Space of modular forms of level 2700 and weight 2

• Label: 2700.2
• Level: 2700
• Weight: 2
• Dimension: 81925
• Nonzero newspaces: 36
• Sturm bound: 777600
• Trace bound: 16

Defining parameters

Level:	\( N \)	=	\( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 36 \)
Sturm bound:			\(777600\)
Trace bound:			\(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2700))\).

	Total	New	Old
Modular forms	198600	83237	115363
Cusp forms	190201	81925	108276
Eisenstein series	8399	1312	7087

Trace form

81925 * q - 51 * q^2 - 89 * q^4 - 128 * q^5 - 126 * q^6 + 6 * q^7 - 57 * q^8 - 150 * q^9 - 112 * q^10 + 22 * q^11 - 87 * q^12 - 168 * q^13 - 89 * q^14 - 169 * q^16 - 114 * q^17 - 99 * q^18 + 7 * q^19 - 80 * q^20 - 282 * q^21 - 137 * q^22 - 57 * q^23 - 84 * q^24 - 240 * q^25 - 224 * q^26 - 27 * q^27 - 262 * q^28 - 211 * q^29 - 96 * q^30 - 32 * q^31 - 71 * q^32 - 228 * q^33 - 125 * q^34 - 84 * q^35 - 96 * q^36 - 279 * q^37 - 43 * q^38 - 117 * q^39 - 128 * q^40 - 378 * q^41 - 18 * q^42 - 128 * q^43 + 55 * q^44 - 252 * q^45 - 115 * q^46 - 180 * q^47 - 3 * q^48 - 376 * q^49 - 24 * q^50 - 33 * q^51 - 29 * q^52 - 330 * q^53 + 6 * q^54 - 40 * q^55 + 113 * q^56 - 186 * q^57 + 19 * q^58 - 43 * q^59 - 96 * q^60 - 420 * q^61 + 146 * q^62 + 57 * q^63 + 25 * q^64 - 256 * q^65 - 33 * q^66 - 89 * q^67 + 282 * q^68 - 141 * q^69 - 32 * q^70 - 20 * q^71 + 132 * q^72 - 180 * q^73 + 351 * q^74 + 72 * q^75 - 73 * q^76 - 20 * q^77 + 216 * q^78 + 68 * q^79 + 256 * q^80 - 90 * q^81 + 134 * q^82 + 262 * q^83 + 372 * q^84 - 208 * q^85 + 589 * q^86 + 177 * q^87 + 247 * q^88 + 384 * q^89 + 132 * q^90 + 256 * q^91 + 597 * q^92 + 171 * q^93 + 235 * q^94 + 232 * q^95 + 174 * q^96 - 27 * q^97 + 612 * q^98 + 267 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2700))\)

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
2700.2.a	\(\chi_{2700}(1, \cdot)\)	2700.2.a.a	1	1
		2700.2.a.b	1
		2700.2.a.c	1
		2700.2.a.d	1
		2700.2.a.e	1
		2700.2.a.f	1
		2700.2.a.g	1
		2700.2.a.h	1
		2700.2.a.i	1
		2700.2.a.j	1
		2700.2.a.k	1
		2700.2.a.l	1
		2700.2.a.m	1
		2700.2.a.n	1
		2700.2.a.o	1
		2700.2.a.p	1
		2700.2.a.q	1
		2700.2.a.r	1
		2700.2.a.s	1
		2700.2.a.t	1
		2700.2.a.u	1
		2700.2.a.v	2
		2700.2.a.w	2
2700.2.d	\(\chi_{2700}(649, \cdot)\)	2700.2.d.a	2	1
		2700.2.d.b	2
		2700.2.d.c	2
		2700.2.d.d	2
		2700.2.d.e	2
		2700.2.d.f	2
		2700.2.d.g	2
		2700.2.d.h	2
		2700.2.d.i	2
		2700.2.d.j	2
		2700.2.d.k	2
		2700.2.d.l	2
2700.2.e	\(\chi_{2700}(2051, \cdot)\)	n/a	152	1
2700.2.h	\(\chi_{2700}(2699, \cdot)\)	n/a	144	1
2700.2.i	\(\chi_{2700}(901, \cdot)\)	2700.2.i.a	2	2
		2700.2.i.b	2
		2700.2.i.c	6
		2700.2.i.d	8
		2700.2.i.e	8
		2700.2.i.f	12
2700.2.j	\(\chi_{2700}(593, \cdot)\)	2700.2.j.a	4	2
		2700.2.j.b	4
		2700.2.j.c	4
		2700.2.j.d	4
		2700.2.j.e	4
		2700.2.j.f	4
		2700.2.j.g	4
		2700.2.j.h	4
		2700.2.j.i	8
		2700.2.j.j	8
2700.2.k	\(\chi_{2700}(1243, \cdot)\)	n/a	288	2
2700.2.n	\(\chi_{2700}(541, \cdot)\)	n/a	160	4
2700.2.o	\(\chi_{2700}(899, \cdot)\)	n/a	208	2
2700.2.r	\(\chi_{2700}(251, \cdot)\)	n/a	216	2
2700.2.s	\(\chi_{2700}(1549, \cdot)\)	2700.2.s.a	4	2
		2700.2.s.b	4
		2700.2.s.c	12
		2700.2.s.d	16
2700.2.v	\(\chi_{2700}(301, \cdot)\)	n/a	342	6
2700.2.w	\(\chi_{2700}(431, \cdot)\)	n/a	960	4
2700.2.x	\(\chi_{2700}(109, \cdot)\)	n/a	160	4
2700.2.ba	\(\chi_{2700}(539, \cdot)\)	n/a	960	4
2700.2.bf	\(\chi_{2700}(557, \cdot)\)	2700.2.bf.a	4	4
		2700.2.bf.b	4
		2700.2.bf.c	4
		2700.2.bf.d	4
		2700.2.bf.e	24
		2700.2.bf.f	32
2700.2.bg	\(\chi_{2700}(307, \cdot)\)	n/a	416	4
2700.2.bh	\(\chi_{2700}(181, \cdot)\)	n/a	240	8
2700.2.bk	\(\chi_{2700}(299, \cdot)\)	n/a	1920	6
2700.2.bm	\(\chi_{2700}(49, \cdot)\)	n/a	324	6
2700.2.bn	\(\chi_{2700}(551, \cdot)\)	n/a	2016	6
2700.2.br	\(\chi_{2700}(163, \cdot)\)	n/a	1920	8
2700.2.bs	\(\chi_{2700}(53, \cdot)\)	n/a	320	8
2700.2.bv	\(\chi_{2700}(179, \cdot)\)	n/a	1408	8
2700.2.by	\(\chi_{2700}(289, \cdot)\)	n/a	240	8
2700.2.bz	\(\chi_{2700}(71, \cdot)\)	n/a	1408	8
2700.2.cb	\(\chi_{2700}(7, \cdot)\)	n/a	3840	12
2700.2.cd	\(\chi_{2700}(257, \cdot)\)	n/a	648	12
2700.2.ce	\(\chi_{2700}(61, \cdot)\)	n/a	2160	24
2700.2.cf	\(\chi_{2700}(127, \cdot)\)	n/a	2816	16
2700.2.cg	\(\chi_{2700}(17, \cdot)\)	n/a	480	16
2700.2.ck	\(\chi_{2700}(11, \cdot)\)	n/a	12864	24
2700.2.cl	\(\chi_{2700}(169, \cdot)\)	n/a	2160	24
2700.2.cn	\(\chi_{2700}(59, \cdot)\)	n/a	12864	24
2700.2.cq	\(\chi_{2700}(77, \cdot)\)	n/a	4320	48
2700.2.cs	\(\chi_{2700}(67, \cdot)\)	n/a	25728	48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2700))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2700)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 27}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(270))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(450))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(540))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(675))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(900))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1350))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2700))\)\(^{\oplus 1}\)