Space of modular forms of level 171 and weight 4

• Label: 171.4
• Level: 171
• Weight: 4
• Dimension: 2474
• Nonzero newspaces: 16
• Newform subspaces: 36
• Sturm bound: 8640
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 16 \)
Newform subspaces:			\( 36 \)
Sturm bound:			\(8640\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(171))\).

	Total	New	Old
Modular forms	3384	2626	758
Cusp forms	3096	2474	622
Eisenstein series	288	152	136

Trace form

2474 * q - 21 * q^2 - 30 * q^3 - q^4 + 3 * q^5 - 54 * q^6 - 53 * q^7 - 159 * q^8 - 126 * q^9 - 105 * q^10 + 105 * q^11 + 276 * q^12 - 53 * q^13 + 57 * q^14 - 90 * q^15 + 263 * q^16 - 279 * q^17 - 468 * q^18 + 395 * q^19 + 498 * q^20 - 78 * q^21 + 69 * q^22 + 21 * q^23 + 162 * q^24 - 451 * q^25 + 345 * q^26 + 828 * q^27 - 2720 * q^28 - 759 * q^29 - 612 * q^30 - 647 * q^31 - 558 * q^32 - 432 * q^33 + 1692 * q^34 + 1077 * q^35 + 558 * q^36 + 556 * q^37 + 1743 * q^38 - 1590 * q^39 + 2382 * q^40 + 687 * q^41 + 936 * q^42 + 2575 * q^43 + 8772 * q^44 + 5418 * q^45 + 5232 * q^46 + 2571 * q^47 + 2022 * q^48 - 2877 * q^49 - 7122 * q^50 - 2970 * q^51 - 9815 * q^52 - 4995 * q^53 - 7866 * q^54 - 8421 * q^55 - 18012 * q^56 - 3855 * q^57 - 6006 * q^58 - 5181 * q^59 - 9468 * q^60 - 7451 * q^61 - 9510 * q^62 - 2250 * q^63 - 253 * q^64 + 573 * q^65 + 6840 * q^66 + 7327 * q^67 + 16920 * q^68 + 3582 * q^69 + 19077 * q^70 + 8955 * q^71 + 8118 * q^72 + 6892 * q^73 + 7077 * q^74 + 690 * q^75 + 5642 * q^76 + 4278 * q^77 + 1944 * q^78 - 737 * q^79 - 987 * q^80 + 1098 * q^81 - 5118 * q^82 + 1257 * q^83 - 1320 * q^84 + 225 * q^85 - 1374 * q^86 + 270 * q^87 + 1263 * q^88 - 2493 * q^89 + 3726 * q^90 + 875 * q^91 - 4272 * q^92 + 390 * q^93 + 20544 * q^94 + 27111 * q^95 + 25560 * q^96 + 23653 * q^97 + 45288 * q^98 + 11592 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(171))\)

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
171.4.a	\(\chi_{171}(1, \cdot)\)	171.4.a.a	1	1
		171.4.a.b	1
		171.4.a.c	1
		171.4.a.d	1
		171.4.a.e	2
		171.4.a.f	3
		171.4.a.g	3
		171.4.a.h	4
		171.4.a.i	6
171.4.d	\(\chi_{171}(170, \cdot)\)	171.4.d.a	4	1
		171.4.d.b	16
171.4.e	\(\chi_{171}(58, \cdot)\)	171.4.e.a	54	2
		171.4.e.b	54
171.4.f	\(\chi_{171}(64, \cdot)\)	171.4.f.a	2	2
		171.4.f.b	2
		171.4.f.c	4
		171.4.f.d	4
		171.4.f.e	4
		171.4.f.f	10
		171.4.f.g	10
		171.4.f.h	12
171.4.g	\(\chi_{171}(106, \cdot)\)	171.4.g.a	116	2
171.4.h	\(\chi_{171}(7, \cdot)\)	171.4.h.a	116	2
171.4.k	\(\chi_{171}(50, \cdot)\)	171.4.k.a	116	2
171.4.l	\(\chi_{171}(56, \cdot)\)	171.4.l.a	116	2
171.4.m	\(\chi_{171}(8, \cdot)\)	171.4.m.a	40	2
171.4.t	\(\chi_{171}(122, \cdot)\)	171.4.t.a	116	2
171.4.u	\(\chi_{171}(28, \cdot)\)	171.4.u.a	24	6
		171.4.u.b	24
		171.4.u.c	36
		171.4.u.d	60
171.4.v	\(\chi_{171}(25, \cdot)\)	171.4.v.a	348	6
171.4.w	\(\chi_{171}(4, \cdot)\)	171.4.w.a	348	6
171.4.x	\(\chi_{171}(14, \cdot)\)	171.4.x.a	348	6
171.4.y	\(\chi_{171}(53, \cdot)\)	171.4.y.a	120	6
171.4.bd	\(\chi_{171}(2, \cdot)\)	171.4.bd.a	348	6

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(171))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(171)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 2}\)