Space of modular forms of level 170 and weight 2

• Label: 170.2
• Level: 170
• Weight: 2
• Dimension: 265
• Nonzero newspaces: 10
• Newform subspaces: 30
• Sturm bound: 3456
• Trace bound: 10

Defining parameters

Level:	\( N \)	=	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 10 \)
Newform subspaces:			\( 30 \)
Sturm bound:			\(3456\)
Trace bound:			\(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(170))\).

	Total	New	Old
Modular forms	992	265	727
Cusp forms	737	265	472
Eisenstein series	255	0	255

Trace form

265 * q + q^2 + 4 * q^3 + q^4 + q^5 + 4 * q^6 + 8 * q^7 + q^8 + 13 * q^9 - 3 * q^10 - 20 * q^11 - 12 * q^12 - 18 * q^13 - 24 * q^14 - 44 * q^15 - 7 * q^16 - 15 * q^17 - 51 * q^18 - 12 * q^19 - 3 * q^20 - 64 * q^21 - 20 * q^22 - 8 * q^23 - 12 * q^24 - 35 * q^25 + 6 * q^26 - 8 * q^27 + 8 * q^28 - 10 * q^29 + 4 * q^30 - 32 * q^31 + q^32 - 16 * q^33 + 17 * q^34 - 24 * q^35 + 13 * q^36 - 26 * q^37 + 4 * q^38 - 72 * q^39 + q^40 - 94 * q^41 - 64 * q^42 - 68 * q^43 - 52 * q^44 - 71 * q^45 - 40 * q^46 - 112 * q^47 + 4 * q^48 - 71 * q^49 - 15 * q^50 - 60 * q^51 - 50 * q^52 - 82 * q^53 - 72 * q^54 - 68 * q^55 + 8 * q^56 - 96 * q^57 - 34 * q^58 - 100 * q^59 - 28 * q^60 - 34 * q^61 - 64 * q^62 - 88 * q^63 + q^64 - 22 * q^65 + 32 * q^66 + 36 * q^67 + 25 * q^68 + 96 * q^69 + 104 * q^70 + 104 * q^71 + 53 * q^72 + 226 * q^73 + 110 * q^74 + 148 * q^75 + 20 * q^76 + 192 * q^77 + 184 * q^78 + 176 * q^79 + 49 * q^80 + 297 * q^81 + 178 * q^82 + 132 * q^83 + 96 * q^84 + 269 * q^85 + 108 * q^86 + 216 * q^87 + 76 * q^88 + 90 * q^89 + 217 * q^90 + 176 * q^91 + 56 * q^92 + 128 * q^93 + 176 * q^94 + 132 * q^95 + 4 * q^96 + 162 * q^97 + 129 * q^98 + 108 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(170))\)

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
170.2.a	\(\chi_{170}(1, \cdot)\)	170.2.a.a	1	1
		170.2.a.b	1
		170.2.a.c	1
		170.2.a.d	1
		170.2.a.e	1
		170.2.a.f	2
170.2.b	\(\chi_{170}(101, \cdot)\)	170.2.b.a	2	1
		170.2.b.b	2
		170.2.b.c	2
170.2.c	\(\chi_{170}(69, \cdot)\)	170.2.c.a	2	1
		170.2.c.b	6
170.2.d	\(\chi_{170}(169, \cdot)\)	170.2.d.a	2	1
		170.2.d.b	2
		170.2.d.c	4
170.2.g	\(\chi_{170}(89, \cdot)\)	170.2.g.a	2	2
		170.2.g.b	2
		170.2.g.c	2
		170.2.g.d	2
		170.2.g.e	4
		170.2.g.f	4
170.2.h	\(\chi_{170}(21, \cdot)\)	170.2.h.a	4	2
		170.2.h.b	8
170.2.k	\(\chi_{170}(111, \cdot)\)	170.2.k.a	8	4
		170.2.k.b	16
170.2.n	\(\chi_{170}(9, \cdot)\)	170.2.n.a	20	4
		170.2.n.b	20
170.2.o	\(\chi_{170}(3, \cdot)\)	170.2.o.a	32	8
		170.2.o.b	40
170.2.r	\(\chi_{170}(23, \cdot)\)	170.2.r.a	32	8
		170.2.r.b	40

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(170))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(170)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(170))\)\(^{\oplus 1}\)