Space of modular forms of level 2175 and weight 4

• Label: 2175.4
• Level: 2175
• Weight: 4
• Dimension: 346454
• Nonzero newspaces: 40
• Sturm bound: 1344000
• Trace bound: 6

Defining parameters

Level:	\( N \)	=	\( 2175 = 3 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 40 \)
Sturm bound:			\(1344000\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2175))\).

	Total	New	Old
Modular forms	507136	348670	158466
Cusp forms	500864	346454	154410
Eisenstein series	6272	2216	4056

Trace form

346454 * q + 16 * q^2 - 186 * q^3 - 420 * q^4 + 12 * q^5 - 258 * q^6 - 404 * q^7 - 144 * q^8 - 234 * q^9 - 600 * q^10 - 224 * q^11 + 270 * q^12 + 332 * q^13 + 1056 * q^14 + 144 * q^15 - 324 * q^16 - 1120 * q^17 - 1338 * q^18 - 1828 * q^19 - 312 * q^20 - 1346 * q^21 + 1260 * q^22 + 664 * q^23 + 874 * q^24 + 2644 * q^25 + 1148 * q^26 + 1554 * q^27 + 2232 * q^28 + 168 * q^29 + 1324 * q^30 - 660 * q^31 - 5808 * q^32 - 2466 * q^33 - 9056 * q^34 - 4480 * q^35 - 1714 * q^36 - 6272 * q^37 - 8056 * q^38 - 5242 * q^39 - 8912 * q^40 - 3296 * q^41 - 410 * q^42 + 2604 * q^43 + 11732 * q^44 + 4688 * q^45 + 20432 * q^46 + 10776 * q^47 + 12794 * q^48 + 10736 * q^49 + 16448 * q^50 + 2506 * q^51 + 9364 * q^52 + 2446 * q^53 + 6514 * q^54 + 2584 * q^55 - 9100 * q^56 - 476 * q^57 - 22604 * q^58 - 7656 * q^59 - 372 * q^60 - 7732 * q^61 - 27404 * q^62 - 190 * q^63 - 18528 * q^64 - 2444 * q^65 + 2910 * q^66 + 3868 * q^67 + 10996 * q^68 - 1546 * q^69 - 3528 * q^70 + 4248 * q^71 - 33830 * q^72 + 566 * q^73 - 7484 * q^74 - 19016 * q^75 - 18764 * q^76 - 6912 * q^77 - 15374 * q^78 - 6404 * q^79 + 2008 * q^80 + 6550 * q^81 - 17796 * q^82 - 22208 * q^83 + 4920 * q^84 - 25524 * q^85 - 2384 * q^86 + 3876 * q^87 - 7792 * q^88 - 6804 * q^89 + 21564 * q^90 + 14492 * q^91 + 21424 * q^92 + 29118 * q^93 + 57500 * q^94 + 31888 * q^95 + 40352 * q^96 + 83938 * q^97 + 82676 * q^98 + 16534 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2175))\)

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
2175.4.a	\(\chi_{2175}(1, \cdot)\)	2175.4.a.a	1	1
		2175.4.a.b	1
		2175.4.a.c	1
		2175.4.a.d	2
		2175.4.a.e	2
		2175.4.a.f	2
		2175.4.a.g	2
		2175.4.a.h	5
		2175.4.a.i	5
		2175.4.a.j	5
		2175.4.a.k	6
		2175.4.a.l	6
		2175.4.a.m	7
		2175.4.a.n	7
		2175.4.a.o	8
		2175.4.a.p	10
		2175.4.a.q	10
		2175.4.a.r	10
		2175.4.a.s	12
		2175.4.a.t	12
		2175.4.a.u	16
		2175.4.a.v	16
		2175.4.a.w	18
		2175.4.a.x	18
		2175.4.a.y	21
		2175.4.a.z	21
		2175.4.a.ba	21
		2175.4.a.bb	21
2175.4.c	\(\chi_{2175}(349, \cdot)\)	n/a	252	1
2175.4.d	\(\chi_{2175}(376, \cdot)\)	n/a	284	1
2175.4.f	\(\chi_{2175}(724, \cdot)\)	n/a	272	1
2175.4.j	\(\chi_{2175}(157, \cdot)\)	n/a	540	2
2175.4.l	\(\chi_{2175}(824, \cdot)\)	n/a	1072	2
2175.4.m	\(\chi_{2175}(407, \cdot)\)	n/a	1008	2
2175.4.p	\(\chi_{2175}(782, \cdot)\)	n/a	1072	2
2175.4.q	\(\chi_{2175}(476, \cdot)\)	n/a	1128	2
2175.4.s	\(\chi_{2175}(307, \cdot)\)	n/a	540	2
2175.4.u	\(\chi_{2175}(436, \cdot)\)	n/a	1680	4
2175.4.v	\(\chi_{2175}(226, \cdot)\)	n/a	1716	6
2175.4.x	\(\chi_{2175}(289, \cdot)\)	n/a	1792	4
2175.4.z	\(\chi_{2175}(784, \cdot)\)	n/a	1680	4
2175.4.bc	\(\chi_{2175}(811, \cdot)\)	n/a	1808	4
2175.4.bf	\(\chi_{2175}(274, \cdot)\)	n/a	1632	6
2175.4.bh	\(\chi_{2175}(151, \cdot)\)	n/a	1704	6
2175.4.bi	\(\chi_{2175}(49, \cdot)\)	n/a	1608	6
2175.4.bl	\(\chi_{2175}(742, \cdot)\)	n/a	3600	8
2175.4.bm	\(\chi_{2175}(104, \cdot)\)	n/a	7168	8
2175.4.bo	\(\chi_{2175}(173, \cdot)\)	n/a	7168	8
2175.4.br	\(\chi_{2175}(233, \cdot)\)	n/a	6720	8
2175.4.bt	\(\chi_{2175}(41, \cdot)\)	n/a	7168	8
2175.4.bu	\(\chi_{2175}(133, \cdot)\)	n/a	3600	8
2175.4.bx	\(\chi_{2175}(757, \cdot)\)	n/a	3240	12
2175.4.bz	\(\chi_{2175}(26, \cdot)\)	n/a	6768	12
2175.4.ca	\(\chi_{2175}(332, \cdot)\)	n/a	6432	12
2175.4.cd	\(\chi_{2175}(107, \cdot)\)	n/a	6432	12
2175.4.ce	\(\chi_{2175}(224, \cdot)\)	n/a	6432	12
2175.4.cg	\(\chi_{2175}(43, \cdot)\)	n/a	3240	12
2175.4.ci	\(\chi_{2175}(16, \cdot)\)	n/a	10752	24
2175.4.cj	\(\chi_{2175}(91, \cdot)\)	n/a	10848	24
2175.4.cm	\(\chi_{2175}(94, \cdot)\)	n/a	10848	24
2175.4.co	\(\chi_{2175}(4, \cdot)\)	n/a	10752	24
2175.4.cr	\(\chi_{2175}(37, \cdot)\)	n/a	21600	48
2175.4.cs	\(\chi_{2175}(11, \cdot)\)	n/a	43008	48
2175.4.cu	\(\chi_{2175}(23, \cdot)\)	n/a	43008	48
2175.4.cx	\(\chi_{2175}(38, \cdot)\)	n/a	43008	48
2175.4.cz	\(\chi_{2175}(14, \cdot)\)	n/a	43008	48
2175.4.da	\(\chi_{2175}(73, \cdot)\)	n/a	21600	48

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2175))\) into lower level spaces

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