Space of modular forms of level 1725 and weight 2

• Label: 1725.2
• Level: 1725
• Weight: 2
• Dimension: 71856
• Nonzero newspaces: 24
• Sturm bound: 422400
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 1725 = 3 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(422400\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1725))\).

	Total	New	Old
Modular forms	108064	73580	34484
Cusp forms	103137	71856	31281
Eisenstein series	4927	1724	3203

Trace form

71856 * q + 2 * q^2 - 125 * q^3 - 236 * q^4 + 12 * q^5 - 185 * q^6 - 230 * q^7 + 42 * q^8 - 117 * q^9 - 284 * q^10 + 8 * q^11 - 105 * q^12 - 226 * q^13 + 48 * q^14 - 148 * q^15 - 352 * q^16 + 26 * q^17 - 97 * q^18 - 248 * q^19 - 72 * q^20 - 186 * q^21 - 252 * q^22 + 28 * q^23 - 322 * q^24 - 380 * q^25 + 56 * q^26 - 92 * q^27 - 286 * q^28 - 6 * q^29 - 204 * q^30 - 384 * q^31 + 10 * q^32 - 112 * q^33 - 202 * q^34 + 40 * q^35 - 227 * q^36 - 142 * q^37 + 94 * q^38 - 123 * q^39 - 356 * q^40 + 88 * q^41 - 165 * q^42 - 214 * q^43 + 58 * q^44 - 304 * q^45 - 298 * q^46 + 56 * q^47 - 167 * q^48 - 248 * q^49 - 212 * q^50 - 443 * q^51 - 262 * q^52 - 68 * q^53 - 373 * q^54 - 360 * q^55 + 110 * q^56 - 248 * q^57 - 228 * q^58 - 12 * q^59 - 204 * q^60 - 354 * q^61 - 8 * q^62 - 142 * q^63 - 84 * q^64 + 116 * q^65 - 170 * q^66 - 62 * q^67 + 244 * q^68 - 94 * q^69 - 424 * q^70 + 112 * q^71 + 67 * q^72 - 58 * q^73 + 290 * q^74 + 52 * q^75 - 544 * q^76 + 280 * q^77 + 137 * q^78 + 2 * q^79 + 308 * q^80 - 21 * q^81 - 62 * q^82 + 144 * q^83 + 157 * q^84 - 428 * q^85 + 228 * q^86 + 17 * q^87 - 854 * q^88 - 12 * q^89 - 128 * q^90 - 288 * q^91 + 166 * q^92 - 290 * q^93 - 388 * q^94 - 200 * q^95 - 440 * q^96 - 932 * q^97 - 630 * q^98 - 157 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1725))\)

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
1725.2.a	\(\chi_{1725}(1, \cdot)\)	1725.2.a.a	1	1
		1725.2.a.b	1
		1725.2.a.c	1
		1725.2.a.d	1
		1725.2.a.e	1
		1725.2.a.f	1
		1725.2.a.g	1
		1725.2.a.h	1
		1725.2.a.i	1
		1725.2.a.j	1
		1725.2.a.k	1
		1725.2.a.l	1
		1725.2.a.m	1
		1725.2.a.n	1
		1725.2.a.o	1
		1725.2.a.p	1
		1725.2.a.q	1
		1725.2.a.r	1
		1725.2.a.s	1
		1725.2.a.t	1
		1725.2.a.u	1
		1725.2.a.v	2
		1725.2.a.w	2
		1725.2.a.x	2
		1725.2.a.y	2
		1725.2.a.z	2
		1725.2.a.ba	2
		1725.2.a.bb	2
		1725.2.a.bc	2
		1725.2.a.bd	2
		1725.2.a.be	2
		1725.2.a.bf	3
		1725.2.a.bg	3
		1725.2.a.bh	3
		1725.2.a.bi	3
		1725.2.a.bj	3
		1725.2.a.bk	7
		1725.2.a.bl	7
1725.2.b	\(\chi_{1725}(1174, \cdot)\)	1725.2.b.a	2	1
		1725.2.b.b	2
		1725.2.b.c	2
		1725.2.b.d	2
		1725.2.b.e	2
		1725.2.b.f	2
		1725.2.b.g	2
		1725.2.b.h	2
		1725.2.b.i	2
		1725.2.b.j	2
		1725.2.b.k	2
		1725.2.b.l	2
		1725.2.b.m	4
		1725.2.b.n	4
		1725.2.b.o	4
		1725.2.b.p	4
		1725.2.b.q	4
		1725.2.b.r	4
		1725.2.b.s	4
		1725.2.b.t	6
		1725.2.b.u	6
1725.2.c	\(\chi_{1725}(551, \cdot)\)	n/a	146	1
1725.2.h	\(\chi_{1725}(1724, \cdot)\)	n/a	140	1
1725.2.i	\(\chi_{1725}(668, \cdot)\)	n/a	264	2
1725.2.j	\(\chi_{1725}(643, \cdot)\)	n/a	144	2
1725.2.m	\(\chi_{1725}(346, \cdot)\)	n/a	432	4
1725.2.p	\(\chi_{1725}(344, \cdot)\)	n/a	944	4
1725.2.q	\(\chi_{1725}(206, \cdot)\)	n/a	944	4
1725.2.r	\(\chi_{1725}(139, \cdot)\)	n/a	448	4
1725.2.u	\(\chi_{1725}(151, \cdot)\)	n/a	760	10
1725.2.x	\(\chi_{1725}(22, \cdot)\)	n/a	960	8
1725.2.y	\(\chi_{1725}(47, \cdot)\)	n/a	1760	8
1725.2.z	\(\chi_{1725}(74, \cdot)\)	n/a	1400	10
1725.2.be	\(\chi_{1725}(176, \cdot)\)	n/a	1460	10
1725.2.bf	\(\chi_{1725}(49, \cdot)\)	n/a	720	10
1725.2.bi	\(\chi_{1725}(7, \cdot)\)	n/a	1440	20
1725.2.bj	\(\chi_{1725}(32, \cdot)\)	n/a	2800	20
1725.2.bk	\(\chi_{1725}(16, \cdot)\)	n/a	4800	40
1725.2.bn	\(\chi_{1725}(4, \cdot)\)	n/a	4800	40
1725.2.bo	\(\chi_{1725}(11, \cdot)\)	n/a	9440	40
1725.2.bp	\(\chi_{1725}(14, \cdot)\)	n/a	9440	40
1725.2.bs	\(\chi_{1725}(2, \cdot)\)	n/a	18880	80
1725.2.bt	\(\chi_{1725}(28, \cdot)\)	n/a	9600	80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1725))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1725)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(345))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(575))\)\(^{\oplus 2}\)