Space of modular forms of level 175 and weight 2

• Label: 175.2
• Level: 175
• Weight: 2
• Dimension: 959
• Nonzero newspaces: 12
• Newform subspaces: 32
• Sturm bound: 4800
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 32 \)
Sturm bound:			\(4800\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(175))\).

	Total	New	Old
Modular forms	1368	1163	205
Cusp forms	1033	959	74
Eisenstein series	335	204	131

Trace form

959 * q - 25 * q^2 - 28 * q^3 - 37 * q^4 - 38 * q^5 - 60 * q^6 - 41 * q^7 - 97 * q^8 - 55 * q^9 - 58 * q^10 - 60 * q^11 - 100 * q^12 - 58 * q^13 - 71 * q^14 - 116 * q^15 - 85 * q^16 - 50 * q^17 - 83 * q^18 - 36 * q^19 - 28 * q^20 - 82 * q^21 - 80 * q^22 - 48 * q^23 + 40 * q^24 - 6 * q^25 - 102 * q^26 - 4 * q^27 + 25 * q^28 - 54 * q^29 + 4 * q^30 - 32 * q^31 + 9 * q^32 - 8 * q^34 - 32 * q^35 - 53 * q^36 - 48 * q^37 - 40 * q^38 + 16 * q^39 - 6 * q^40 - 62 * q^41 + 38 * q^42 - 56 * q^43 - 32 * q^44 + 38 * q^45 - 72 * q^46 - 56 * q^47 + 56 * q^48 - 105 * q^49 - 46 * q^50 - 160 * q^51 + 6 * q^52 - 88 * q^53 + 28 * q^54 - 44 * q^55 - 79 * q^56 - 36 * q^57 + 46 * q^58 + 92 * q^60 + 14 * q^61 + 132 * q^62 + 61 * q^63 + 75 * q^64 + 14 * q^65 + 48 * q^66 + 52 * q^67 + 158 * q^68 + 52 * q^69 + 102 * q^70 - 124 * q^71 + 147 * q^72 + 34 * q^73 + 126 * q^74 + 28 * q^75 + 28 * q^76 + 18 * q^77 - 8 * q^78 + 16 * q^79 + 98 * q^80 - 91 * q^81 + 86 * q^82 + 48 * q^83 + 90 * q^84 + 22 * q^85 - 36 * q^86 + 4 * q^87 + 180 * q^88 + 84 * q^89 + 170 * q^90 - 56 * q^91 + 12 * q^92 + 28 * q^93 + 64 * q^94 + 28 * q^95 - 4 * q^96 + 114 * q^97 + 125 * q^98 - 68 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(175))\)

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
175.2.a	\(\chi_{175}(1, \cdot)\)	175.2.a.a	1	1
		175.2.a.b	1
		175.2.a.c	1
		175.2.a.d	2
		175.2.a.e	2
		175.2.a.f	2
175.2.b	\(\chi_{175}(99, \cdot)\)	175.2.b.a	2	1
		175.2.b.b	4
		175.2.b.c	4
175.2.e	\(\chi_{175}(51, \cdot)\)	175.2.e.a	2	2
		175.2.e.b	2
		175.2.e.c	4
		175.2.e.d	6
		175.2.e.e	6
175.2.f	\(\chi_{175}(118, \cdot)\)	175.2.f.a	4	2
		175.2.f.b	4
		175.2.f.c	4
		175.2.f.d	8
175.2.h	\(\chi_{175}(36, \cdot)\)	175.2.h.a	4	4
		175.2.h.b	28
		175.2.h.c	32
175.2.k	\(\chi_{175}(74, \cdot)\)	175.2.k.a	8	2
		175.2.k.b	12
175.2.n	\(\chi_{175}(29, \cdot)\)	175.2.n.a	56	4
175.2.o	\(\chi_{175}(68, \cdot)\)	175.2.o.a	4	4
		175.2.o.b	4
		175.2.o.c	8
		175.2.o.d	24
175.2.q	\(\chi_{175}(11, \cdot)\)	175.2.q.a	144	8
175.2.s	\(\chi_{175}(13, \cdot)\)	175.2.s.a	144	8
175.2.t	\(\chi_{175}(4, \cdot)\)	175.2.t.a	144	8
175.2.x	\(\chi_{175}(3, \cdot)\)	175.2.x.a	288	16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(175))\) into lower level spaces

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