Space of modular forms of level 3700 and weight 2

• Label: 3700.2
• Level: 3700
• Weight: 2
• Dimension: 218889
• Nonzero newspaces: 60
• Sturm bound: 1641600
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 3700 = 2^{2} \cdot 5^{2} \cdot 37 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 60 \)
Sturm bound:			\(1641600\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3700))\).

	Total	New	Old
Modular forms	415440	221761	193679
Cusp forms	405361	218889	186472
Eisenstein series	10079	2872	7207

Trace form

218889 * q - 222 * q^2 - 8 * q^3 - 214 * q^4 - 546 * q^5 - 342 * q^6 + 8 * q^7 - 198 * q^8 - 424 * q^9 - 256 * q^10 - 214 * q^12 - 428 * q^13 - 214 * q^14 + 4 * q^15 - 374 * q^16 - 408 * q^17 - 238 * q^18 + 24 * q^19 - 276 * q^20 - 660 * q^21 - 214 * q^22 + 64 * q^23 - 234 * q^24 - 462 * q^25 - 666 * q^26 + 52 * q^27 - 214 * q^28 - 382 * q^29 - 268 * q^30 - 30 * q^31 - 182 * q^32 - 424 * q^33 - 214 * q^34 + 16 * q^35 - 340 * q^36 - 519 * q^37 - 508 * q^38 - 138 * q^39 - 376 * q^40 - 818 * q^41 - 414 * q^42 - 156 * q^43 - 354 * q^44 - 686 * q^45 - 462 * q^46 - 122 * q^47 - 474 * q^48 - 594 * q^49 - 476 * q^50 - 72 * q^51 - 410 * q^52 - 470 * q^53 - 474 * q^54 - 80 * q^55 - 462 * q^56 - 556 * q^57 - 304 * q^58 + 24 * q^59 - 468 * q^60 - 535 * q^61 - 224 * q^62 + 136 * q^63 - 148 * q^64 - 446 * q^65 - 186 * q^66 + 124 * q^67 - 154 * q^68 - 192 * q^69 - 268 * q^70 + 104 * q^71 + 50 * q^72 - 320 * q^73 - 90 * q^74 + 156 * q^75 - 474 * q^76 - 196 * q^77 - 22 * q^78 + 184 * q^79 - 236 * q^80 - 720 * q^81 + 38 * q^82 + 160 * q^83 + 198 * q^84 - 630 * q^85 - 96 * q^86 + 80 * q^87 + 116 * q^88 - 577 * q^89 + 44 * q^90 + 6 * q^91 + 4 * q^92 - 670 * q^93 + 106 * q^94 - 72 * q^95 - 142 * q^96 - 828 * q^97 + 82 * q^98 - 210 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3700))\)

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
3700.2.a	\(\chi_{3700}(1, \cdot)\)	3700.2.a.a	1	1
		3700.2.a.b	1
		3700.2.a.c	1
		3700.2.a.d	1
		3700.2.a.e	1
		3700.2.a.f	1
		3700.2.a.g	2
		3700.2.a.h	2
		3700.2.a.i	3
		3700.2.a.j	4
		3700.2.a.k	5
		3700.2.a.l	5
		3700.2.a.m	6
		3700.2.a.n	6
		3700.2.a.o	9
		3700.2.a.p	9
3700.2.d	\(\chi_{3700}(149, \cdot)\)	3700.2.d.a	2	1
		3700.2.d.b	2
		3700.2.d.c	2
		3700.2.d.d	2
		3700.2.d.e	2
		3700.2.d.f	4
		3700.2.d.g	4
		3700.2.d.h	6
		3700.2.d.i	8
		3700.2.d.j	10
		3700.2.d.k	12
3700.2.e	\(\chi_{3700}(1849, \cdot)\)	3700.2.e.a	2	1
		3700.2.e.b	2
		3700.2.e.c	4
		3700.2.e.d	4
		3700.2.e.e	12
		3700.2.e.f	12
		3700.2.e.g	20
3700.2.h	\(\chi_{3700}(1701, \cdot)\)	3700.2.h.a	2	1
		3700.2.h.b	2
		3700.2.h.c	2
		3700.2.h.d	2
		3700.2.h.e	10
		3700.2.h.f	10
		3700.2.h.g	12
		3700.2.h.h	20
3700.2.i	\(\chi_{3700}(1601, \cdot)\)	n/a	118	2
3700.2.k	\(\chi_{3700}(2399, \cdot)\)	n/a	676	2
3700.2.l	\(\chi_{3700}(1893, \cdot)\)	n/a	114	2
3700.2.m	\(\chi_{3700}(443, \cdot)\)	n/a	676	2
3700.2.n	\(\chi_{3700}(1407, \cdot)\)	n/a	648	2
3700.2.o	\(\chi_{3700}(857, \cdot)\)	n/a	114	2
3700.2.u	\(\chi_{3700}(2251, \cdot)\)	n/a	710	2
3700.2.v	\(\chi_{3700}(741, \cdot)\)	n/a	360	4
3700.2.y	\(\chi_{3700}(101, \cdot)\)	n/a	120	2
3700.2.bb	\(\chi_{3700}(249, \cdot)\)	n/a	112	2
3700.2.bc	\(\chi_{3700}(1749, \cdot)\)	n/a	116	2
3700.2.bd	\(\chi_{3700}(201, \cdot)\)	n/a	360	6
3700.2.be	\(\chi_{3700}(221, \cdot)\)	n/a	376	4
3700.2.bh	\(\chi_{3700}(369, \cdot)\)	n/a	384	4
3700.2.bi	\(\chi_{3700}(889, \cdot)\)	n/a	360	4
3700.2.bm	\(\chi_{3700}(51, \cdot)\)	n/a	1420	4
3700.2.bn	\(\chi_{3700}(2493, \cdot)\)	n/a	228	4
3700.2.bo	\(\chi_{3700}(343, \cdot)\)	n/a	1352	4
3700.2.bp	\(\chi_{3700}(307, \cdot)\)	n/a	1352	4
3700.2.bq	\(\chi_{3700}(193, \cdot)\)	n/a	228	4
3700.2.bw	\(\chi_{3700}(199, \cdot)\)	n/a	1352	4
3700.2.bx	\(\chi_{3700}(121, \cdot)\)	n/a	768	8
3700.2.by	\(\chi_{3700}(1249, \cdot)\)	n/a	336	6
3700.2.bz	\(\chi_{3700}(1101, \cdot)\)	n/a	366	6
3700.2.ca	\(\chi_{3700}(49, \cdot)\)	n/a	348	6
3700.2.cf	\(\chi_{3700}(31, \cdot)\)	n/a	4528	8
3700.2.cl	\(\chi_{3700}(117, \cdot)\)	n/a	760	8
3700.2.cm	\(\chi_{3700}(223, \cdot)\)	n/a	4320	8
3700.2.cn	\(\chi_{3700}(147, \cdot)\)	n/a	4528	8
3700.2.co	\(\chi_{3700}(413, \cdot)\)	n/a	760	8
3700.2.cp	\(\chi_{3700}(179, \cdot)\)	n/a	4528	8
3700.2.cr	\(\chi_{3700}(269, \cdot)\)	n/a	752	8
3700.2.cs	\(\chi_{3700}(529, \cdot)\)	n/a	768	8
3700.2.cv	\(\chi_{3700}(381, \cdot)\)	n/a	752	8
3700.2.cz	\(\chi_{3700}(351, \cdot)\)	n/a	4260	12
3700.2.dc	\(\chi_{3700}(499, \cdot)\)	n/a	4056	12
3700.2.de	\(\chi_{3700}(257, \cdot)\)	n/a	684	12
3700.2.dg	\(\chi_{3700}(243, \cdot)\)	n/a	4056	12
3700.2.dh	\(\chi_{3700}(7, \cdot)\)	n/a	4056	12
3700.2.dj	\(\chi_{3700}(57, \cdot)\)	n/a	684	12
3700.2.dk	\(\chi_{3700}(81, \cdot)\)	n/a	2304	24
3700.2.dl	\(\chi_{3700}(119, \cdot)\)	n/a	9056	16
3700.2.dr	\(\chi_{3700}(177, \cdot)\)	n/a	1520	16
3700.2.ds	\(\chi_{3700}(27, \cdot)\)	n/a	9056	16
3700.2.dt	\(\chi_{3700}(47, \cdot)\)	n/a	9056	16
3700.2.du	\(\chi_{3700}(97, \cdot)\)	n/a	1520	16
3700.2.dv	\(\chi_{3700}(171, \cdot)\)	n/a	9056	16
3700.2.eb	\(\chi_{3700}(9, \cdot)\)	n/a	2256	24
3700.2.ec	\(\chi_{3700}(21, \cdot)\)	n/a	2256	24
3700.2.ed	\(\chi_{3700}(169, \cdot)\)	n/a	2304	24
3700.2.ee	\(\chi_{3700}(13, \cdot)\)	n/a	4560	48
3700.2.eg	\(\chi_{3700}(83, \cdot)\)	n/a	27168	48
3700.2.eh	\(\chi_{3700}(3, \cdot)\)	n/a	27168	48
3700.2.ej	\(\chi_{3700}(17, \cdot)\)	n/a	4560	48
3700.2.el	\(\chi_{3700}(19, \cdot)\)	n/a	27168	48
3700.2.eo	\(\chi_{3700}(91, \cdot)\)	n/a	27168	48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3700))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3700)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(148))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(185))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(370))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(740))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(925))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1850))\)\(^{\oplus 2}\)