Space of modular forms of level 105 and weight 2

• Label: 105.2
• Level: 105
• Weight: 2
• Dimension: 227
• Nonzero newspaces: 12
• Newform subspaces: 25
• Sturm bound: 1536
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 25 \)
Sturm bound:			\(1536\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(105))\).

	Total	New	Old
Modular forms	480	283	197
Cusp forms	289	227	62
Eisenstein series	191	56	135

Trace form

227 * q + 5 * q^2 - 5 * q^3 - 19 * q^4 - 7 * q^5 - 35 * q^6 - 21 * q^7 - 27 * q^8 - 21 * q^9 - 43 * q^10 - 16 * q^11 - 27 * q^12 - 34 * q^13 - 27 * q^14 - 21 * q^15 - 75 * q^16 - 10 * q^17 - 7 * q^18 - 40 * q^19 - 27 * q^20 - 25 * q^21 - 68 * q^22 - 24 * q^23 + 21 * q^24 - 37 * q^25 + 2 * q^26 + 19 * q^27 - 11 * q^28 + 10 * q^29 + 37 * q^30 - 44 * q^31 + 85 * q^32 + 16 * q^33 + 34 * q^34 + 37 * q^35 + 61 * q^36 + 26 * q^37 + 56 * q^38 + 30 * q^39 + 45 * q^40 + 22 * q^41 + 57 * q^42 - 44 * q^43 + 4 * q^44 + 17 * q^45 - 72 * q^46 - 52 * q^47 + 45 * q^48 - 57 * q^49 - 55 * q^50 - 26 * q^51 - 18 * q^52 - 22 * q^53 - 11 * q^54 - 28 * q^55 - 3 * q^56 - 36 * q^57 + 86 * q^58 - 4 * q^59 + 65 * q^60 + 38 * q^61 + 48 * q^62 - 25 * q^63 + 85 * q^64 + 72 * q^65 + 92 * q^66 + 80 * q^67 + 130 * q^68 + 72 * q^69 + 249 * q^70 + 64 * q^71 + 57 * q^72 + 134 * q^73 + 154 * q^74 + 91 * q^75 + 108 * q^76 + 84 * q^77 + 70 * q^78 + 92 * q^79 + 69 * q^80 - 9 * q^81 + 74 * q^82 - 12 * q^83 - 31 * q^84 - 58 * q^85 - 16 * q^86 - 46 * q^87 - 12 * q^88 - 18 * q^89 - 115 * q^90 - 158 * q^91 - 168 * q^92 - 80 * q^93 - 176 * q^94 - 102 * q^95 - 271 * q^96 - 138 * q^97 - 167 * q^98 - 124 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)

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
105.2.a	\(\chi_{105}(1, \cdot)\)	105.2.a.a	1	1
		105.2.a.b	2
105.2.b	\(\chi_{105}(41, \cdot)\)	105.2.b.a	2	1
		105.2.b.b	2
		105.2.b.c	4
		105.2.b.d	4
105.2.d	\(\chi_{105}(64, \cdot)\)	105.2.d.a	2	1
		105.2.d.b	6
105.2.g	\(\chi_{105}(104, \cdot)\)	105.2.g.a	4	1
		105.2.g.b	4
		105.2.g.c	4
105.2.i	\(\chi_{105}(16, \cdot)\)	105.2.i.a	2	2
		105.2.i.b	2
		105.2.i.c	4
		105.2.i.d	4
105.2.j	\(\chi_{105}(8, \cdot)\)	105.2.j.a	24	2
105.2.m	\(\chi_{105}(13, \cdot)\)	105.2.m.a	16	2
105.2.p	\(\chi_{105}(59, \cdot)\)	105.2.p.a	24	2
105.2.q	\(\chi_{105}(4, \cdot)\)	105.2.q.a	16	2
105.2.s	\(\chi_{105}(26, \cdot)\)	105.2.s.a	2	2
		105.2.s.b	2
		105.2.s.c	8
		105.2.s.d	8
105.2.u	\(\chi_{105}(52, \cdot)\)	105.2.u.a	32	4
105.2.x	\(\chi_{105}(2, \cdot)\)	105.2.x.a	48	4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(105))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(105)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 2}\)