 * q^31 + 448 * q^32 + 805 * q^33 + 7216 * q^34 + 7136 * q^35 + 2164 * q^36 + 5936 * q^37 + 1488 * q^38 + 5868 * q^39 - 288 * q^40 + 1328 * q^41 + 3372 * q^42 + 10676 * q^43 + 6000 * q^44 - 7260 * q^45 - 2608 * q^46 - 6572 * q^47 - 416 * q^48 - 21754 * q^49 - 4936 * q^50 - 13979 * q^51 - 11120 * q^52 - 26736 * q^53 - 3024 * q^54 - 16936 * q^55 - 512 * q^56 - 8455 * q^57 - 13128 * q^58 - 5120 * q^59 - 5184 * q^60 - 4348 * q^61 + 2968 * q^62 + 1236 * q^63 + 384 * q^64 + 19732 * q^65 + 10248 * q^66 + 46208 * q^67 + 13824 * q^68 + 28480 * q^69 + 9504 * q^70 + 1520 * q^71 + 944 * q^72 + 4480 * q^73 + 72 * q^74 + 22512 * q^75 - 816 * q^76 + 68 * q^77 + 1272 * q^78 - 7208 * q^79 + 320 * q^80 + 1778 * q^81 + 11932 * q^82 + 8320 * q^83 + 3024 * q^84 + 8372 * q^85 + 5608 * q^86 + 4692 * q^87 + 1280 * q^88 + 9212 * q^89 - 9368 * q^90 + 22644 * q^91 + 5184 * q^92 + 15210 * q^93 + 1600 * q^94 + 1408 * q^95 - 704 * q^96 - 22370 * q^97 - 7020 * q^98 - 11630 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1650))\)

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
1650.4.a	\(\chi_{1650}(1, \cdot)\)	1650.4.a.a	1	1
		1650.4.a.b	1
		1650.4.a.c	1
		1650.4.a.d	1
		1650.4.a.e	1
		1650.4.a.f	1
		1650.4.a.g	1
		1650.4.a.h	1
		1650.4.a.i	1
		1650.4.a.j	1
		1650.4.a.k	1
		1650.4.a.l	1
		1650.4.a.m	1
		1650.4.a.n	1
		1650.4.a.o	1
		1650.4.a.p	1
		1650.4.a.q	2
		1650.4.a.r	2
		1650.4.a.s	2
		1650.4.a.t	2
		1650.4.a.u	2
		1650.4.a.v	2
		1650.4.a.w	2
		1650.4.a.x	2
		1650.4.a.y	2
		1650.4.a.z	2
		1650.4.a.ba	2
		1650.4.a.bb	2
		1650.4.a.bc	2
		1650.4.a.bd	2
		1650.4.a.be	2
		1650.4.a.bf	2
		1650.4.a.bg	3
		1650.4.a.bh	3
		1650.4.a.bi	3
		1650.4.a.bj	3
		1650.4.a.bk	3
		1650.4.a.bl	3
		1650.4.a.bm	3
		1650.4.a.bn	3
		1650.4.a.bo	3
		1650.4.a.bp	3
		1650.4.a.bq	4
		1650.4.a.br	4
		1650.4.a.bs	5
		1650.4.a.bt	5
1650.4.c	\(\chi_{1650}(199, \cdot)\)	1650.4.c.a	2	1
		1650.4.c.b	2
		1650.4.c.c	2
		1650.4.c.d	2
		1650.4.c.e	2
		1650.4.c.f	2
		1650.4.c.g	2
		1650.4.c.h	2
		1650.4.c.i	2
		1650.4.c.j	2
		1650.4.c.k	2
		1650.4.c.l	2
		1650.4.c.m	2
		1650.4.c.n	2
		1650.4.c.o	4
		1650.4.c.p	4
		1650.4.c.q	4
		1650.4.c.r	4
		1650.4.c.s	4
		1650.4.c.t	4
		1650.4.c.u	4
		1650.4.c.v	4
		1650.4.c.w	4
		1650.4.c.x	4
		1650.4.c.y	6
		1650.4.c.z	6
		1650.4.c.ba	8
1650.4.d	\(\chi_{1650}(1451, \cdot)\)	n/a	228	1
1650.4.f	\(\chi_{1650}(1649, \cdot)\)	n/a	216	1
1650.4.j	\(\chi_{1650}(1343, \cdot)\)	n/a	360	2
1650.4.l	\(\chi_{1650}(43, \cdot)\)	n/a	216	2
1650.4.m	\(\chi_{1650}(361, \cdot)\)	n/a	720	4
1650.4.n	\(\chi_{1650}(301, \cdot)\)	n/a	456	4
1650.4.o	\(\chi_{1650}(31, \cdot)\)	n/a	720	4
1650.4.p	\(\chi_{1650}(421, \cdot)\)	n/a	720	4
1650.4.q	\(\chi_{1650}(181, \cdot)\)	n/a	720	4
1650.4.r	\(\chi_{1650}(331, \cdot)\)	n/a	592	4
1650.4.t	\(\chi_{1650}(131, \cdot)\)	n/a	1440	4
1650.4.u	\(\chi_{1650}(529, \cdot)\)	n/a	608	4
1650.4.x	\(\chi_{1650}(959, \cdot)\)	n/a	1440	4
1650.4.bb	\(\chi_{1650}(479, \cdot)\)	n/a	1440	4
1650.4.be	\(\chi_{1650}(29, \cdot)\)	n/a	1440	4
1650.4.bf	\(\chi_{1650}(149, \cdot)\)	n/a	864	4
1650.4.bk	\(\chi_{1650}(239, \cdot)\)	n/a	1440	4
1650.4.bm	\(\chi_{1650}(281, \cdot)\)	n/a	1440	4
1650.4.bn	\(\chi_{1650}(229, \cdot)\)	n/a	720	4
1650.4.bp	\(\chi_{1650}(169, \cdot)\)	n/a	720	4
1650.4.br	\(\chi_{1650}(41, \cdot)\)	n/a	1440	4
1650.4.bu	\(\chi_{1650}(101, \cdot)\)	n/a	912	4
1650.4.bv	\(\chi_{1650}(761, \cdot)\)	n/a	1440	4
1650.4.by	\(\chi_{1650}(49, \cdot)\)	n/a	432	4
1650.4.bz	\(\chi_{1650}(619, \cdot)\)	n/a	720	4
1650.4.cc	\(\chi_{1650}(379, \cdot)\)	n/a	720	4
1650.4.ce	\(\chi_{1650}(371, \cdot)\)	n/a	1440	4
1650.4.ch	\(\chi_{1650}(329, \cdot)\)	n/a	1440	4
1650.4.cj	\(\chi_{1650}(113, \cdot)\)	n/a	2880	8
1650.4.ck	\(\chi_{1650}(373, \cdot)\)	n/a	1440	8
1650.4.cl	\(\chi_{1650}(13, \cdot)\)	n/a	1440	8
1650.4.cm	\(\chi_{1650}(337, \cdot)\)	n/a	1440	8
1650.4.cn	\(\chi_{1650}(7, \cdot)\)	n/a	864	8
1650.4.co	\(\chi_{1650}(217, \cdot)\)	n/a	1440	8
1650.4.cu	\(\chi_{1650}(23, \cdot)\)	n/a	2400	8
1650.4.cv	\(\chi_{1650}(257, \cdot)\)	n/a	1728	8
1650.4.cw	\(\chi_{1650}(53, \cdot)\)	n/a	2880	8
1650.4.cx	\(\chi_{1650}(47, \cdot)\)	n/a	2880	8
1650.4.cy	\(\chi_{1650}(137, \cdot)\)	n/a	2880	8
1650.4.df	\(\chi_{1650}(73, \cdot)\)	n/a	1440	8

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1650))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1650)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(275))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(330))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(550))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(825))\)\(^{\oplus 2}\)