Space of modular forms of level 140 and weight 2

• Label: 140.2
• Level: 140
• Weight: 2
• Dimension: 266
• Nonzero newspaces: 12
• Newform subspaces: 21
• Sturm bound: 2304
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 21 \)
Sturm bound:			\(2304\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(140))\).

	Total	New	Old
Modular forms	696	322	374
Cusp forms	457	266	191
Eisenstein series	239	56	183

Trace form

266 * q - 2 * q^2 + 6 * q^3 - 6 * q^4 - 5 * q^5 - 24 * q^6 + 6 * q^7 - 26 * q^8 - 18 * q^9 - 30 * q^10 - 6 * q^11 - 36 * q^12 - 32 * q^13 - 30 * q^14 - 10 * q^15 - 26 * q^16 - 6 * q^17 - 6 * q^18 + 6 * q^19 - 4 * q^20 - 54 * q^21 + 12 * q^22 - 6 * q^23 + 12 * q^24 - 57 * q^25 - 8 * q^26 - 24 * q^27 + 42 * q^28 - 84 * q^29 - 6 * q^30 - 30 * q^31 - 22 * q^32 - 102 * q^33 - 49 * q^35 - 90 * q^36 - 50 * q^37 - 48 * q^38 - 48 * q^39 - 16 * q^40 - 76 * q^41 - 36 * q^42 + 12 * q^43 - 48 * q^44 - 76 * q^45 - 48 * q^46 - 18 * q^47 - 12 * q^48 + 18 * q^49 - 14 * q^50 - 18 * q^51 + 44 * q^52 - 6 * q^53 + 96 * q^54 + 42 * q^55 + 6 * q^56 + 60 * q^57 + 80 * q^58 + 42 * q^59 + 120 * q^60 + 6 * q^61 + 96 * q^62 + 114 * q^63 + 102 * q^64 + 42 * q^65 + 132 * q^66 + 78 * q^67 + 144 * q^68 + 108 * q^69 + 162 * q^70 + 72 * q^71 + 222 * q^72 + 50 * q^73 + 144 * q^74 + 99 * q^75 + 120 * q^76 + 6 * q^77 + 72 * q^78 + 54 * q^79 + 88 * q^80 + 12 * q^81 + 52 * q^82 - 12 * q^83 + 84 * q^84 - 6 * q^85 + 60 * q^86 + 48 * q^88 - 150 * q^89 + 48 * q^90 - 36 * q^91 - 12 * q^92 - 150 * q^93 + 48 * q^94 - 107 * q^95 + 24 * q^96 - 112 * q^97 - 10 * q^98 - 120 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(140))\)

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
140.2.a	\(\chi_{140}(1, \cdot)\)	140.2.a.a	1	1
		140.2.a.b	1
140.2.c	\(\chi_{140}(139, \cdot)\)	140.2.c.a	4	1
		140.2.c.b	16
140.2.e	\(\chi_{140}(29, \cdot)\)	140.2.e.a	2	1
		140.2.e.b	2
140.2.g	\(\chi_{140}(111, \cdot)\)	140.2.g.a	4	1
		140.2.g.b	4
		140.2.g.c	8
140.2.i	\(\chi_{140}(81, \cdot)\)	140.2.i.a	2	2
		140.2.i.b	2
140.2.k	\(\chi_{140}(43, \cdot)\)	140.2.k.a	36	2
140.2.m	\(\chi_{140}(13, \cdot)\)	140.2.m.a	8	2
140.2.o	\(\chi_{140}(31, \cdot)\)	140.2.o.a	32	2
140.2.q	\(\chi_{140}(9, \cdot)\)	140.2.q.a	4	2
		140.2.q.b	4
140.2.s	\(\chi_{140}(19, \cdot)\)	140.2.s.a	8	2
		140.2.s.b	32
140.2.u	\(\chi_{140}(17, \cdot)\)	140.2.u.a	16	4
140.2.w	\(\chi_{140}(23, \cdot)\)	140.2.w.a	8	4
		140.2.w.b	72

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(140))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(140)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 1}\)