Space of modular forms of level 2175 and weight 2

• Label: 2175.2
• Level: 2175
• Weight: 2
• Dimension: 114744
• Nonzero newspaces: 40
• Sturm bound: 672000
• Trace bound: 6

Defining parameters

Level:	\( N \)	=	\( 2175 = 3 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 40 \)
Sturm bound:			\(672000\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2175))\).

	Total	New	Old
Modular forms	171136	116960	54176
Cusp forms	164865	114744	50121
Eisenstein series	6271	2216	4055

Trace form

114744 * q + 2 * q^2 - 164 * q^3 - 314 * q^4 + 12 * q^5 - 248 * q^6 - 308 * q^7 + 42 * q^8 - 156 * q^9 - 380 * q^10 + 8 * q^11 - 144 * q^12 - 304 * q^13 + 48 * q^14 - 196 * q^15 - 522 * q^16 + 4 * q^17 - 180 * q^18 - 348 * q^19 - 72 * q^20 - 254 * q^21 - 340 * q^22 - 4 * q^23 - 200 * q^24 - 476 * q^25 + 82 * q^26 - 122 * q^27 - 312 * q^28 + 42 * q^29 - 476 * q^30 - 476 * q^31 + 78 * q^32 - 120 * q^33 - 254 * q^34 + 40 * q^35 - 228 * q^36 - 280 * q^37 + 40 * q^38 - 178 * q^39 - 452 * q^40 + 44 * q^41 - 314 * q^42 - 380 * q^43 - 68 * q^44 - 352 * q^45 - 472 * q^46 + 24 * q^47 - 204 * q^48 - 346 * q^49 - 212 * q^50 - 554 * q^51 - 336 * q^52 + 14 * q^53 - 412 * q^54 - 456 * q^55 + 196 * q^56 - 228 * q^57 - 54 * q^58 - 252 * q^60 - 368 * q^61 + 188 * q^62 - 98 * q^63 + 90 * q^64 + 116 * q^65 - 66 * q^66 - 28 * q^67 + 440 * q^68 + 82 * q^69 - 168 * q^70 + 168 * q^71 + 104 * q^72 - 66 * q^73 + 296 * q^74 + 4 * q^75 - 900 * q^76 + 192 * q^77 - 58 * q^78 - 164 * q^79 + 308 * q^80 - 284 * q^81 - 272 * q^82 + 56 * q^83 - 96 * q^84 - 524 * q^85 + 8 * q^86 - 238 * q^87 - 856 * q^88 - 144 * q^89 - 176 * q^90 - 612 * q^91 - 64 * q^92 - 374 * q^93 - 708 * q^94 - 112 * q^95 - 514 * q^96 - 582 * q^97 - 50 * q^98 - 132 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2175))\)

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
2175.2.a	\(\chi_{2175}(1, \cdot)\)	2175.2.a.a	1	1
		2175.2.a.b	1
		2175.2.a.c	1
		2175.2.a.d	1
		2175.2.a.e	1
		2175.2.a.f	1
		2175.2.a.g	1
		2175.2.a.h	1
		2175.2.a.i	1
		2175.2.a.j	1
		2175.2.a.k	2
		2175.2.a.l	2
		2175.2.a.m	2
		2175.2.a.n	2
		2175.2.a.o	2
		2175.2.a.p	2
		2175.2.a.q	2
		2175.2.a.r	2
		2175.2.a.s	2
		2175.2.a.t	3
		2175.2.a.u	3
		2175.2.a.v	4
		2175.2.a.w	5
		2175.2.a.x	5
		2175.2.a.y	5
		2175.2.a.z	5
		2175.2.a.ba	7
		2175.2.a.bb	7
		2175.2.a.bc	8
		2175.2.a.bd	8
2175.2.c	\(\chi_{2175}(349, \cdot)\)	2175.2.c.a	2	1
		2175.2.c.b	2
		2175.2.c.c	2
		2175.2.c.d	2
		2175.2.c.e	2
		2175.2.c.f	4
		2175.2.c.g	4
		2175.2.c.h	4
		2175.2.c.i	4
		2175.2.c.j	4
		2175.2.c.k	4
		2175.2.c.l	6
		2175.2.c.m	6
		2175.2.c.n	8
		2175.2.c.o	14
		2175.2.c.p	16
2175.2.d	\(\chi_{2175}(376, \cdot)\)	2175.2.d.a	2	1
		2175.2.d.b	2
		2175.2.d.c	2
		2175.2.d.d	2
		2175.2.d.e	4
		2175.2.d.f	10
		2175.2.d.g	10
		2175.2.d.h	20
		2175.2.d.i	20
		2175.2.d.j	24
2175.2.f	\(\chi_{2175}(724, \cdot)\)	2175.2.f.a	4	1
		2175.2.f.b	4
		2175.2.f.c	10
		2175.2.f.d	10
		2175.2.f.e	10
		2175.2.f.f	10
		2175.2.f.g	20
		2175.2.f.h	20
2175.2.j	\(\chi_{2175}(157, \cdot)\)	n/a	180	2
2175.2.l	\(\chi_{2175}(824, \cdot)\)	n/a	352	2
2175.2.m	\(\chi_{2175}(407, \cdot)\)	n/a	336	2
2175.2.p	\(\chi_{2175}(782, \cdot)\)	n/a	352	2
2175.2.q	\(\chi_{2175}(476, \cdot)\)	n/a	368	2
2175.2.s	\(\chi_{2175}(307, \cdot)\)	n/a	180	2
2175.2.u	\(\chi_{2175}(436, \cdot)\)	n/a	560	4
2175.2.v	\(\chi_{2175}(226, \cdot)\)	n/a	564	6
2175.2.x	\(\chi_{2175}(289, \cdot)\)	n/a	608	4
2175.2.z	\(\chi_{2175}(784, \cdot)\)	n/a	560	4
2175.2.bc	\(\chi_{2175}(811, \cdot)\)	n/a	592	4
2175.2.bf	\(\chi_{2175}(274, \cdot)\)	n/a	528	6
2175.2.bh	\(\chi_{2175}(151, \cdot)\)	n/a	576	6
2175.2.bi	\(\chi_{2175}(49, \cdot)\)	n/a	552	6
2175.2.bl	\(\chi_{2175}(742, \cdot)\)	n/a	1200	8
2175.2.bm	\(\chi_{2175}(104, \cdot)\)	n/a	2368	8
2175.2.bo	\(\chi_{2175}(173, \cdot)\)	n/a	2368	8
2175.2.br	\(\chi_{2175}(233, \cdot)\)	n/a	2240	8
2175.2.bt	\(\chi_{2175}(41, \cdot)\)	n/a	2368	8
2175.2.bu	\(\chi_{2175}(133, \cdot)\)	n/a	1200	8
2175.2.bx	\(\chi_{2175}(757, \cdot)\)	n/a	1080	12
2175.2.bz	\(\chi_{2175}(26, \cdot)\)	n/a	2208	12
2175.2.ca	\(\chi_{2175}(332, \cdot)\)	n/a	2112	12
2175.2.cd	\(\chi_{2175}(107, \cdot)\)	n/a	2112	12
2175.2.ce	\(\chi_{2175}(224, \cdot)\)	n/a	2112	12
2175.2.cg	\(\chi_{2175}(43, \cdot)\)	n/a	1080	12
2175.2.ci	\(\chi_{2175}(16, \cdot)\)	n/a	3648	24
2175.2.cj	\(\chi_{2175}(91, \cdot)\)	n/a	3552	24
2175.2.cm	\(\chi_{2175}(94, \cdot)\)	n/a	3552	24
2175.2.co	\(\chi_{2175}(4, \cdot)\)	n/a	3648	24
2175.2.cr	\(\chi_{2175}(37, \cdot)\)	n/a	7200	48
2175.2.cs	\(\chi_{2175}(11, \cdot)\)	n/a	14208	48
2175.2.cu	\(\chi_{2175}(23, \cdot)\)	n/a	14208	48
2175.2.cx	\(\chi_{2175}(38, \cdot)\)	n/a	14208	48
2175.2.cz	\(\chi_{2175}(14, \cdot)\)	n/a	14208	48
2175.2.da	\(\chi_{2175}(73, \cdot)\)	n/a	7200	48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2175))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2175)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(145))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(435))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(725))\)\(^{\oplus 2}\)