Space of modular forms of level 70 and weight 6

• Label: 70.6
• Level: 70
• Weight: 6
• Dimension: 210
• Nonzero newspaces: 6
• Newform subspaces: 21
• Sturm bound: 1728
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 21 \)
Sturm bound:			\(1728\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(70))\).

	Total	New	Old
Modular forms	768	210	558
Cusp forms	672	210	462
Eisenstein series	96	0	96

Trace form

210 * q + 8 * q^2 - 44 * q^3 + 32 * q^4 - 236 * q^5 - 272 * q^6 - 152 * q^7 + 128 * q^8 + 1130 * q^9 + 1104 * q^10 + 2368 * q^11 - 704 * q^12 - 7528 * q^13 - 1328 * q^14 + 928 * q^15 - 1536 * q^16 + 4620 * q^17 + 4808 * q^18 + 4124 * q^19 + 1920 * q^20 - 17740 * q^21 - 12288 * q^22 - 2064 * q^23 - 768 * q^24 + 5002 * q^25 + 11584 * q^26 - 704 * q^27 - 4352 * q^28 - 31596 * q^29 - 3216 * q^30 - 2792 * q^31 + 2048 * q^32 + 52656 * q^33 - 9872 * q^34 + 89230 * q^35 - 19680 * q^36 + 11324 * q^37 + 31216 * q^38 + 248 * q^39 + 12544 * q^40 - 75908 * q^41 - 55312 * q^42 - 65584 * q^43 - 11392 * q^44 - 18600 * q^45 - 40960 * q^46 + 1296 * q^47 - 11264 * q^48 - 77590 * q^49 - 43016 * q^50 - 13240 * q^51 + 40832 * q^52 + 270492 * q^53 + 243456 * q^54 + 265912 * q^55 + 57600 * q^56 + 234344 * q^57 - 17904 * q^58 - 302036 * q^59 - 86784 * q^60 - 356808 * q^61 - 282272 * q^62 - 563408 * q^63 - 90112 * q^64 + 210784 * q^65 + 334720 * q^66 + 202712 * q^67 + 73920 * q^68 + 160816 * q^69 + 34888 * q^70 + 314160 * q^71 + 76928 * q^72 + 311204 * q^73 - 50416 * q^74 - 110644 * q^75 - 159040 * q^76 - 322920 * q^77 - 589184 * q^78 - 246880 * q^79 - 60416 * q^80 - 221910 * q^81 + 281712 * q^82 + 402540 * q^83 + 278592 * q^84 + 502816 * q^85 + 744288 * q^86 + 890520 * q^87 + 76800 * q^88 - 437932 * q^89 - 604272 * q^90 - 872620 * q^91 - 530688 * q^92 - 2044768 * q^93 - 677056 * q^94 - 964424 * q^95 - 20480 * q^96 + 297236 * q^97 + 75656 * q^98 - 74800 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(70))\)

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
70.6.a	\(\chi_{70}(1, \cdot)\)	70.6.a.a	1	1
		70.6.a.b	1
		70.6.a.c	1
		70.6.a.d	1
		70.6.a.e	1
		70.6.a.f	1
		70.6.a.g	2
		70.6.a.h	2
70.6.c	\(\chi_{70}(29, \cdot)\)	70.6.c.a	2	1
		70.6.c.b	2
		70.6.c.c	2
		70.6.c.d	10
70.6.e	\(\chi_{70}(11, \cdot)\)	70.6.e.a	2	2
		70.6.e.b	2
		70.6.e.c	4
		70.6.e.d	4
		70.6.e.e	4
		70.6.e.f	8
70.6.g	\(\chi_{70}(13, \cdot)\)	70.6.g.a	40	2
70.6.i	\(\chi_{70}(9, \cdot)\)	70.6.i.a	40	2
70.6.k	\(\chi_{70}(3, \cdot)\)	70.6.k.a	80	4

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(70))\) into lower level spaces

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