Space of modular forms of level 163 and weight 2

• Label: 163.2
• Level: 163
• Weight: 2
• Dimension: 1027
• Nonzero newspaces: 5
• Newform subspaces: 7
• Sturm bound: 4428
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 163 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 5 \)
Newform subspaces:			\( 7 \)
Sturm bound:			\(4428\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(163))\).

	Total	New	Old
Modular forms	1188	1188	0
Cusp forms	1027	1027	0
Eisenstein series	161	161	0

Trace form

1027 * q - 78 * q^2 - 77 * q^3 - 74 * q^4 - 75 * q^5 - 69 * q^6 - 73 * q^7 - 66 * q^8 - 68 * q^9 - 63 * q^10 - 69 * q^11 - 53 * q^12 - 67 * q^13 - 57 * q^14 - 57 * q^15 - 50 * q^16 - 63 * q^17 - 42 * q^18 - 61 * q^19 - 39 * q^20 - 49 * q^21 - 45 * q^22 - 57 * q^23 - 21 * q^24 - 50 * q^25 - 39 * q^26 - 41 * q^27 - 25 * q^28 - 51 * q^29 - 9 * q^30 - 49 * q^31 - 18 * q^32 - 33 * q^33 - 27 * q^34 - 33 * q^35 + 10 * q^36 - 43 * q^37 - 21 * q^38 - 25 * q^39 + 9 * q^40 - 39 * q^41 + 15 * q^42 - 37 * q^43 + 3 * q^44 - 3 * q^45 - 9 * q^46 - 33 * q^47 + 43 * q^48 - 24 * q^49 + 12 * q^50 - 9 * q^51 + 17 * q^52 - 27 * q^53 + 39 * q^54 - 9 * q^55 + 39 * q^56 - q^57 + 9 * q^58 - 21 * q^59 + 87 * q^60 - 19 * q^61 + 15 * q^62 + 23 * q^63 + 46 * q^64 + 3 * q^65 + 63 * q^66 - 13 * q^67 + 45 * q^68 + 15 * q^69 + 63 * q^70 - 9 * q^71 + 114 * q^72 - 7 * q^73 + 33 * q^74 + 43 * q^75 + 59 * q^76 + 15 * q^77 + 87 * q^78 - q^79 + 105 * q^80 + 40 * q^81 + 45 * q^82 + 3 * q^83 + 143 * q^84 + 27 * q^85 + 51 * q^86 + 39 * q^87 + 99 * q^88 + 9 * q^89 + 153 * q^90 + 31 * q^91 + 87 * q^92 + 47 * q^93 + 63 * q^94 + 39 * q^95 + 171 * q^96 + 17 * q^97 + 90 * q^98 + 75 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(163))\)

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
163.2.a	\(\chi_{163}(1, \cdot)\)	163.2.a.a	1	1
		163.2.a.b	5
		163.2.a.c	7
163.2.c	\(\chi_{163}(58, \cdot)\)	163.2.c.a	24	2
163.2.e	\(\chi_{163}(38, \cdot)\)	163.2.e.a	72	6
163.2.g	\(\chi_{163}(6, \cdot)\)	163.2.g.a	216	18
163.2.i	\(\chi_{163}(4, \cdot)\)	163.2.i.a	702	54