Space of modular forms of level 70 and weight 2

• Label: 70.2
• Level: 70
• Weight: 2
• Dimension: 45
• Nonzero newspaces: 6
• Newform subspaces: 10
• Sturm bound: 576
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 10 \)
Sturm bound:			\(576\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(70))\).

	Total	New	Old
Modular forms	192	45	147
Cusp forms	97	45	52
Eisenstein series	95	0	95

Trace form

45 * q + q^2 - 3 * q^4 - 5 * q^5 - 8 * q^6 - 9 * q^7 + q^8 - 15 * q^9 - 5 * q^10 - 12 * q^11 - 6 * q^13 - 5 * q^14 - 20 * q^15 - 3 * q^16 - 30 * q^17 - 11 * q^18 - 24 * q^19 - 5 * q^20 - 24 * q^21 - 12 * q^22 - 24 * q^23 - 8 * q^24 + 9 * q^25 + 2 * q^26 + 24 * q^27 + 15 * q^28 + 30 * q^29 + 52 * q^30 + 24 * q^31 + q^32 + 72 * q^33 + 42 * q^34 + 37 * q^35 + 33 * q^36 + 30 * q^37 + 32 * q^38 + 48 * q^39 - 5 * q^40 - 6 * q^41 + 40 * q^42 - 12 * q^43 + 12 * q^44 + 7 * q^45 - 51 * q^49 - 35 * q^50 - 48 * q^51 - 6 * q^52 - 66 * q^53 - 32 * q^54 - 36 * q^55 - 5 * q^56 - 24 * q^57 - 42 * q^58 - 20 * q^60 - 6 * q^61 - 40 * q^62 + 3 * q^63 - 3 * q^64 + 2 * q^65 - 48 * q^66 + 36 * q^67 - 30 * q^68 - 35 * q^70 - 24 * q^71 - 11 * q^72 + 18 * q^73 - 34 * q^74 - 24 * q^75 - 24 * q^76 - 12 * q^77 - 40 * q^78 - 5 * q^80 - 27 * q^81 - 30 * q^82 - 24 * q^83 - 24 * q^84 - 42 * q^85 - 4 * q^86 - 48 * q^87 + 12 * q^88 + 42 * q^89 + 31 * q^90 + 6 * q^91 + 24 * q^92 + 24 * q^93 + 24 * q^94 + 92 * q^95 + 16 * q^96 + 66 * q^97 + 97 * q^98 + 36 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)

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
70.2.a	\(\chi_{70}(1, \cdot)\)	70.2.a.a	1	1
70.2.c	\(\chi_{70}(29, \cdot)\)	70.2.c.a	4	1
70.2.e	\(\chi_{70}(11, \cdot)\)	70.2.e.a	2	2
		70.2.e.b	2
		70.2.e.c	2
		70.2.e.d	2
70.2.g	\(\chi_{70}(13, \cdot)\)	70.2.g.a	8	2
70.2.i	\(\chi_{70}(9, \cdot)\)	70.2.i.a	4	2
		70.2.i.b	4
70.2.k	\(\chi_{70}(3, \cdot)\)	70.2.k.a	16	4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(70))\) into lower level spaces

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