Space of modular forms of level 69 and weight 2

• Label: 69.2
• Level: 69
• Weight: 2
• Dimension: 109
• Nonzero newspaces: 4
• Newform subspaces: 7
• Sturm bound: 704
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 7 \)
Sturm bound:			\(704\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(69))\).

	Total	New	Old
Modular forms	220	153	67
Cusp forms	133	109	24
Eisenstein series	87	44	43

Trace form

109 * q - 3 * q^2 - 12 * q^3 - 29 * q^4 - 6 * q^5 - 14 * q^6 - 30 * q^7 - 15 * q^8 - 12 * q^9 - 40 * q^10 - 12 * q^11 - 18 * q^12 - 36 * q^13 - 24 * q^14 - 6 * q^15 - 9 * q^16 + 4 * q^17 + 30 * q^18 - 20 * q^19 + 46 * q^20 + 14 * q^21 + 8 * q^22 + 21 * q^23 + 29 * q^24 - 9 * q^25 + 2 * q^26 + 21 * q^27 + 10 * q^28 - 8 * q^29 + 15 * q^30 - 32 * q^31 - 19 * q^32 - 12 * q^33 - 32 * q^34 - 4 * q^35 + 4 * q^36 + 28 * q^37 + 50 * q^38 + 19 * q^39 + 64 * q^40 + 2 * q^41 + 75 * q^42 + 22 * q^43 + 70 * q^44 - 6 * q^45 + 85 * q^46 + 40 * q^47 + 68 * q^48 + 53 * q^49 + 61 * q^50 + 15 * q^51 + 100 * q^52 - 10 * q^53 - 14 * q^54 - 6 * q^55 - 10 * q^56 - 20 * q^57 - 2 * q^58 - 16 * q^59 - 141 * q^60 - 84 * q^61 - 96 * q^62 - 74 * q^63 - 149 * q^64 - 84 * q^65 - 102 * q^66 - 90 * q^67 - 126 * q^68 - 89 * q^69 - 188 * q^70 - 72 * q^71 - 158 * q^72 - 96 * q^73 - 92 * q^74 - 75 * q^75 - 52 * q^76 - 8 * q^77 - 9 * q^78 - 14 * q^79 + 12 * q^80 + 76 * q^81 - 16 * q^82 + 4 * q^83 + 21 * q^84 + 90 * q^85 + 88 * q^86 + 91 * q^87 + 62 * q^88 + 42 * q^89 + 158 * q^90 + 64 * q^91 + 37 * q^92 + 78 * q^93 + 76 * q^94 + 78 * q^95 + 135 * q^96 + 78 * q^97 + 93 * q^98 + 131 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)

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
69.2.a	\(\chi_{69}(1, \cdot)\)	69.2.a.a	1	1
		69.2.a.b	2
69.2.c	\(\chi_{69}(68, \cdot)\)	69.2.c.a	6	1
69.2.e	\(\chi_{69}(4, \cdot)\)	69.2.e.a	10	10
		69.2.e.b	10
		69.2.e.c	20
69.2.g	\(\chi_{69}(5, \cdot)\)	69.2.g.a	60	10

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(69))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(69)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 2}\)