Space of modular forms of level 88 and weight 2

• Label: 88.2
• Level: 88
• Weight: 2
• Dimension: 115
• Nonzero newspaces: 6
• Newform subspaces: 10
• Sturm bound: 960
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 88 = 2^{3} \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 10 \)
Sturm bound:			\(960\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(88))\).

	Total	New	Old
Modular forms	300	151	149
Cusp forms	181	115	66
Eisenstein series	119	36	83

Trace form

115 * q - 10 * q^2 - 10 * q^3 - 10 * q^4 - 10 * q^6 - 10 * q^7 - 10 * q^8 - 20 * q^9 - 10 * q^10 - 10 * q^11 - 20 * q^12 - 10 * q^14 - 20 * q^15 - 10 * q^16 - 30 * q^17 - 10 * q^18 - 25 * q^19 - 10 * q^20 - 20 * q^21 - 10 * q^22 - 30 * q^23 - 10 * q^24 - 40 * q^25 - 10 * q^26 - 25 * q^27 - 10 * q^28 - 10 * q^29 + 20 * q^30 - 20 * q^31 - 5 * q^33 + 20 * q^34 + 20 * q^35 + 70 * q^36 + 40 * q^38 + 50 * q^39 + 60 * q^40 + 10 * q^41 + 100 * q^42 + 30 * q^43 + 60 * q^44 + 30 * q^45 + 60 * q^46 + 20 * q^47 + 100 * q^48 + 10 * q^49 + 60 * q^50 + 45 * q^51 + 40 * q^52 - 20 * q^53 + 70 * q^54 + 20 * q^56 - 45 * q^57 - 45 * q^59 + 40 * q^60 - 20 * q^61 - 10 * q^62 - 20 * q^63 - 10 * q^64 - 60 * q^65 - 10 * q^66 - 60 * q^67 - 10 * q^68 - 40 * q^69 - 80 * q^70 - 30 * q^71 - 60 * q^72 - 10 * q^73 - 60 * q^74 + 35 * q^75 - 90 * q^76 - 10 * q^77 - 140 * q^78 + 70 * q^79 - 120 * q^80 + 5 * q^81 - 110 * q^82 + 85 * q^83 - 130 * q^84 + 60 * q^85 - 70 * q^86 + 100 * q^87 - 170 * q^88 - 10 * q^89 - 150 * q^90 + 100 * q^91 - 90 * q^92 + 30 * q^93 - 130 * q^94 + 70 * q^95 - 80 * q^96 - 5 * q^97 - 120 * q^98 + 40 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)

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
88.2.a	\(\chi_{88}(1, \cdot)\)	88.2.a.a	1	1
		88.2.a.b	2
88.2.c	\(\chi_{88}(45, \cdot)\)	88.2.c.a	10	1
88.2.e	\(\chi_{88}(87, \cdot)\)	None	0	1
88.2.g	\(\chi_{88}(43, \cdot)\)	88.2.g.a	2	1
		88.2.g.b	8
88.2.i	\(\chi_{88}(9, \cdot)\)	88.2.i.a	4	4
		88.2.i.b	8
88.2.k	\(\chi_{88}(19, \cdot)\)	88.2.k.a	8	4
		88.2.k.b	32
88.2.m	\(\chi_{88}(7, \cdot)\)	None	0	4
88.2.o	\(\chi_{88}(5, \cdot)\)	88.2.o.a	40	4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(88))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(88)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 2}\)