Space of modular forms of level 1650 and weight 2

• Label: 1650.2
• Level: 1650
• Weight: 2
• Dimension: 16316
• Nonzero newspaces: 42
• Sturm bound: 288000
• Trace bound: 13

Defining parameters

Level:	\( N \)	=	\( 1650 = 2 \cdot 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 42 \)
Sturm bound:			\(288000\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1650))\).

	Total	New	Old
Modular forms	74240	16316	57924
Cusp forms	69761	16316	53445
Eisenstein series	4479	0	4479

Trace form

16316 * q - 6 * q^2 - 14 * q^3 - 6 * q^4 - 20 * q^5 - 19 * q^6 - 68 * q^7 - 6 * q^8 - 26 * q^9 - 4 * q^10 - 24 * q^11 + 8 * q^12 - 40 * q^13 - 4 * q^14 + 8 * q^15 - 6 * q^16 + 28 * q^17 + 41 * q^18 + 74 * q^19 + 16 * q^20 + 44 * q^21 + 60 * q^22 + 92 * q^23 + 31 * q^24 + 172 * q^25 - 4 * q^26 + 16 * q^27 + 32 * q^28 + 56 * q^29 + 40 * q^30 + 12 * q^31 + 14 * q^32 + 65 * q^33 + 56 * q^34 + 16 * q^35 - q^36 + 48 * q^37 - 24 * q^38 + 118 * q^39 + 12 * q^40 - 32 * q^41 + 106 * q^42 + 412 * q^43 + 120 * q^44 + 140 * q^45 + 328 * q^46 + 464 * q^47 + 18 * q^48 + 806 * q^49 + 124 * q^50 + 325 * q^51 + 260 * q^52 + 468 * q^53 + 56 * q^54 + 344 * q^55 - 16 * q^56 + 355 * q^57 + 444 * q^58 + 380 * q^59 + 16 * q^60 + 376 * q^61 + 164 * q^62 - 18 * q^63 - 6 * q^64 + 92 * q^65 + 52 * q^66 + 164 * q^67 + 108 * q^68 - 230 * q^69 - 16 * q^70 - 128 * q^71 - 58 * q^72 - 300 * q^73 - 108 * q^74 - 328 * q^75 - 12 * q^76 - 176 * q^77 - 276 * q^78 - 188 * q^79 - 20 * q^80 - 78 * q^81 - 134 * q^82 - 100 * q^83 - 136 * q^84 - 68 * q^85 - 100 * q^86 - 124 * q^87 - 40 * q^88 - 68 * q^89 - 108 * q^90 + 200 * q^91 - 48 * q^92 + 250 * q^93 - 120 * q^94 + 128 * q^95 + 18 * q^96 + 390 * q^97 - 150 * q^98 + 410 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1650))\)

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
1650.2.a	\(\chi_{1650}(1, \cdot)\)	1650.2.a.a	1	1
		1650.2.a.b	1
		1650.2.a.c	1
		1650.2.a.d	1
		1650.2.a.e	1
		1650.2.a.f	1
		1650.2.a.g	1
		1650.2.a.h	1
		1650.2.a.i	1
		1650.2.a.j	1
		1650.2.a.k	1
		1650.2.a.l	1
		1650.2.a.m	1
		1650.2.a.n	1
		1650.2.a.o	1
		1650.2.a.p	1
		1650.2.a.q	1
		1650.2.a.r	1
		1650.2.a.s	1
		1650.2.a.t	1
		1650.2.a.u	2
		1650.2.a.v	2
		1650.2.a.w	2
		1650.2.a.x	2
		1650.2.a.y	2
		1650.2.a.z	2
1650.2.c	\(\chi_{1650}(199, \cdot)\)	1650.2.c.a	2	1
		1650.2.c.b	2
		1650.2.c.c	2
		1650.2.c.d	2
		1650.2.c.e	2
		1650.2.c.f	2
		1650.2.c.g	2
		1650.2.c.h	2
		1650.2.c.i	2
		1650.2.c.j	2
		1650.2.c.k	2
		1650.2.c.l	2
		1650.2.c.m	2
		1650.2.c.n	2
		1650.2.c.o	4
1650.2.d	\(\chi_{1650}(1451, \cdot)\)	1650.2.d.a	2	1
		1650.2.d.b	2
		1650.2.d.c	8
		1650.2.d.d	8
		1650.2.d.e	8
		1650.2.d.f	8
		1650.2.d.g	8
		1650.2.d.h	8
		1650.2.d.i	12
		1650.2.d.j	12
1650.2.f	\(\chi_{1650}(1649, \cdot)\)	1650.2.f.a	4	1
		1650.2.f.b	4
		1650.2.f.c	8
		1650.2.f.d	8
		1650.2.f.e	8
		1650.2.f.f	8
		1650.2.f.g	16
		1650.2.f.h	16
1650.2.j	\(\chi_{1650}(1343, \cdot)\)	n/a	120	2
1650.2.l	\(\chi_{1650}(43, \cdot)\)	1650.2.l.a	4	2
		1650.2.l.b	4
		1650.2.l.c	8
		1650.2.l.d	8
		1650.2.l.e	8
		1650.2.l.f	8
		1650.2.l.g	16
		1650.2.l.h	16
1650.2.m	\(\chi_{1650}(361, \cdot)\)	n/a	240	4
1650.2.n	\(\chi_{1650}(301, \cdot)\)	n/a	152	4
1650.2.o	\(\chi_{1650}(31, \cdot)\)	n/a	240	4
1650.2.p	\(\chi_{1650}(421, \cdot)\)	n/a	240	4
1650.2.q	\(\chi_{1650}(181, \cdot)\)	n/a	240	4
1650.2.r	\(\chi_{1650}(331, \cdot)\)	n/a	208	4
1650.2.t	\(\chi_{1650}(131, \cdot)\)	n/a	480	4
1650.2.u	\(\chi_{1650}(529, \cdot)\)	n/a	192	4
1650.2.x	\(\chi_{1650}(959, \cdot)\)	n/a	480	4
1650.2.bb	\(\chi_{1650}(479, \cdot)\)	n/a	480	4
1650.2.be	\(\chi_{1650}(29, \cdot)\)	n/a	480	4
1650.2.bf	\(\chi_{1650}(149, \cdot)\)	n/a	288	4
1650.2.bk	\(\chi_{1650}(239, \cdot)\)	n/a	480	4
1650.2.bm	\(\chi_{1650}(281, \cdot)\)	n/a	480	4
1650.2.bn	\(\chi_{1650}(229, \cdot)\)	n/a	240	4
1650.2.bp	\(\chi_{1650}(169, \cdot)\)	n/a	240	4
1650.2.br	\(\chi_{1650}(41, \cdot)\)	n/a	480	4
1650.2.bu	\(\chi_{1650}(101, \cdot)\)	n/a	304	4
1650.2.bv	\(\chi_{1650}(761, \cdot)\)	n/a	480	4
1650.2.by	\(\chi_{1650}(49, \cdot)\)	n/a	144	4
1650.2.bz	\(\chi_{1650}(619, \cdot)\)	n/a	240	4
1650.2.cc	\(\chi_{1650}(379, \cdot)\)	n/a	240	4
1650.2.ce	\(\chi_{1650}(371, \cdot)\)	n/a	480	4
1650.2.ch	\(\chi_{1650}(329, \cdot)\)	n/a	480	4
1650.2.cj	\(\chi_{1650}(113, \cdot)\)	n/a	960	8
1650.2.ck	\(\chi_{1650}(373, \cdot)\)	n/a	480	8
1650.2.cl	\(\chi_{1650}(13, \cdot)\)	n/a	480	8
1650.2.cm	\(\chi_{1650}(337, \cdot)\)	n/a	480	8
1650.2.cn	\(\chi_{1650}(7, \cdot)\)	n/a	288	8
1650.2.co	\(\chi_{1650}(217, \cdot)\)	n/a	480	8
1650.2.cu	\(\chi_{1650}(23, \cdot)\)	n/a	800	8
1650.2.cv	\(\chi_{1650}(257, \cdot)\)	n/a	576	8
1650.2.cw	\(\chi_{1650}(53, \cdot)\)	n/a	960	8
1650.2.cx	\(\chi_{1650}(47, \cdot)\)	n/a	960	8
1650.2.cy	\(\chi_{1650}(137, \cdot)\)	n/a	960	8
1650.2.df	\(\chi_{1650}(73, \cdot)\)	n/a	480	8

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1650))\) into lower level spaces

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