Space of modular forms of level 2850 and weight 2

• Label: 2850.2
• Level: 2850
• Weight: 2
• Dimension: 49496
• Nonzero newspaces: 36
• Sturm bound: 864000
• Trace bound: 15

Defining parameters

Level:	\( N \)	=	\( 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 36 \)
Sturm bound:			\(864000\)
Trace bound:			\(15\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2850))\).

	Total	New	Old
Modular forms	220032	49496	170536
Cusp forms	211969	49496	162473
Eisenstein series	8063	0	8063

Trace form

49496 * q - 6 * q^2 - 14 * q^3 - 6 * q^4 - 20 * q^5 - 14 * q^6 - 48 * q^7 - 6 * q^8 - 6 * q^9 - 4 * q^10 - 8 * q^11 + 12 * q^12 - 68 * q^13 - 20 * q^14 + 8 * q^15 - 6 * q^16 + 32 * q^17 + 46 * q^18 - 32 * q^19 + 16 * q^20 + 22 * q^21 + 66 * q^22 + 76 * q^23 + 26 * q^24 + 172 * q^25 - 40 * q^26 - 29 * q^27 + 20 * q^28 + 40 * q^29 + 40 * q^30 - 4 * q^31 + 14 * q^32 - 14 * q^33 + 56 * q^34 + 16 * q^35 - 6 * q^36 + 12 * q^37 - 12 * q^38 + 54 * q^39 + 12 * q^40 - 48 * q^41 + 16 * q^42 + 80 * q^43 - 40 * q^44 + 140 * q^45 + 48 * q^46 + 28 * q^47 + 27 * q^48 + 90 * q^49 - 36 * q^50 + 141 * q^51 - 20 * q^52 + 48 * q^53 + 40 * q^54 + 48 * q^55 - 16 * q^56 + 110 * q^57 - 116 * q^58 - 40 * q^59 - 64 * q^60 - 176 * q^61 - 96 * q^62 - 102 * q^63 - 6 * q^64 - 148 * q^65 - 24 * q^66 - 288 * q^67 - 12 * q^68 - 306 * q^69 - 96 * q^70 - 84 * q^71 - 29 * q^72 - 274 * q^73 - 68 * q^74 - 328 * q^75 + 4 * q^76 + 24 * q^77 + 16 * q^78 + 292 * q^79 - 20 * q^80 + 466 * q^81 + 380 * q^82 + 680 * q^83 + 242 * q^84 + 508 * q^85 + 464 * q^86 + 848 * q^87 - 40 * q^88 + 712 * q^89 + 252 * q^90 + 960 * q^91 + 456 * q^92 + 1042 * q^93 + 848 * q^94 + 416 * q^95 + 18 * q^96 + 696 * q^97 + 858 * q^98 + 1031 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2850))\)

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
2850.2.a	\(\chi_{2850}(1, \cdot)\)	2850.2.a.a	1	1
		2850.2.a.b	1
		2850.2.a.c	1
		2850.2.a.d	1
		2850.2.a.e	1
		2850.2.a.f	1
		2850.2.a.g	1
		2850.2.a.h	1
		2850.2.a.i	1
		2850.2.a.j	1
		2850.2.a.k	1
		2850.2.a.l	1
		2850.2.a.m	1
		2850.2.a.n	1
		2850.2.a.o	1
		2850.2.a.p	1
		2850.2.a.q	1
		2850.2.a.r	1
		2850.2.a.s	1
		2850.2.a.t	1
		2850.2.a.u	1
		2850.2.a.v	1
		2850.2.a.w	1
		2850.2.a.x	1
		2850.2.a.y	1
		2850.2.a.z	1
		2850.2.a.ba	1
		2850.2.a.bb	1
		2850.2.a.bc	2
		2850.2.a.bd	2
		2850.2.a.be	2
		2850.2.a.bf	2
		2850.2.a.bg	2
		2850.2.a.bh	2
		2850.2.a.bi	2
		2850.2.a.bj	2
		2850.2.a.bk	3
		2850.2.a.bl	3
		2850.2.a.bm	3
		2850.2.a.bn	3
2850.2.c	\(\chi_{2850}(2849, \cdot)\)	n/a	120	1
2850.2.d	\(\chi_{2850}(799, \cdot)\)	2850.2.d.a	2	1
		2850.2.d.b	2
		2850.2.d.c	2
		2850.2.d.d	2
		2850.2.d.e	2
		2850.2.d.f	2
		2850.2.d.g	2
		2850.2.d.h	2
		2850.2.d.i	2
		2850.2.d.j	2
		2850.2.d.k	2
		2850.2.d.l	2
		2850.2.d.m	2
		2850.2.d.n	2
		2850.2.d.o	2
		2850.2.d.p	2
		2850.2.d.q	2
		2850.2.d.r	2
		2850.2.d.s	2
		2850.2.d.t	2
		2850.2.d.u	4
		2850.2.d.v	4
		2850.2.d.w	4
		2850.2.d.x	4
2850.2.f	\(\chi_{2850}(2051, \cdot)\)	n/a	128	1
2850.2.i	\(\chi_{2850}(2101, \cdot)\)	n/a	124	2
2850.2.k	\(\chi_{2850}(2243, \cdot)\)	n/a	216	2
2850.2.m	\(\chi_{2850}(493, \cdot)\)	n/a	120	2
2850.2.n	\(\chi_{2850}(571, \cdot)\)	n/a	368	4
2850.2.o	\(\chi_{2850}(449, \cdot)\)	n/a	240	2
2850.2.r	\(\chi_{2850}(49, \cdot)\)	n/a	120	2
2850.2.t	\(\chi_{2850}(2501, \cdot)\)	n/a	256	2
2850.2.v	\(\chi_{2850}(301, \cdot)\)	n/a	384	6
2850.2.x	\(\chi_{2850}(229, \cdot)\)	n/a	352	4
2850.2.y	\(\chi_{2850}(569, \cdot)\)	n/a	800	4
2850.2.bc	\(\chi_{2850}(341, \cdot)\)	n/a	800	4
2850.2.bd	\(\chi_{2850}(1493, \cdot)\)	n/a	480	4
2850.2.bf	\(\chi_{2850}(943, \cdot)\)	n/a	240	4
2850.2.bh	\(\chi_{2850}(121, \cdot)\)	n/a	800	8
2850.2.bk	\(\chi_{2850}(401, \cdot)\)	n/a	756	6
2850.2.bl	\(\chi_{2850}(199, \cdot)\)	n/a	360	6
2850.2.bo	\(\chi_{2850}(299, \cdot)\)	n/a	720	6
2850.2.bp	\(\chi_{2850}(37, \cdot)\)	n/a	800	8
2850.2.br	\(\chi_{2850}(77, \cdot)\)	n/a	1440	8
2850.2.bt	\(\chi_{2850}(619, \cdot)\)	n/a	800	8
2850.2.bw	\(\chi_{2850}(179, \cdot)\)	n/a	1600	8
2850.2.by	\(\chi_{2850}(221, \cdot)\)	n/a	1600	8
2850.2.cb	\(\chi_{2850}(193, \cdot)\)	n/a	720	12
2850.2.cc	\(\chi_{2850}(443, \cdot)\)	n/a	1440	12
2850.2.ce	\(\chi_{2850}(61, \cdot)\)	n/a	2400	24
2850.2.cg	\(\chi_{2850}(103, \cdot)\)	n/a	1600	16
2850.2.ci	\(\chi_{2850}(83, \cdot)\)	n/a	3200	16
2850.2.cj	\(\chi_{2850}(41, \cdot)\)	n/a	4800	24
2850.2.cm	\(\chi_{2850}(29, \cdot)\)	n/a	4800	24
2850.2.cp	\(\chi_{2850}(139, \cdot)\)	n/a	2400	24
2850.2.cr	\(\chi_{2850}(17, \cdot)\)	n/a	9600	48
2850.2.cs	\(\chi_{2850}(13, \cdot)\)	n/a	4800	48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2850))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2850)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(190))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(285))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(475))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(570))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(950))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1425))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2850))\)\(^{\oplus 1}\)