Space of modular forms of level 169 and weight 2

• Label: 169.2
• Level: 169
• Weight: 2
• Dimension: 1066
• Nonzero newspaces: 8
• Newform subspaces: 14
• Sturm bound: 4732
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 169 = 13^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 14 \)
Sturm bound:			\(4732\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(169))\).

	Total	New	Old
Modular forms	1297	1271	26
Cusp forms	1070	1066	4
Eisenstein series	227	205	22

Trace form

1066 * q - 69 * q^2 - 70 * q^3 - 73 * q^4 - 72 * q^5 - 78 * q^6 - 70 * q^7 - 63 * q^8 - 63 * q^9 - 54 * q^10 - 66 * q^11 - 42 * q^12 - 60 * q^13 - 126 * q^14 - 66 * q^15 - 57 * q^16 - 66 * q^17 - 39 * q^18 - 46 * q^19 - 42 * q^20 - 46 * q^21 - 42 * q^22 - 66 * q^23 - 6 * q^24 - 55 * q^25 - 42 * q^26 - 94 * q^27 - 22 * q^28 - 42 * q^29 + 6 * q^30 - 46 * q^31 + 3 * q^32 - 30 * q^33 - 24 * q^34 - 30 * q^35 + 11 * q^36 - 70 * q^37 - 42 * q^38 - 40 * q^39 - 72 * q^40 - 18 * q^41 + 18 * q^42 - 18 * q^43 + 6 * q^44 + 6 * q^45 + 30 * q^46 - 30 * q^47 + 26 * q^48 - 7 * q^49 + 27 * q^50 + 18 * q^51 + 11 * q^52 - 84 * q^53 + 18 * q^54 - 6 * q^55 + 42 * q^56 + 2 * q^57 - 6 * q^58 - 42 * q^59 + 90 * q^60 - 14 * q^61 + 6 * q^62 + 26 * q^63 + 53 * q^64 + 9 * q^65 - 6 * q^66 - 22 * q^67 + 54 * q^68 - 6 * q^69 + 66 * q^70 - 18 * q^71 + 111 * q^72 - 4 * q^73 + 66 * q^74 + 54 * q^75 + 74 * q^76 + 18 * q^77 + 102 * q^78 - 86 * q^79 + 138 * q^80 + 21 * q^81 + 30 * q^82 + 6 * q^83 + 146 * q^84 + 12 * q^85 + 54 * q^86 + 54 * q^87 + 102 * q^88 + 36 * q^89 + 144 * q^90 + 26 * q^91 - 6 * q^92 + 74 * q^93 + 78 * q^94 + 30 * q^95 + 174 * q^96 - 4 * q^97 + 51 * q^98 + 78 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)

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
169.2.a	\(\chi_{169}(1, \cdot)\)	169.2.a.a	2	1
		169.2.a.b	3
		169.2.a.c	3
169.2.b	\(\chi_{169}(168, \cdot)\)	169.2.b.a	2	1
		169.2.b.b	6
169.2.c	\(\chi_{169}(22, \cdot)\)	169.2.c.a	4	2
		169.2.c.b	6
		169.2.c.c	6
169.2.e	\(\chi_{169}(23, \cdot)\)	169.2.e.a	2	2
		169.2.e.b	12
169.2.g	\(\chi_{169}(14, \cdot)\)	169.2.g.a	156	12
169.2.h	\(\chi_{169}(12, \cdot)\)	169.2.h.a	168	12
169.2.i	\(\chi_{169}(3, \cdot)\)	169.2.i.a	336	24
169.2.k	\(\chi_{169}(4, \cdot)\)	169.2.k.a	360	24

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(169))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(169)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)