Space of modular forms of level 140 and weight 3

• Label: 140.3
• Level: 140
• Weight: 3
• Dimension: 560
• Nonzero newspaces: 12
• Newform subspaces: 17
• Sturm bound: 3456
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 17 \)
Sturm bound:			\(3456\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(140))\).

	Total	New	Old
Modular forms	1272	624	648
Cusp forms	1032	560	472
Eisenstein series	240	64	176

Trace form

560 * q - 2 * q^2 - 10 * q^3 + 2 * q^4 - q^5 + 20 * q^6 + 22 * q^7 + 34 * q^8 + 76 * q^9 + 6 * q^10 + 14 * q^11 - 56 * q^12 - 4 * q^13 - 86 * q^14 - 58 * q^15 - 186 * q^16 - 70 * q^17 - 254 * q^18 - 54 * q^19 - 44 * q^20 + 74 * q^21 - 56 * q^22 + 194 * q^23 + 120 * q^24 + 25 * q^25 + 192 * q^26 + 188 * q^27 + 82 * q^28 - 16 * q^29 + 46 * q^30 + 170 * q^31 + 158 * q^32 - 206 * q^33 + 180 * q^34 - 65 * q^35 + 350 * q^36 - 502 * q^37 + 212 * q^38 - 252 * q^39 + 144 * q^40 - 88 * q^41 - 168 * q^42 - 236 * q^43 - 308 * q^44 - 130 * q^45 - 316 * q^46 - 150 * q^47 - 840 * q^48 - 188 * q^49 - 490 * q^50 - 494 * q^51 - 772 * q^52 - 154 * q^53 - 944 * q^54 - 216 * q^55 - 726 * q^56 - 100 * q^57 - 312 * q^58 - 198 * q^59 - 764 * q^60 - 466 * q^61 + 160 * q^62 - 458 * q^63 + 134 * q^64 - 560 * q^65 - 4 * q^66 + 18 * q^67 + 140 * q^68 - 296 * q^69 + 74 * q^70 + 40 * q^71 + 66 * q^72 + 458 * q^73 - 24 * q^74 + 841 * q^75 - 12 * q^76 + 662 * q^77 + 808 * q^78 + 518 * q^79 + 1152 * q^80 + 1674 * q^81 + 944 * q^82 + 924 * q^83 + 1648 * q^84 + 1378 * q^85 + 704 * q^86 + 1112 * q^87 + 1012 * q^88 + 1026 * q^89 + 1236 * q^90 + 780 * q^91 + 1320 * q^92 + 898 * q^93 + 544 * q^94 + 469 * q^95 + 788 * q^96 - 1116 * q^97 + 350 * q^98 - 240 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(140))\)

We only show spaces with odd 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
140.3.b	\(\chi_{140}(71, \cdot)\)	140.3.b.a	24	1
140.3.d	\(\chi_{140}(41, \cdot)\)	140.3.d.a	4	1
140.3.f	\(\chi_{140}(99, \cdot)\)	140.3.f.a	36	1
140.3.h	\(\chi_{140}(69, \cdot)\)	140.3.h.a	2	1
		140.3.h.b	2
		140.3.h.c	4
140.3.j	\(\chi_{140}(27, \cdot)\)	140.3.j.a	88	2
140.3.l	\(\chi_{140}(57, \cdot)\)	140.3.l.a	4	2
		140.3.l.b	8
140.3.n	\(\chi_{140}(89, \cdot)\)	140.3.n.a	16	2
140.3.p	\(\chi_{140}(39, \cdot)\)	140.3.p.a	4	2
		140.3.p.b	4
		140.3.p.c	80
140.3.r	\(\chi_{140}(61, \cdot)\)	140.3.r.a	12	2
140.3.t	\(\chi_{140}(11, \cdot)\)	140.3.t.a	64	2
140.3.v	\(\chi_{140}(37, \cdot)\)	140.3.v.a	32	4
140.3.x	\(\chi_{140}(3, \cdot)\)	140.3.x.a	176	4

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(140))\) into lower level spaces

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