Space of modular forms of level 175 and weight 4

• Label: 175.4
• Level: 175
• Weight: 4
• Dimension: 3077
• Nonzero newspaces: 12
• Newform subspaces: 46
• Sturm bound: 9600
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 46 \)
Sturm bound:			\(9600\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(175))\).

	Total	New	Old
Modular forms	3768	3281	487
Cusp forms	3432	3077	355
Eisenstein series	336	204	132

Trace form

3077 * q - 35 * q^2 - 17 * q^3 + 13 * q^4 - 38 * q^5 - 26 * q^6 + 7 * q^7 - 85 * q^8 - 153 * q^9 + 12 * q^10 + 101 * q^11 + 90 * q^12 - 168 * q^13 - 53 * q^14 - 96 * q^15 + 289 * q^16 + 803 * q^17 + 1231 * q^18 + 465 * q^19 - 388 * q^20 - 489 * q^21 - 2016 * q^22 - 1001 * q^23 - 1202 * q^24 - 746 * q^25 + 1488 * q^26 + 118 * q^27 + 307 * q^28 - 598 * q^29 - 476 * q^30 - 927 * q^31 - 1105 * q^32 - 1629 * q^33 - 510 * q^34 - 432 * q^35 - 4227 * q^36 - 363 * q^37 + 1264 * q^38 + 2922 * q^39 + 3784 * q^40 + 2250 * q^41 + 4124 * q^42 + 2860 * q^43 + 3760 * q^44 - 1702 * q^45 + 1758 * q^46 - 2785 * q^47 - 7710 * q^48 - 1659 * q^49 - 9096 * q^50 - 5457 * q^51 - 7528 * q^52 - 3803 * q^53 - 802 * q^54 + 1516 * q^55 + 10121 * q^56 + 11126 * q^57 + 16094 * q^58 + 13435 * q^59 + 25412 * q^60 + 5901 * q^61 + 20020 * q^62 + 3049 * q^63 + 2817 * q^64 + 334 * q^65 - 14194 * q^66 - 13219 * q^67 - 24822 * q^68 - 22346 * q^69 - 16658 * q^70 - 11460 * q^71 - 40821 * q^72 - 19821 * q^73 - 32180 * q^74 - 15512 * q^75 - 14758 * q^76 - 6723 * q^77 - 10168 * q^78 + 2639 * q^79 - 6512 * q^80 + 15264 * q^81 + 33310 * q^82 + 26402 * q^83 + 45328 * q^84 + 27402 * q^85 + 40856 * q^86 + 42638 * q^87 + 61424 * q^88 + 32013 * q^89 + 29040 * q^90 + 8202 * q^91 + 23324 * q^92 - 5549 * q^93 - 14094 * q^94 - 15012 * q^95 - 21166 * q^96 - 32894 * q^97 - 25153 * q^98 - 40980 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(175))\)

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
175.4.a	\(\chi_{175}(1, \cdot)\)	175.4.a.a	1	1
		175.4.a.b	1
		175.4.a.c	2
		175.4.a.d	2
		175.4.a.e	2
		175.4.a.f	3
		175.4.a.g	4
		175.4.a.h	4
		175.4.a.i	5
		175.4.a.j	5
175.4.b	\(\chi_{175}(99, \cdot)\)	175.4.b.a	2	1
		175.4.b.b	2
		175.4.b.c	4
		175.4.b.d	4
		175.4.b.e	6
		175.4.b.f	8
175.4.e	\(\chi_{175}(51, \cdot)\)	175.4.e.a	2	2
		175.4.e.b	2
		175.4.e.c	4
		175.4.e.d	10
		175.4.e.e	16
		175.4.e.f	16
		175.4.e.g	20
175.4.f	\(\chi_{175}(118, \cdot)\)	175.4.f.a	4	2
		175.4.f.b	4
		175.4.f.c	4
		175.4.f.d	4
		175.4.f.e	4
		175.4.f.f	8
		175.4.f.g	16
		175.4.f.h	24
175.4.h	\(\chi_{175}(36, \cdot)\)	175.4.h.a	88	4
		175.4.h.b	88
175.4.k	\(\chi_{175}(74, \cdot)\)	175.4.k.a	4	2
		175.4.k.b	4
		175.4.k.c	8
		175.4.k.d	20
		175.4.k.e	32
175.4.n	\(\chi_{175}(29, \cdot)\)	175.4.n.a	184	4
175.4.o	\(\chi_{175}(68, \cdot)\)	175.4.o.a	32	4
		175.4.o.b	40
		175.4.o.c	64
175.4.q	\(\chi_{175}(11, \cdot)\)	175.4.q.a	464	8
175.4.s	\(\chi_{175}(13, \cdot)\)	175.4.s.a	464	8
175.4.t	\(\chi_{175}(4, \cdot)\)	175.4.t.a	464	8
175.4.x	\(\chi_{175}(3, \cdot)\)	175.4.x.a	928	16

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(175))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(175)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 2}\)