Space of modular forms of level 161 and weight 4

• Label: 161.4
• Level: 161
• Weight: 4
• Dimension: 2920
• Nonzero newspaces: 8
• Newform subspaces: 16
• Sturm bound: 8448
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 16 \)
Sturm bound:			\(8448\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(161))\).

	Total	New	Old
Modular forms	3300	3132	168
Cusp forms	3036	2920	116
Eisenstein series	264	212	52

Trace form

2920 * q - 38 * q^2 - 26 * q^3 - 38 * q^4 - 62 * q^5 - 104 * q^6 - 97 * q^7 - 44 * q^8 + 46 * q^9 + 16 * q^10 - 38 * q^11 - 128 * q^12 - 44 * q^13 - 97 * q^14 + 506 * q^15 + 722 * q^16 - 18 * q^17 - 178 * q^18 + 54 * q^19 - 1116 * q^20 - 253 * q^21 - 1032 * q^22 - 1219 * q^23 - 3004 * q^24 - 1162 * q^25 - 484 * q^26 - 236 * q^27 - 81 * q^28 + 318 * q^29 + 3080 * q^30 + 1326 * q^31 + 3590 * q^32 + 1790 * q^33 + 4060 * q^34 + 1501 * q^35 + 4870 * q^36 + 3262 * q^37 + 1142 * q^38 - 392 * q^39 - 3500 * q^40 - 2908 * q^41 - 4441 * q^42 - 3302 * q^43 - 6562 * q^44 - 4918 * q^45 - 8234 * q^46 - 3470 * q^47 - 6120 * q^48 - 2527 * q^49 - 3090 * q^50 - 1442 * q^51 - 200 * q^52 + 1370 * q^53 + 11016 * q^54 + 9328 * q^55 + 10882 * q^56 + 9958 * q^57 + 15874 * q^58 + 6090 * q^59 + 7256 * q^60 - 950 * q^61 - 4628 * q^62 - 2775 * q^63 - 10016 * q^64 - 9760 * q^65 - 10470 * q^66 - 2606 * q^67 - 17050 * q^68 - 5202 * q^69 - 5162 * q^70 - 3666 * q^71 - 14600 * q^72 - 2978 * q^73 - 1618 * q^74 + 11340 * q^75 + 13478 * q^76 + 4939 * q^77 + 23486 * q^78 + 8286 * q^79 + 20618 * q^80 + 10196 * q^81 + 11620 * q^82 + 5892 * q^83 + 6495 * q^84 - 3054 * q^85 - 3232 * q^86 - 18416 * q^87 - 12060 * q^88 - 13382 * q^89 - 39038 * q^90 - 6876 * q^91 - 19064 * q^92 - 21478 * q^93 - 13950 * q^94 - 3890 * q^95 - 6654 * q^96 + 7516 * q^97 + 4300 * q^98 + 4582 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(161))\)

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
161.4.a	\(\chi_{161}(1, \cdot)\)	161.4.a.a	5	1
		161.4.a.b	8
		161.4.a.c	9
		161.4.a.d	12
161.4.c	\(\chi_{161}(160, \cdot)\)	161.4.c.a	2	1
		161.4.c.b	8
		161.4.c.c	36
161.4.e	\(\chi_{161}(93, \cdot)\)	161.4.e.a	44	2
		161.4.e.b	44
161.4.g	\(\chi_{161}(45, \cdot)\)	161.4.g.a	92	2
161.4.i	\(\chi_{161}(8, \cdot)\)	161.4.i.a	170	10
		161.4.i.b	190
161.4.k	\(\chi_{161}(20, \cdot)\)	161.4.k.a	20	10
		161.4.k.b	440
161.4.m	\(\chi_{161}(2, \cdot)\)	161.4.m.a	920	20
161.4.o	\(\chi_{161}(5, \cdot)\)	161.4.o.a	920	20

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(161))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(161)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 2}\)