Space of modular forms of level 70 and weight 4

• Label: 70.4
• Level: 70
• Weight: 4
• Dimension: 126
• Nonzero newspaces: 6
• Newform subspaces: 16
• Sturm bound: 1152
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 16 \)
Sturm bound:			\(1152\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(70))\).

	Total	New	Old
Modular forms	480	126	354
Cusp forms	384	126	258
Eisenstein series	96	0	96

Trace form

126 * q - 4 * q^2 - 8 * q^3 + 8 * q^4 + 34 * q^5 + 88 * q^6 + 100 * q^7 - 16 * q^8 - 250 * q^9 - 136 * q^10 + 4 * q^11 - 32 * q^12 - 16 * q^13 - 152 * q^14 + 172 * q^15 - 96 * q^16 + 168 * q^17 + 188 * q^18 + 80 * q^19 + 8 * q^21 + 384 * q^22 + 324 * q^23 + 288 * q^24 + 1384 * q^25 + 352 * q^26 + 592 * q^27 - 32 * q^28 - 804 * q^29 - 936 * q^30 - 1268 * q^31 - 64 * q^32 - 2508 * q^33 - 1592 * q^34 - 2528 * q^35 - 1128 * q^36 - 2032 * q^37 - 872 * q^38 - 2008 * q^39 + 96 * q^40 + 1876 * q^41 + 872 * q^42 + 2792 * q^43 + 464 * q^44 + 5640 * q^45 + 2624 * q^46 + 3372 * q^47 + 448 * q^48 + 830 * q^49 + 676 * q^50 - 700 * q^51 - 160 * q^52 - 3048 * q^53 - 192 * q^54 + 1372 * q^55 - 480 * q^56 + 1952 * q^57 + 1368 * q^58 + 1576 * q^59 + 504 * q^60 - 5436 * q^61 - 848 * q^62 - 2348 * q^63 - 640 * q^64 - 452 * q^65 + 1600 * q^66 + 116 * q^67 + 672 * q^68 - 2312 * q^69 + 276 * q^70 + 2016 * q^71 + 752 * q^72 - 5008 * q^73 - 1000 * q^74 - 2878 * q^75 - 1168 * q^76 - 5340 * q^77 - 4160 * q^78 - 2644 * q^79 + 544 * q^80 + 3402 * q^81 + 3720 * q^82 + 5292 * q^83 + 2112 * q^84 + 9868 * q^85 + 1008 * q^86 + 14184 * q^87 + 1152 * q^88 + 8120 * q^89 + 5208 * q^90 + 4820 * q^91 + 2304 * q^92 + 6548 * q^93 + 4832 * q^94 + 1570 * q^95 - 128 * q^96 - 676 * q^97 - 2308 * q^98 - 5056 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(70))\)

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
70.4.a	\(\chi_{70}(1, \cdot)\)	70.4.a.a	1	1
		70.4.a.b	1
		70.4.a.c	1
		70.4.a.d	1
		70.4.a.e	1
		70.4.a.f	1
70.4.c	\(\chi_{70}(29, \cdot)\)	70.4.c.a	2	1
		70.4.c.b	6
70.4.e	\(\chi_{70}(11, \cdot)\)	70.4.e.a	2	2
		70.4.e.b	2
		70.4.e.c	2
		70.4.e.d	4
		70.4.e.e	6
70.4.g	\(\chi_{70}(13, \cdot)\)	70.4.g.a	24	2
70.4.i	\(\chi_{70}(9, \cdot)\)	70.4.i.a	24	2
70.4.k	\(\chi_{70}(3, \cdot)\)	70.4.k.a	48	4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(70))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(70)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 2}\)