Space of modular forms of level 140 and weight 4

• Label: 140.4
• Level: 140
• Weight: 4
• Dimension: 854
• Nonzero newspaces: 12
• Newform subspaces: 25
• Sturm bound: 4608
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 25 \)
Sturm bound:			\(4608\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(140))\).

	Total	New	Old
Modular forms	1848	910	938
Cusp forms	1608	854	754
Eisenstein series	240	56	184

Trace form

854 * q - 2 * q^2 + 4 * q^3 - 6 * q^4 - 60 * q^5 - 40 * q^6 - 32 * q^7 - 26 * q^8 + 122 * q^9 + 148 * q^10 + 208 * q^11 + 484 * q^12 + 20 * q^13 + 306 * q^14 - 152 * q^15 - 218 * q^16 + 88 * q^17 - 666 * q^18 - 388 * q^19 - 644 * q^20 - 1276 * q^21 - 996 * q^22 - 264 * q^23 - 708 * q^24 - 298 * q^25 + 104 * q^26 + 736 * q^27 - 422 * q^28 + 2196 * q^29 + 1568 * q^30 + 400 * q^31 - 422 * q^32 + 416 * q^33 + 958 * q^35 + 190 * q^36 - 1256 * q^37 + 28 * q^38 - 664 * q^39 - 2136 * q^40 - 92 * q^41 + 2836 * q^42 + 176 * q^43 + 4152 * q^44 - 1436 * q^45 + 5156 * q^46 - 1224 * q^47 + 5428 * q^48 - 1510 * q^49 + 3330 * q^50 + 776 * q^51 - 1380 * q^52 + 112 * q^53 - 6564 * q^54 + 1552 * q^55 - 3722 * q^56 + 2264 * q^57 - 4416 * q^58 + 844 * q^59 - 6260 * q^60 + 3760 * q^61 - 6296 * q^62 - 872 * q^63 - 2106 * q^64 + 644 * q^65 + 3672 * q^66 - 2632 * q^67 + 8168 * q^68 - 5816 * q^69 - 2048 * q^70 - 6192 * q^71 + 4974 * q^72 - 8976 * q^73 - 2652 * q^74 - 7132 * q^75 - 5512 * q^76 + 1344 * q^77 - 14280 * q^78 + 3464 * q^79 - 6808 * q^80 - 4002 * q^81 - 6028 * q^82 - 132 * q^83 - 7812 * q^84 - 684 * q^85 + 124 * q^86 + 840 * q^87 + 3792 * q^88 + 10484 * q^89 + 6888 * q^90 + 2564 * q^91 + 10388 * q^92 + 14968 * q^93 + 13548 * q^94 + 4180 * q^95 + 21368 * q^96 + 15032 * q^97 + 18494 * q^98 + 14000 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(140))\)

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
140.4.a	\(\chi_{140}(1, \cdot)\)	140.4.a.a	1	1
		140.4.a.b	1
		140.4.a.c	1
		140.4.a.d	1
		140.4.a.e	1
		140.4.a.f	1
140.4.c	\(\chi_{140}(139, \cdot)\)	140.4.c.a	4	1
		140.4.c.b	64
140.4.e	\(\chi_{140}(29, \cdot)\)	140.4.e.a	2	1
		140.4.e.b	2
		140.4.e.c	4
140.4.g	\(\chi_{140}(111, \cdot)\)	140.4.g.a	48	1
140.4.i	\(\chi_{140}(81, \cdot)\)	140.4.i.a	2	2
		140.4.i.b	2
		140.4.i.c	4
		140.4.i.d	4
		140.4.i.e	4
140.4.k	\(\chi_{140}(43, \cdot)\)	140.4.k.a	108	2
140.4.m	\(\chi_{140}(13, \cdot)\)	140.4.m.a	24	2
140.4.o	\(\chi_{140}(31, \cdot)\)	140.4.o.a	96	2
140.4.q	\(\chi_{140}(9, \cdot)\)	140.4.q.a	24	2
140.4.s	\(\chi_{140}(19, \cdot)\)	140.4.s.a	8	2
		140.4.s.b	128
140.4.u	\(\chi_{140}(17, \cdot)\)	140.4.u.a	48	4
140.4.w	\(\chi_{140}(23, \cdot)\)	140.4.w.a	272	4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(140))\) into lower level spaces

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