Space of modular forms of level 2890 and weight 2

• Label: 2890.2
• Level: 2890
• Weight: 2
• Dimension: 75767
• Nonzero newspaces: 20
• Sturm bound: 998784
• Trace bound: 10

Defining parameters

Level:	\( N \)	=	\( 2890 = 2 \cdot 5 \cdot 17^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 20 \)
Sturm bound:			\(998784\)
Trace bound:			\(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2890))\).

	Total	New	Old
Modular forms	252896	75767	177129
Cusp forms	246497	75767	170730
Eisenstein series	6399	0	6399

Trace form

75767 * q - q^2 - 4 * q^3 - q^4 - q^5 - 4 * q^6 - 8 * q^7 - q^8 - 13 * q^9 + 7 * q^10 + 52 * q^11 + 28 * q^12 + 50 * q^13 + 56 * q^14 + 92 * q^15 + 15 * q^16 + 32 * q^17 + 115 * q^18 + 44 * q^19 + 7 * q^20 + 160 * q^21 + 52 * q^22 + 40 * q^23 + 28 * q^24 + 71 * q^25 + 2 * q^26 + 56 * q^27 - 8 * q^28 + 50 * q^29 - 4 * q^30 + 96 * q^31 - q^32 + 80 * q^33 + 56 * q^35 - 13 * q^36 + 90 * q^37 + 12 * q^38 + 200 * q^39 - q^40 + 230 * q^41 + 160 * q^42 + 180 * q^43 + 116 * q^44 + 155 * q^45 + 104 * q^46 + 272 * q^47 - 4 * q^48 + 199 * q^49 + 31 * q^50 + 128 * q^51 + 114 * q^52 + 218 * q^53 + 184 * q^54 + 148 * q^55 - 8 * q^56 + 272 * q^57 + 98 * q^58 + 260 * q^59 + 60 * q^60 + 130 * q^61 + 160 * q^62 + 280 * q^63 - q^64 + 58 * q^65 - 16 * q^66 - 4 * q^67 - 8 * q^68 - 96 * q^69 - 200 * q^70 - 136 * q^71 - 93 * q^72 - 378 * q^73 - 182 * q^74 - 292 * q^75 - 20 * q^76 - 288 * q^77 - 312 * q^78 - 272 * q^79 - 97 * q^80 - 473 * q^81 - 314 * q^82 - 180 * q^83 - 160 * q^84 - 252 * q^85 - 172 * q^86 - 312 * q^87 - 140 * q^88 - 90 * q^89 - 421 * q^90 - 240 * q^91 - 88 * q^92 - 128 * q^93 - 304 * q^94 - 244 * q^95 - 4 * q^96 - 226 * q^97 - 201 * q^98 - 60 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2890))\)

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
2890.2.a	\(\chi_{2890}(1, \cdot)\)	2890.2.a.a	1	1
		2890.2.a.b	1
		2890.2.a.c	1
		2890.2.a.d	1
		2890.2.a.e	1
		2890.2.a.f	1
		2890.2.a.g	1
		2890.2.a.h	1
		2890.2.a.i	1
		2890.2.a.j	1
		2890.2.a.k	1
		2890.2.a.l	1
		2890.2.a.m	1
		2890.2.a.n	1
		2890.2.a.o	1
		2890.2.a.p	1
		2890.2.a.q	1
		2890.2.a.r	2
		2890.2.a.s	2
		2890.2.a.t	2
		2890.2.a.u	2
		2890.2.a.v	2
		2890.2.a.w	3
		2890.2.a.x	3
		2890.2.a.y	3
		2890.2.a.z	3
		2890.2.a.ba	3
		2890.2.a.bb	3
		2890.2.a.bc	4
		2890.2.a.bd	4
		2890.2.a.be	4
		2890.2.a.bf	4
		2890.2.a.bg	6
		2890.2.a.bh	6
		2890.2.a.bi	8
		2890.2.a.bj	8
2890.2.b	\(\chi_{2890}(2311, \cdot)\)	2890.2.b.a	2	1
		2890.2.b.b	2
		2890.2.b.c	2
		2890.2.b.d	2
		2890.2.b.e	2
		2890.2.b.f	2
		2890.2.b.g	2
		2890.2.b.h	2
		2890.2.b.i	4
		2890.2.b.j	4
		2890.2.b.k	4
		2890.2.b.l	6
		2890.2.b.m	6
		2890.2.b.n	6
		2890.2.b.o	8
		2890.2.b.p	8
		2890.2.b.q	12
		2890.2.b.r	16
2890.2.c	\(\chi_{2890}(579, \cdot)\)	n/a	136	1
2890.2.d	\(\chi_{2890}(2889, \cdot)\)	n/a	136	1
2890.2.g	\(\chi_{2890}(829, \cdot)\)	n/a	272	2
2890.2.h	\(\chi_{2890}(251, \cdot)\)	n/a	180	2
2890.2.k	\(\chi_{2890}(1001, \cdot)\)	n/a	360	4
2890.2.n	\(\chi_{2890}(179, \cdot)\)	n/a	536	4
2890.2.o	\(\chi_{2890}(513, \cdot)\)	n/a	1080	8
2890.2.r	\(\chi_{2890}(447, \cdot)\)	n/a	1080	8
2890.2.s	\(\chi_{2890}(171, \cdot)\)	n/a	1632	16
2890.2.t	\(\chi_{2890}(169, \cdot)\)	n/a	2432	16
2890.2.u	\(\chi_{2890}(69, \cdot)\)	n/a	2432	16
2890.2.v	\(\chi_{2890}(101, \cdot)\)	n/a	1632	16
2890.2.y	\(\chi_{2890}(21, \cdot)\)	n/a	3264	32
2890.2.z	\(\chi_{2890}(89, \cdot)\)	n/a	4864	32
2890.2.bc	\(\chi_{2890}(9, \cdot)\)	n/a	9856	64
2890.2.bf	\(\chi_{2890}(111, \cdot)\)	n/a	6528	64
2890.2.bg	\(\chi_{2890}(23, \cdot)\)	n/a	19584	128
2890.2.bj	\(\chi_{2890}(3, \cdot)\)	n/a	19584	128

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2890))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2890)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(170))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(578))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1445))\)\(^{\oplus 2}\)