Space of modular forms of level 171 and weight 2

• Label: 171.2
• Level: 171
• Weight: 2
• Dimension: 774
• Nonzero newspaces: 16
• Newform subspaces: 32
• Sturm bound: 4320
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Newform subspaces:			\( 32 \)
Sturm bound:			\(4320\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(171))\).

	Total	New	Old
Modular forms	1224	926	298
Cusp forms	937	774	163
Eisenstein series	287	152	135

Trace form

774 * q - 27 * q^2 - 36 * q^3 - 27 * q^4 - 27 * q^5 - 36 * q^6 - 27 * q^7 - 27 * q^8 - 36 * q^9 - 81 * q^10 - 27 * q^11 - 36 * q^12 - 39 * q^13 - 45 * q^14 - 36 * q^15 - 63 * q^16 - 36 * q^17 - 36 * q^18 - 102 * q^19 - 90 * q^20 - 36 * q^21 - 54 * q^22 - 36 * q^23 - 36 * q^24 - 45 * q^25 - 45 * q^26 - 36 * q^27 - 120 * q^28 - 45 * q^29 - 36 * q^30 - 45 * q^31 - 72 * q^32 - 36 * q^33 - 72 * q^34 - 63 * q^35 - 108 * q^37 - 90 * q^38 - 72 * q^39 - 108 * q^40 - 45 * q^41 - 36 * q^42 - 54 * q^43 + 9 * q^44 + 18 * q^45 - 18 * q^46 + 36 * q^47 + 90 * q^48 + 18 * q^49 + 162 * q^50 + 54 * q^51 + 171 * q^52 + 81 * q^53 + 72 * q^54 + 27 * q^55 + 324 * q^56 + 54 * q^57 + 54 * q^58 + 108 * q^59 + 180 * q^60 + 51 * q^61 + 90 * q^62 + 36 * q^63 + 45 * q^64 + 54 * q^65 + 108 * q^66 - 36 * q^67 + 99 * q^68 + 18 * q^69 - 27 * q^70 + 18 * q^71 + 18 * q^72 - 153 * q^73 - 45 * q^74 - 36 * q^75 - 117 * q^76 - 153 * q^77 - 36 * q^78 - 129 * q^79 - 45 * q^80 - 36 * q^81 - 252 * q^82 - 90 * q^83 - 36 * q^84 - 135 * q^85 - 126 * q^86 - 36 * q^87 - 189 * q^88 - 108 * q^89 + 54 * q^90 - 165 * q^91 - 144 * q^92 - 36 * q^93 - 72 * q^94 + 54 * q^95 + 72 * q^96 + 54 * q^97 + 198 * q^98 + 90 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(171))\)

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
171.2.a	\(\chi_{171}(1, \cdot)\)	171.2.a.a	1	1
		171.2.a.b	1
		171.2.a.c	1
		171.2.a.d	1
		171.2.a.e	4
171.2.d	\(\chi_{171}(170, \cdot)\)	171.2.d.a	4	1
		171.2.d.b	4
171.2.e	\(\chi_{171}(58, \cdot)\)	171.2.e.a	18	2
		171.2.e.b	18
171.2.f	\(\chi_{171}(64, \cdot)\)	171.2.f.a	2	2
		171.2.f.b	6
		171.2.f.c	8
171.2.g	\(\chi_{171}(106, \cdot)\)	171.2.g.a	2	2
		171.2.g.b	2
		171.2.g.c	32
171.2.h	\(\chi_{171}(7, \cdot)\)	171.2.h.a	2	2
		171.2.h.b	2
		171.2.h.c	32
171.2.k	\(\chi_{171}(50, \cdot)\)	171.2.k.a	36	2
171.2.l	\(\chi_{171}(56, \cdot)\)	171.2.l.a	36	2
171.2.m	\(\chi_{171}(8, \cdot)\)	171.2.m.a	16	2
171.2.t	\(\chi_{171}(122, \cdot)\)	171.2.t.a	36	2
171.2.u	\(\chi_{171}(28, \cdot)\)	171.2.u.a	6	6
		171.2.u.b	6
		171.2.u.c	6
		171.2.u.d	12
		171.2.u.e	12
171.2.v	\(\chi_{171}(25, \cdot)\)	171.2.v.a	108	6
171.2.w	\(\chi_{171}(4, \cdot)\)	171.2.w.a	108	6
171.2.x	\(\chi_{171}(14, \cdot)\)	171.2.x.a	108	6
171.2.y	\(\chi_{171}(53, \cdot)\)	171.2.y.a	36	6
171.2.bd	\(\chi_{171}(2, \cdot)\)	171.2.bd.a	108	6

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(171))\) into lower level spaces

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