Space of modular forms of level 2100 and weight 3

• Label: 2100.3
• Level: 2100
• Weight: 3
• Dimension: 88622
• Nonzero newspaces: 48
• Sturm bound: 691200
• Trace bound: 18

Defining parameters

Level:	\( N \)	=	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 48 \)
Sturm bound:			\(691200\)
Trace bound:			\(18\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(2100))\).

	Total	New	Old
Modular forms	233760	89446	144314
Cusp forms	227040	88622	138418
Eisenstein series	6720	824	5896

Trace form

88622 * q + 4 * q^2 - 5 * q^3 - 30 * q^4 + 24 * q^5 - 4 * q^6 + 62 * q^7 + 46 * q^8 + 63 * q^9 - 96 * q^10 - 10 * q^11 - 156 * q^12 - 62 * q^13 - 240 * q^14 - 28 * q^15 - 542 * q^16 + 192 * q^17 - 202 * q^18 + 148 * q^19 + 40 * q^20 - 253 * q^21 - 208 * q^22 - 32 * q^23 - 120 * q^24 - 344 * q^25 + 426 * q^26 + 40 * q^27 + 22 * q^28 - 292 * q^29 - 36 * q^30 + 72 * q^31 - 346 * q^32 - 321 * q^33 - 428 * q^34 - 236 * q^35 + 174 * q^36 - 754 * q^37 - 850 * q^38 - 540 * q^39 - 1424 * q^40 - 616 * q^41 - 188 * q^42 - 1444 * q^43 - 448 * q^44 - 1036 * q^45 + 588 * q^46 - 878 * q^47 + 988 * q^48 - 292 * q^49 + 728 * q^50 - 421 * q^51 + 864 * q^52 + 476 * q^53 + 1482 * q^54 - 128 * q^55 - 1558 * q^56 - 310 * q^57 - 848 * q^58 + 52 * q^59 + 884 * q^60 - 1132 * q^61 + 252 * q^62 - 199 * q^63 - 1194 * q^64 - 336 * q^65 - 1710 * q^66 - 72 * q^67 - 1048 * q^68 - 470 * q^69 - 204 * q^70 - 104 * q^71 - 1534 * q^72 - 1318 * q^73 + 654 * q^74 + 380 * q^75 + 680 * q^76 + 1112 * q^77 + 296 * q^78 + 772 * q^79 + 1664 * q^80 + 239 * q^81 + 5152 * q^82 + 448 * q^83 + 3154 * q^84 - 2656 * q^85 + 4086 * q^86 - 32 * q^87 + 6764 * q^88 - 1244 * q^89 + 1892 * q^90 + 980 * q^91 + 4864 * q^92 + 1237 * q^93 + 5272 * q^94 + 160 * q^95 + 2828 * q^96 + 1704 * q^97 + 1062 * q^98 + 1382 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(2100))\)

We only show spaces with odd 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
2100.3.b	\(\chi_{2100}(799, \cdot)\)	n/a	216	1
2100.3.e	\(\chi_{2100}(449, \cdot)\)	2100.3.e.a	8	1
		2100.3.e.b	32
		2100.3.e.c	32
2100.3.g	\(\chi_{2100}(701, \cdot)\)	2100.3.g.a	4	1
		2100.3.g.b	16
		2100.3.g.c	16
		2100.3.g.d	16
		2100.3.g.e	24
2100.3.h	\(\chi_{2100}(1051, \cdot)\)	n/a	228	1
2100.3.j	\(\chi_{2100}(601, \cdot)\)	2100.3.j.a	2	1
		2100.3.j.b	2
		2100.3.j.c	2
		2100.3.j.d	8
		2100.3.j.e	8
		2100.3.j.f	12
		2100.3.j.g	16
2100.3.m	\(\chi_{2100}(251, \cdot)\)	n/a	596	1
2100.3.o	\(\chi_{2100}(2099, \cdot)\)	n/a	568	1
2100.3.p	\(\chi_{2100}(349, \cdot)\)	2100.3.p.a	4	1
		2100.3.p.b	4
		2100.3.p.c	16
		2100.3.p.d	24
2100.3.r	\(\chi_{2100}(307, \cdot)\)	n/a	576	2
2100.3.u	\(\chi_{2100}(293, \cdot)\)	n/a	192	2
2100.3.v	\(\chi_{2100}(757, \cdot)\)	2100.3.v.a	16	2
		2100.3.v.b	16
		2100.3.v.c	16
		2100.3.v.d	24
2100.3.y	\(\chi_{2100}(407, \cdot)\)	n/a	864	2
2100.3.ba	\(\chi_{2100}(551, \cdot)\)	n/a	1192	2
2100.3.bd	\(\chi_{2100}(901, \cdot)\)	2100.3.bd.a	2	2
		2100.3.bd.b	2
		2100.3.bd.c	2
		2100.3.bd.d	2
		2100.3.bd.e	2
		2100.3.bd.f	4
		2100.3.bd.g	8
		2100.3.bd.h	8
		2100.3.bd.i	8
		2100.3.bd.j	10
		2100.3.bd.k	10
		2100.3.bd.l	12
		2100.3.bd.m	16
		2100.3.bd.n	16
2100.3.be	\(\chi_{2100}(649, \cdot)\)	2100.3.be.a	4	2
		2100.3.be.b	4
		2100.3.be.c	4
		2100.3.be.d	8
		2100.3.be.e	16
		2100.3.be.f	16
		2100.3.be.g	20
		2100.3.be.h	24
2100.3.bf	\(\chi_{2100}(299, \cdot)\)	n/a	1136	2
2100.3.bh	\(\chi_{2100}(149, \cdot)\)	n/a	192	2
2100.3.bk	\(\chi_{2100}(499, \cdot)\)	n/a	576	2
2100.3.bm	\(\chi_{2100}(151, \cdot)\)	n/a	608	2
2100.3.bn	\(\chi_{2100}(401, \cdot)\)	n/a	202	2
2100.3.bp	\(\chi_{2100}(769, \cdot)\)	n/a	320	4
2100.3.bq	\(\chi_{2100}(419, \cdot)\)	n/a	3808	4
2100.3.bs	\(\chi_{2100}(671, \cdot)\)	n/a	3808	4
2100.3.bv	\(\chi_{2100}(181, \cdot)\)	n/a	320	4
2100.3.bx	\(\chi_{2100}(211, \cdot)\)	n/a	1440	4
2100.3.by	\(\chi_{2100}(281, \cdot)\)	n/a	480	4
2100.3.ca	\(\chi_{2100}(29, \cdot)\)	n/a	480	4
2100.3.cd	\(\chi_{2100}(379, \cdot)\)	n/a	1440	4
2100.3.cf	\(\chi_{2100}(107, \cdot)\)	n/a	2272	4
2100.3.cg	\(\chi_{2100}(193, \cdot)\)	n/a	192	4
2100.3.cj	\(\chi_{2100}(257, \cdot)\)	n/a	384	4
2100.3.ck	\(\chi_{2100}(607, \cdot)\)	n/a	1152	4
2100.3.cn	\(\chi_{2100}(323, \cdot)\)	n/a	5760	8
2100.3.cq	\(\chi_{2100}(253, \cdot)\)	n/a	480	8
2100.3.cr	\(\chi_{2100}(377, \cdot)\)	n/a	1280	8
2100.3.cu	\(\chi_{2100}(223, \cdot)\)	n/a	3840	8
2100.3.cw	\(\chi_{2100}(221, \cdot)\)	n/a	1280	8
2100.3.cx	\(\chi_{2100}(331, \cdot)\)	n/a	3840	8
2100.3.cz	\(\chi_{2100}(79, \cdot)\)	n/a	3840	8
2100.3.dc	\(\chi_{2100}(389, \cdot)\)	n/a	1280	8
2100.3.de	\(\chi_{2100}(59, \cdot)\)	n/a	7616	8
2100.3.df	\(\chi_{2100}(229, \cdot)\)	n/a	640	8
2100.3.dg	\(\chi_{2100}(61, \cdot)\)	n/a	640	8
2100.3.dj	\(\chi_{2100}(131, \cdot)\)	n/a	7616	8
2100.3.dl	\(\chi_{2100}(103, \cdot)\)	n/a	7680	16
2100.3.dm	\(\chi_{2100}(17, \cdot)\)	n/a	2560	16
2100.3.dp	\(\chi_{2100}(37, \cdot)\)	n/a	1280	16
2100.3.dq	\(\chi_{2100}(23, \cdot)\)	n/a	15232	16

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(2100))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(2100)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 18}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 24}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 18}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(350))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(420))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(525))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(700))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(1050))\)\(^{\oplus 2}\)