Space of modular forms of level 175 and weight 5

• Label: 175.5
• Level: 175
• Weight: 5
• Dimension: 4137
• Nonzero newspaces: 12
• Sturm bound: 12000
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(12000\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(175))\).

	Total	New	Old
Modular forms	4968	4343	625
Cusp forms	4632	4137	495
Eisenstein series	336	206	130

Trace form

4137 * q - 27 * q^2 - 58 * q^3 - 51 * q^4 + 52 * q^5 + 72 * q^6 - 81 * q^7 - 19 * q^8 + 41 * q^9 - 48 * q^10 - 352 * q^11 + 68 * q^12 + 1096 * q^13 + 583 * q^14 - 916 * q^15 - 3247 * q^16 - 2370 * q^17 + 353 * q^18 + 3226 * q^19 + 7532 * q^20 + 2136 * q^21 + 4942 * q^22 + 12 * q^23 - 5460 * q^24 - 5616 * q^25 - 9728 * q^26 - 9916 * q^27 - 325 * q^28 + 326 * q^29 + 2084 * q^30 + 12162 * q^31 + 24705 * q^32 + 15638 * q^33 + 15960 * q^34 + 2828 * q^35 - 21763 * q^36 - 26028 * q^37 - 57484 * q^38 - 50844 * q^39 - 24136 * q^40 - 18856 * q^41 + 6234 * q^42 + 35718 * q^43 + 61106 * q^44 + 59068 * q^45 + 64114 * q^46 + 56034 * q^47 + 63340 * q^48 + 1385 * q^49 - 16196 * q^50 - 28222 * q^51 - 75900 * q^52 - 69156 * q^53 - 150036 * q^54 - 65084 * q^55 - 96197 * q^56 - 96200 * q^57 - 58186 * q^58 - 26710 * q^59 - 39148 * q^60 + 65366 * q^61 + 138508 * q^62 + 150173 * q^63 + 272257 * q^64 + 116524 * q^65 + 188940 * q^66 + 108124 * q^67 + 199540 * q^68 + 79060 * q^69 + 13062 * q^70 - 50698 * q^71 - 74619 * q^72 - 89370 * q^73 - 159654 * q^74 - 108132 * q^75 - 239008 * q^76 - 156658 * q^77 - 300560 * q^78 - 176332 * q^79 - 270872 * q^80 - 85021 * q^81 - 272944 * q^82 - 136764 * q^83 - 16382 * q^84 - 31768 * q^85 + 12962 * q^86 + 68940 * q^87 + 109362 * q^88 + 136874 * q^89 + 408500 * q^90 + 116810 * q^91 + 538158 * q^92 + 382594 * q^93 + 457512 * q^94 + 194708 * q^95 + 403536 * q^96 + 200136 * q^97 + 254367 * q^98 + 159690 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(175))\)

We only show spaces with odd 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
175.5.c	\(\chi_{175}(174, \cdot)\)	175.5.c.a	2	1
		175.5.c.b	4
		175.5.c.c	16
		175.5.c.d	24
175.5.d	\(\chi_{175}(76, \cdot)\)	175.5.d.a	1	1
		175.5.d.b	2
		175.5.d.c	2
		175.5.d.d	2
		175.5.d.e	4
		175.5.d.f	8
		175.5.d.g	8
		175.5.d.h	8
		175.5.d.i	12
175.5.g	\(\chi_{175}(43, \cdot)\)	175.5.g.a	4	2
		175.5.g.b	12
		175.5.g.c	24
		175.5.g.d	32
175.5.i	\(\chi_{175}(26, \cdot)\)	175.5.i.a	4	2
		175.5.i.b	20
		175.5.i.c	22
		175.5.i.d	22
		175.5.i.e	28
175.5.j	\(\chi_{175}(24, \cdot)\)	175.5.j.a	8	2
		175.5.j.b	40
		175.5.j.c	44
175.5.l	\(\chi_{175}(6, \cdot)\)	n/a	312	4
175.5.m	\(\chi_{175}(34, \cdot)\)	n/a	312	4
175.5.p	\(\chi_{175}(18, \cdot)\)	n/a	184	4
175.5.r	\(\chi_{175}(8, \cdot)\)	n/a	480	8
175.5.u	\(\chi_{175}(19, \cdot)\)	n/a	624	8
175.5.v	\(\chi_{175}(31, \cdot)\)	n/a	624	8
175.5.w	\(\chi_{175}(2, \cdot)\)	n/a	1248	16

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(175))\) into lower level spaces

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