Space of modular forms of level 175 and weight 10

• Label: 175.10
• Level: 175
• Weight: 10
• Dimension: 9437
• Nonzero newspaces: 12
• Sturm bound: 24000
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 10 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(24000\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(175))\).

	Total	New	Old
Modular forms	10968	9641	1327
Cusp forms	10632	9437	1195
Eisenstein series	336	204	132

Trace form

9437 * q - 91 * q^2 + 727 * q^3 - 3107 * q^4 + 3502 * q^5 - 14270 * q^6 + 13223 * q^7 + 491 * q^8 - 20925 * q^9 - 140848 * q^10 + 425037 * q^11 + 989946 * q^12 - 369660 * q^13 - 1772369 * q^14 - 326016 * q^15 + 8850009 * q^16 + 1489207 * q^17 + 261115 * q^18 - 3989431 * q^19 - 11172868 * q^20 + 3024519 * q^21 + 7795552 * q^22 + 5613351 * q^23 + 31649494 * q^24 + 5742034 * q^25 - 4749084 * q^26 - 155834 * q^27 - 939541 * q^28 - 27880830 * q^29 - 24057116 * q^30 - 13590839 * q^31 + 72985263 * q^32 + 51165855 * q^33 + 116187830 * q^34 + 41048128 * q^35 - 30286203 * q^36 - 45574371 * q^37 - 322749460 * q^38 - 268898790 * q^39 + 240206264 * q^40 + 405466 * q^41 + 412162472 * q^42 + 295782980 * q^43 - 202078832 * q^44 - 689958082 * q^45 - 629053010 * q^46 + 214201975 * q^47 + 993315378 * q^48 + 5902701 * q^49 + 592439804 * q^50 + 442829583 * q^51 + 202825200 * q^52 - 604350451 * q^53 - 1949702914 * q^54 - 549396084 * q^55 - 1366793695 * q^56 + 213461606 * q^57 + 2315216774 * q^58 + 1428657555 * q^59 + 1697794052 * q^60 + 79214197 * q^61 - 1986831444 * q^62 - 2828374391 * q^63 - 2036521239 * q^64 + 2356478474 * q^65 + 266835998 * q^66 - 243048899 * q^67 - 676883830 * q^68 + 898935022 * q^69 + 1835549662 * q^70 - 568809796 * q^71 + 1005105459 * q^72 + 126459951 * q^73 + 5857933404 * q^74 + 2598337768 * q^75 - 7189182222 * q^76 - 2589565023 * q^77 - 4599433336 * q^78 - 667739601 * q^79 - 5494678672 * q^80 + 4332036456 * q^81 + 3148391118 * q^82 - 2595306366 * q^83 - 7800065816 * q^84 + 3033016382 * q^85 + 5344866648 * q^86 + 16129498382 * q^87 + 4867662752 * q^88 - 6064502595 * q^89 - 19529978700 * q^90 + 3011859002 * q^91 + 6556513692 * q^92 + 1402371703 * q^93 - 5243796286 * q^94 - 3875382692 * q^95 - 17246665006 * q^96 + 2725042370 * q^97 - 16474642081 * q^98 - 1365247596 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(175))\)

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
175.10.a	\(\chi_{175}(1, \cdot)\)	175.10.a.a	1	1
		175.10.a.b	2
		175.10.a.c	2
		175.10.a.d	3
		175.10.a.e	4
		175.10.a.f	5
		175.10.a.g	6
		175.10.a.h	8
		175.10.a.i	8
		175.10.a.j	10
		175.10.a.k	10
		175.10.a.l	13
		175.10.a.m	13
175.10.b	\(\chi_{175}(99, \cdot)\)	175.10.b.a	2	1
		175.10.b.b	4
		175.10.b.c	4
		175.10.b.d	6
		175.10.b.e	8
		175.10.b.f	10
		175.10.b.g	12
		175.10.b.h	16
		175.10.b.i	20
175.10.e	\(\chi_{175}(51, \cdot)\)	n/a	222	2
175.10.f	\(\chi_{175}(118, \cdot)\)	n/a	212	2
175.10.h	\(\chi_{175}(36, \cdot)\)	n/a	544	4
175.10.k	\(\chi_{175}(74, \cdot)\)	n/a	212	2
175.10.n	\(\chi_{175}(29, \cdot)\)	n/a	536	4
175.10.o	\(\chi_{175}(68, \cdot)\)	n/a	424	4
175.10.q	\(\chi_{175}(11, \cdot)\)	n/a	1424	8
175.10.s	\(\chi_{175}(13, \cdot)\)	n/a	1424	8
175.10.t	\(\chi_{175}(4, \cdot)\)	n/a	1424	8
175.10.x	\(\chi_{175}(3, \cdot)\)	n/a	2848	16

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

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(175))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(175)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 2}\)