Space of modular forms of level 2600 and weight 2

• Label: 2600.2
• Level: 2600
• Weight: 2
• Dimension: 102371
• Nonzero newspaces: 64
• Sturm bound: 806400
• Trace bound: 13

Defining parameters

Level:	\( N \)	=	\( 2600 = 2^{3} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 64 \)
Sturm bound:			\(806400\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2600))\).

	Total	New	Old
Modular forms	205632	104175	101457
Cusp forms	197569	102371	95198
Eisenstein series	8063	1804	6259

Trace form

102371 * q - 132 * q^2 - 132 * q^3 - 132 * q^4 - 2 * q^5 - 212 * q^6 - 148 * q^7 - 132 * q^8 - 284 * q^9 - 160 * q^10 - 228 * q^11 - 84 * q^12 - 4 * q^13 - 240 * q^14 - 144 * q^15 - 148 * q^16 - 259 * q^17 - 20 * q^18 - 80 * q^19 - 120 * q^20 + 8 * q^21 - 52 * q^22 - 128 * q^23 - 20 * q^24 - 330 * q^25 - 420 * q^26 - 276 * q^27 - 148 * q^28 - 39 * q^29 - 152 * q^30 - 192 * q^31 - 212 * q^32 - 288 * q^33 - 260 * q^34 - 136 * q^35 - 304 * q^36 + 31 * q^37 - 212 * q^38 - 68 * q^39 - 432 * q^40 - 383 * q^41 - 140 * q^42 + 92 * q^43 - 120 * q^44 + 158 * q^45 - 188 * q^46 + 96 * q^47 - 52 * q^48 - 102 * q^49 - 120 * q^50 - 144 * q^51 + 12 * q^52 + 150 * q^53 + 88 * q^54 - 16 * q^55 + 120 * q^56 + 4 * q^57 + 156 * q^58 + 80 * q^59 - 72 * q^60 - 3 * q^61 + 168 * q^62 - 44 * q^63 + 84 * q^64 - 325 * q^65 - 320 * q^66 - 208 * q^67 - 36 * q^68 - 4 * q^69 - 152 * q^70 - 324 * q^71 - 284 * q^72 - 176 * q^73 - 196 * q^74 - 304 * q^75 - 508 * q^76 - 112 * q^77 - 264 * q^78 - 616 * q^79 - 200 * q^80 - 396 * q^81 - 420 * q^82 - 536 * q^83 - 648 * q^84 - 146 * q^85 - 436 * q^86 - 524 * q^87 - 656 * q^88 - 206 * q^89 - 760 * q^90 - 296 * q^91 - 808 * q^92 - 204 * q^93 - 724 * q^94 - 416 * q^95 - 604 * q^96 - 372 * q^97 - 736 * q^98 - 340 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2600))\)

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
2600.2.a	\(\chi_{2600}(1, \cdot)\)	2600.2.a.a	1	1
		2600.2.a.b	1
		2600.2.a.c	1
		2600.2.a.d	1
		2600.2.a.e	1
		2600.2.a.f	1
		2600.2.a.g	1
		2600.2.a.h	1
		2600.2.a.i	1
		2600.2.a.j	1
		2600.2.a.k	1
		2600.2.a.l	1
		2600.2.a.m	1
		2600.2.a.n	2
		2600.2.a.o	2
		2600.2.a.p	2
		2600.2.a.q	2
		2600.2.a.r	2
		2600.2.a.s	2
		2600.2.a.t	2
		2600.2.a.u	2
		2600.2.a.v	2
		2600.2.a.w	2
		2600.2.a.x	3
		2600.2.a.y	3
		2600.2.a.z	4
		2600.2.a.ba	4
		2600.2.a.bb	5
		2600.2.a.bc	5
2600.2.d	\(\chi_{2600}(1249, \cdot)\)	2600.2.d.a	2	1
		2600.2.d.b	2
		2600.2.d.c	2
		2600.2.d.d	2
		2600.2.d.e	2
		2600.2.d.f	2
		2600.2.d.g	2
		2600.2.d.h	4
		2600.2.d.i	4
		2600.2.d.j	4
		2600.2.d.k	4
		2600.2.d.l	4
		2600.2.d.m	4
		2600.2.d.n	4
		2600.2.d.o	4
		2600.2.d.p	8
2600.2.e	\(\chi_{2600}(701, \cdot)\)	n/a	260	1
2600.2.f	\(\chi_{2600}(649, \cdot)\)	2600.2.f.a	4	1
		2600.2.f.b	4
		2600.2.f.c	6
		2600.2.f.d	6
		2600.2.f.e	8
		2600.2.f.f	8
		2600.2.f.g	14
		2600.2.f.h	14
2600.2.g	\(\chi_{2600}(1301, \cdot)\)	n/a	228	1
2600.2.j	\(\chi_{2600}(2549, \cdot)\)	n/a	216	1
2600.2.k	\(\chi_{2600}(2001, \cdot)\)	2600.2.k.a	4	1
		2600.2.k.b	6
		2600.2.k.c	8
		2600.2.k.d	14
		2600.2.k.e	14
		2600.2.k.f	20
2600.2.p	\(\chi_{2600}(1949, \cdot)\)	n/a	248	1
2600.2.q	\(\chi_{2600}(601, \cdot)\)	n/a	134	2
2600.2.s	\(\chi_{2600}(151, \cdot)\)	None	0	2
2600.2.t	\(\chi_{2600}(99, \cdot)\)	n/a	496	2
2600.2.w	\(\chi_{2600}(57, \cdot)\)	n/a	126	2
2600.2.y	\(\chi_{2600}(1357, \cdot)\)	n/a	496	2
2600.2.bb	\(\chi_{2600}(807, \cdot)\)	None	0	2
2600.2.bc	\(\chi_{2600}(1507, \cdot)\)	n/a	496	2
2600.2.bd	\(\chi_{2600}(207, \cdot)\)	None	0	2
2600.2.be	\(\chi_{2600}(443, \cdot)\)	n/a	432	2
2600.2.bh	\(\chi_{2600}(993, \cdot)\)	n/a	126	2
2600.2.bj	\(\chi_{2600}(957, \cdot)\)	n/a	496	2
2600.2.bm	\(\chi_{2600}(1451, \cdot)\)	n/a	520	2
2600.2.bn	\(\chi_{2600}(1399, \cdot)\)	None	0	2
2600.2.bp	\(\chi_{2600}(521, \cdot)\)	n/a	360	4
2600.2.bq	\(\chi_{2600}(1349, \cdot)\)	n/a	496	2
2600.2.bv	\(\chi_{2600}(1401, \cdot)\)	n/a	132	2
2600.2.bw	\(\chi_{2600}(549, \cdot)\)	n/a	496	2
2600.2.bz	\(\chi_{2600}(1101, \cdot)\)	n/a	520	2
2600.2.ca	\(\chi_{2600}(49, \cdot)\)	n/a	128	2
2600.2.cb	\(\chi_{2600}(101, \cdot)\)	n/a	520	2
2600.2.cc	\(\chi_{2600}(1049, \cdot)\)	n/a	124	2
2600.2.ch	\(\chi_{2600}(441, \cdot)\)	n/a	424	4
2600.2.ci	\(\chi_{2600}(469, \cdot)\)	n/a	1440	4
2600.2.cj	\(\chi_{2600}(389, \cdot)\)	n/a	1664	4
2600.2.cm	\(\chi_{2600}(181, \cdot)\)	n/a	1664	4
2600.2.cn	\(\chi_{2600}(209, \cdot)\)	n/a	360	4
2600.2.cs	\(\chi_{2600}(261, \cdot)\)	n/a	1440	4
2600.2.ct	\(\chi_{2600}(129, \cdot)\)	n/a	416	4
2600.2.cv	\(\chi_{2600}(799, \cdot)\)	None	0	4
2600.2.cw	\(\chi_{2600}(851, \cdot)\)	n/a	1040	4
2600.2.cz	\(\chi_{2600}(93, \cdot)\)	n/a	992	4
2600.2.db	\(\chi_{2600}(657, \cdot)\)	n/a	252	4
2600.2.dc	\(\chi_{2600}(107, \cdot)\)	n/a	992	4
2600.2.dd	\(\chi_{2600}(407, \cdot)\)	None	0	4
2600.2.di	\(\chi_{2600}(43, \cdot)\)	n/a	992	4
2600.2.dj	\(\chi_{2600}(607, \cdot)\)	None	0	4
2600.2.dk	\(\chi_{2600}(293, \cdot)\)	n/a	992	4
2600.2.dm	\(\chi_{2600}(193, \cdot)\)	n/a	252	4
2600.2.dp	\(\chi_{2600}(899, \cdot)\)	n/a	992	4
2600.2.dq	\(\chi_{2600}(951, \cdot)\)	None	0	4
2600.2.ds	\(\chi_{2600}(81, \cdot)\)	n/a	832	8
2600.2.du	\(\chi_{2600}(239, \cdot)\)	None	0	8
2600.2.dv	\(\chi_{2600}(291, \cdot)\)	n/a	3328	8
2600.2.dx	\(\chi_{2600}(317, \cdot)\)	n/a	3328	8
2600.2.dz	\(\chi_{2600}(73, \cdot)\)	n/a	840	8
2600.2.ed	\(\chi_{2600}(27, \cdot)\)	n/a	2880	8
2600.2.ee	\(\chi_{2600}(103, \cdot)\)	None	0	8
2600.2.ef	\(\chi_{2600}(363, \cdot)\)	n/a	3328	8
2600.2.eg	\(\chi_{2600}(183, \cdot)\)	None	0	8
2600.2.ek	\(\chi_{2600}(213, \cdot)\)	n/a	3328	8
2600.2.em	\(\chi_{2600}(177, \cdot)\)	n/a	840	8
2600.2.eo	\(\chi_{2600}(619, \cdot)\)	n/a	3328	8
2600.2.ep	\(\chi_{2600}(31, \cdot)\)	None	0	8
2600.2.er	\(\chi_{2600}(329, \cdot)\)	n/a	832	8
2600.2.es	\(\chi_{2600}(61, \cdot)\)	n/a	3328	8
2600.2.ex	\(\chi_{2600}(9, \cdot)\)	n/a	848	8
2600.2.ey	\(\chi_{2600}(381, \cdot)\)	n/a	3328	8
2600.2.fb	\(\chi_{2600}(69, \cdot)\)	n/a	3328	8
2600.2.fc	\(\chi_{2600}(29, \cdot)\)	n/a	3328	8
2600.2.fd	\(\chi_{2600}(121, \cdot)\)	n/a	848	8
2600.2.fh	\(\chi_{2600}(71, \cdot)\)	None	0	16
2600.2.fi	\(\chi_{2600}(19, \cdot)\)	n/a	6656	16
2600.2.fk	\(\chi_{2600}(137, \cdot)\)	n/a	1680	16
2600.2.fm	\(\chi_{2600}(37, \cdot)\)	n/a	6656	16
2600.2.fo	\(\chi_{2600}(87, \cdot)\)	None	0	16
2600.2.fp	\(\chi_{2600}(147, \cdot)\)	n/a	6656	16
2600.2.fu	\(\chi_{2600}(23, \cdot)\)	None	0	16
2600.2.fv	\(\chi_{2600}(3, \cdot)\)	n/a	6656	16
2600.2.fx	\(\chi_{2600}(33, \cdot)\)	n/a	1680	16
2600.2.fz	\(\chi_{2600}(197, \cdot)\)	n/a	6656	16
2600.2.gb	\(\chi_{2600}(11, \cdot)\)	n/a	6656	16
2600.2.gc	\(\chi_{2600}(119, \cdot)\)	None	0	16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2600))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2600)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(260))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(325))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(520))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(650))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1300))\)\(^{\oplus 2}\)