Space of modular forms of level 110 and weight 2

• Label: 110.2
• Level: 110
• Weight: 2
• Dimension: 111
• Nonzero newspaces: 6
• Newform subspaces: 16
• Sturm bound: 1440
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 16 \)
Sturm bound:			\(1440\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(110))\).

	Total	New	Old
Modular forms	440	111	329
Cusp forms	281	111	170
Eisenstein series	159	0	159

Trace form

111 * q + q^2 + 4 * q^3 + q^4 + q^5 - 6 * q^6 - 12 * q^7 + q^8 - 27 * q^9 - 9 * q^10 - 9 * q^11 - 16 * q^12 - 6 * q^13 - 12 * q^14 - 26 * q^15 + q^16 - 22 * q^17 + 3 * q^18 - 10 * q^19 + q^20 - 8 * q^21 + 11 * q^22 - 16 * q^23 - 6 * q^24 - 39 * q^25 - 26 * q^26 - 50 * q^27 - 12 * q^28 - 50 * q^29 - 26 * q^30 - 28 * q^31 - 9 * q^32 - 66 * q^33 - 22 * q^34 - 52 * q^35 + 3 * q^36 - 2 * q^37 - 40 * q^38 - 44 * q^39 - 9 * q^40 - 38 * q^41 + 12 * q^42 + 24 * q^43 + 21 * q^44 + 83 * q^45 + 64 * q^46 + 88 * q^47 + 4 * q^48 + 137 * q^49 + 61 * q^50 + 102 * q^51 + 54 * q^52 + 74 * q^53 + 120 * q^54 + 101 * q^55 + 8 * q^56 + 70 * q^57 + 110 * q^58 + 50 * q^59 + 64 * q^60 + 82 * q^61 + 52 * q^62 + 64 * q^63 + q^64 + 34 * q^65 + 4 * q^66 + 8 * q^67 + 18 * q^68 - 44 * q^69 + 8 * q^70 - 88 * q^71 - 27 * q^72 - 46 * q^73 - 2 * q^74 - 86 * q^75 - 72 * q^77 - 24 * q^78 - 20 * q^79 - 9 * q^80 - 149 * q^81 - 28 * q^82 - 46 * q^83 - 48 * q^84 - 92 * q^85 - 86 * q^86 - 80 * q^87 - 9 * q^88 - 70 * q^89 - 77 * q^90 - 48 * q^91 - 36 * q^92 - 12 * q^93 - 72 * q^94 - 10 * q^95 + 4 * q^96 + 28 * q^97 - 33 * q^98 + 83 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)

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
110.2.a	\(\chi_{110}(1, \cdot)\)	110.2.a.a	1	1
		110.2.a.b	1
		110.2.a.c	1
		110.2.a.d	2
110.2.b	\(\chi_{110}(89, \cdot)\)	110.2.b.a	2	1
		110.2.b.b	2
		110.2.b.c	2
110.2.f	\(\chi_{110}(43, \cdot)\)	110.2.f.a	4	2
		110.2.f.b	4
		110.2.f.c	4
110.2.g	\(\chi_{110}(31, \cdot)\)	110.2.g.a	4	4
		110.2.g.b	4
		110.2.g.c	8
110.2.j	\(\chi_{110}(9, \cdot)\)	110.2.j.a	8	4
		110.2.j.b	16
110.2.k	\(\chi_{110}(7, \cdot)\)	110.2.k.a	48	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(110))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(110)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 2}\)