Space of modular forms of level 163 and weight 3

• Label: 163.3
• Level: 163
• Weight: 3
• Dimension: 2133
• Nonzero newspaces: 5
• Newform subspaces: 6
• Sturm bound: 6642
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 163 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 5 \)
Newform subspaces:			\( 6 \)
Sturm bound:			\(6642\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(163))\).

	Total	New	Old
Modular forms	2295	2295	0
Cusp forms	2133	2133	0
Eisenstein series	162	162	0

Trace form

2133 * q - 81 * q^2 - 81 * q^3 - 81 * q^4 - 81 * q^5 - 81 * q^6 - 81 * q^7 - 81 * q^8 - 81 * q^9 - 81 * q^10 - 81 * q^11 - 81 * q^12 - 81 * q^13 - 81 * q^14 - 81 * q^15 - 81 * q^16 - 81 * q^17 - 81 * q^18 - 81 * q^19 - 81 * q^20 - 81 * q^21 - 81 * q^22 - 81 * q^23 - 81 * q^24 - 81 * q^25 - 81 * q^26 - 81 * q^27 - 81 * q^28 - 81 * q^29 - 81 * q^30 - 81 * q^31 - 81 * q^32 - 81 * q^33 - 81 * q^34 - 81 * q^35 - 81 * q^36 - 81 * q^37 - 81 * q^38 - 81 * q^39 - 81 * q^40 - 81 * q^41 - 81 * q^42 - 81 * q^43 - 81 * q^44 - 81 * q^45 - 81 * q^46 - 81 * q^47 - 81 * q^48 - 81 * q^49 - 81 * q^50 - 81 * q^51 - 81 * q^52 - 81 * q^53 - 81 * q^54 - 81 * q^55 - 81 * q^56 - 81 * q^57 - 81 * q^58 - 81 * q^59 - 81 * q^60 - 81 * q^61 - 81 * q^62 - 81 * q^63 - 81 * q^64 - 81 * q^65 - 81 * q^66 - 81 * q^67 - 81 * q^68 - 81 * q^69 - 81 * q^70 - 81 * q^71 - 81 * q^72 - 81 * q^73 - 81 * q^74 - 81 * q^75 - 81 * q^76 - 81 * q^77 - 81 * q^78 - 81 * q^79 - 81 * q^80 - 81 * q^81 - 81 * q^82 - 81 * q^83 - 81 * q^84 - 81 * q^85 - 81 * q^86 - 81 * q^87 - 81 * q^88 - 81 * q^89 - 81 * q^90 - 81 * q^91 - 81 * q^92 - 81 * q^93 - 81 * q^94 - 81 * q^95 - 81 * q^96 - 81 * q^97 - 81 * q^98 - 81 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(163))\)

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
163.3.b	\(\chi_{163}(162, \cdot)\)	163.3.b.a	1	1
		163.3.b.b	26
163.3.d	\(\chi_{163}(59, \cdot)\)	163.3.d.a	54	2
163.3.f	\(\chi_{163}(23, \cdot)\)	163.3.f.a	162	6
163.3.h	\(\chi_{163}(5, \cdot)\)	163.3.h.a	486	18
163.3.j	\(\chi_{163}(2, \cdot)\)	163.3.j.a	1404	54