Space of modular forms of level 1875 and weight 2

• Label: 1875.2
• Level: 1875
• Weight: 2
• Dimension: 85632
• Nonzero newspaces: 12
• Sturm bound: 500000
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 1875 = 3 \cdot 5^{4} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(500000\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1875))\).

	Total	New	Old
Modular forms	127200	87168	40032
Cusp forms	122801	85632	37169
Eisenstein series	4399	1536	2863

Trace form

85632 * q - 160 * q^3 - 320 * q^4 - 288 * q^6 - 320 * q^7 - 160 * q^9 - 400 * q^10 - 160 * q^12 - 320 * q^13 - 200 * q^15 - 544 * q^16 + 20 * q^17 - 150 * q^18 - 280 * q^19 - 268 * q^21 - 240 * q^22 + 40 * q^23 - 90 * q^24 - 400 * q^25 + 40 * q^26 - 160 * q^27 - 200 * q^28 + 40 * q^29 - 200 * q^30 - 536 * q^31 + 70 * q^32 - 140 * q^33 - 270 * q^34 - 256 * q^36 - 310 * q^37 + 60 * q^38 - 120 * q^39 - 400 * q^40 + 40 * q^41 - 60 * q^42 - 240 * q^43 + 140 * q^44 - 200 * q^45 - 456 * q^46 + 80 * q^47 - 50 * q^48 - 210 * q^49 - 358 * q^51 - 100 * q^52 + 90 * q^53 - 30 * q^54 - 400 * q^55 + 120 * q^56 - 80 * q^57 - 180 * q^58 + 80 * q^59 - 200 * q^60 - 536 * q^61 + 100 * q^62 - 170 * q^63 - 260 * q^64 - 300 * q^66 - 320 * q^67 - 230 * q^69 - 400 * q^70 - 300 * q^72 - 320 * q^73 - 200 * q^75 - 772 * q^76 - 230 * q^78 - 320 * q^79 - 328 * q^81 - 240 * q^82 + 80 * q^83 - 200 * q^84 - 400 * q^85 + 120 * q^86 - 130 * q^87 - 80 * q^88 + 150 * q^89 - 200 * q^90 - 416 * q^91 + 200 * q^92 - 50 * q^93 - 484 * q^96 - 40 * q^97 + 280 * q^98 - 150 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1875))\)

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
1875.2.a	\(\chi_{1875}(1, \cdot)\)	1875.2.a.a	2	1
		1875.2.a.b	2
		1875.2.a.c	2
		1875.2.a.d	2
		1875.2.a.e	4
		1875.2.a.f	4
		1875.2.a.g	4
		1875.2.a.h	4
		1875.2.a.i	6
		1875.2.a.j	6
		1875.2.a.k	6
		1875.2.a.l	6
		1875.2.a.m	8
		1875.2.a.n	8
		1875.2.a.o	8
		1875.2.a.p	8
1875.2.b	\(\chi_{1875}(1249, \cdot)\)	1875.2.b.a	4	1
		1875.2.b.b	4
		1875.2.b.c	8
		1875.2.b.d	8
		1875.2.b.e	12
		1875.2.b.f	12
		1875.2.b.g	16
		1875.2.b.h	16
1875.2.e	\(\chi_{1875}(182, \cdot)\)	n/a	288	2
1875.2.g	\(\chi_{1875}(376, \cdot)\)	n/a	320	4
1875.2.i	\(\chi_{1875}(124, \cdot)\)	n/a	320	4
1875.2.l	\(\chi_{1875}(68, \cdot)\)	n/a	1184	8
1875.2.m	\(\chi_{1875}(76, \cdot)\)	n/a	1480	20
1875.2.o	\(\chi_{1875}(49, \cdot)\)	n/a	1520	20
1875.2.r	\(\chi_{1875}(32, \cdot)\)	n/a	5760	40
1875.2.s	\(\chi_{1875}(16, \cdot)\)	n/a	12600	100
1875.2.v	\(\chi_{1875}(4, \cdot)\)	n/a	12400	100
1875.2.x	\(\chi_{1875}(2, \cdot)\)	n/a	49600	200

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1875))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1875)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(125))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(375))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(625))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1875))\)\(^{\oplus 1}\)