Space of modular forms of level 2523 and weight 2

• Label: 2523.2
• Level: 2523
• Weight: 2
• Dimension: 175043
• Nonzero newspaces: 12
• Sturm bound: 941920
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 2523 = 3 \cdot 29^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(941920\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2523))\).

	Total	New	Old
Modular forms	237888	177339	60549
Cusp forms	233073	175043	58030
Eisenstein series	4815	2296	2519

Trace form

175043 * q + 3 * q^2 - 377 * q^3 - 749 * q^4 + 6 * q^5 - 375 * q^6 - 748 * q^7 + 15 * q^8 - 377 * q^9 - 738 * q^10 + 12 * q^11 - 371 * q^12 - 742 * q^13 + 24 * q^14 - 372 * q^15 - 725 * q^16 + 18 * q^17 - 375 * q^18 - 736 * q^19 - 42 * q^20 - 426 * q^21 - 832 * q^22 - 32 * q^23 - 531 * q^24 - 837 * q^25 - 98 * q^26 - 461 * q^27 - 980 * q^28 - 56 * q^29 - 892 * q^30 - 836 * q^31 - 161 * q^32 - 450 * q^33 - 842 * q^34 - 64 * q^35 - 539 * q^36 - 774 * q^37 - 52 * q^38 - 420 * q^39 - 750 * q^40 + 42 * q^41 - 354 * q^42 - 712 * q^43 + 28 * q^44 - 400 * q^45 - 964 * q^46 - 64 * q^47 - 571 * q^48 - 923 * q^49 - 299 * q^50 - 472 * q^51 - 1106 * q^52 - 198 * q^53 - 375 * q^54 - 1132 * q^55 - 272 * q^56 - 498 * q^57 - 1120 * q^58 - 52 * q^59 - 728 * q^60 - 918 * q^61 - 296 * q^62 - 426 * q^63 - 1133 * q^64 - 168 * q^65 - 566 * q^66 - 912 * q^67 - 266 * q^68 - 466 * q^69 - 1060 * q^70 - 40 * q^71 - 251 * q^72 - 822 * q^73 + 58 * q^74 - 207 * q^75 - 616 * q^76 + 96 * q^77 - 112 * q^78 - 676 * q^79 + 186 * q^80 - 153 * q^81 - 630 * q^82 + 84 * q^83 - 70 * q^84 - 648 * q^85 + 132 * q^86 - 322 * q^87 - 1304 * q^88 + 90 * q^89 - 80 * q^90 - 644 * q^91 + 168 * q^92 - 234 * q^93 - 612 * q^94 + 120 * q^95 - 7 * q^96 - 854 * q^97 - 109 * q^98 - 450 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2523))\)

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
2523.2.a	\(\chi_{2523}(1, \cdot)\)	2523.2.a.a	2	1
		2523.2.a.b	2
		2523.2.a.c	2
		2523.2.a.d	2
		2523.2.a.e	2
		2523.2.a.f	2
		2523.2.a.g	2
		2523.2.a.h	3
		2523.2.a.i	3
		2523.2.a.j	3
		2523.2.a.k	6
		2523.2.a.l	6
		2523.2.a.m	8
		2523.2.a.n	8
		2523.2.a.o	9
		2523.2.a.p	9
		2523.2.a.q	9
		2523.2.a.r	9
		2523.2.a.s	12
		2523.2.a.t	12
		2523.2.a.u	12
		2523.2.a.v	12
2523.2.c	\(\chi_{2523}(1681, \cdot)\)	n/a	136	1
2523.2.f	\(\chi_{2523}(41, \cdot)\)	n/a	488	2
2523.2.g	\(\chi_{2523}(190, \cdot)\)	n/a	804	6
2523.2.i	\(\chi_{2523}(196, \cdot)\)	n/a	816	6
2523.2.k	\(\chi_{2523}(14, \cdot)\)	n/a	2928	12
2523.2.m	\(\chi_{2523}(88, \cdot)\)	n/a	4088	28
2523.2.o	\(\chi_{2523}(28, \cdot)\)	n/a	4032	28
2523.2.q	\(\chi_{2523}(17, \cdot)\)	n/a	16128	56
2523.2.s	\(\chi_{2523}(7, \cdot)\)	n/a	24528	168
2523.2.u	\(\chi_{2523}(4, \cdot)\)	n/a	24192	168
2523.2.x	\(\chi_{2523}(2, \cdot)\)	n/a	96768	336

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2523))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2523)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(841))\)\(^{\oplus 2}\)