Space of modular forms of level 168 and weight 2

• Label: 168.2
• Level: 168
• Weight: 2
• Dimension: 290
• Nonzero newspaces: 12
• Newform subspaces: 25
• Sturm bound: 3072
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 25 \)
Sturm bound:			\(3072\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(168))\).

	Total	New	Old
Modular forms	912	330	582
Cusp forms	625	290	335
Eisenstein series	287	40	247

Trace form

290 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 10 * q^6 - 8 * q^7 - 8 * q^8 - 20 * q^10 + 4 * q^11 - 22 * q^12 + 16 * q^13 - 4 * q^14 - 12 * q^15 - 12 * q^16 + 16 * q^17 + 6 * q^18 - 12 * q^19 - 20 * q^20 - 68 * q^22 - 36 * q^23 - 18 * q^24 - 42 * q^25 - 44 * q^26 - 36 * q^27 - 108 * q^28 - 12 * q^29 - 46 * q^30 - 84 * q^31 - 76 * q^32 - 50 * q^33 - 124 * q^34 - 36 * q^35 - 32 * q^36 - 24 * q^37 - 52 * q^38 - 36 * q^39 - 88 * q^40 + 4 * q^41 + 26 * q^42 - 16 * q^43 + 48 * q^44 - 38 * q^45 + 64 * q^46 - 24 * q^47 + 70 * q^48 - 54 * q^49 + 88 * q^50 - 48 * q^51 + 64 * q^52 - 32 * q^53 + 78 * q^54 - 68 * q^55 + 92 * q^56 - 64 * q^57 + 72 * q^58 - 80 * q^59 + 96 * q^60 + 4 * q^61 + 116 * q^62 - 64 * q^63 + 92 * q^64 - 40 * q^65 + 74 * q^66 - 84 * q^67 + 60 * q^68 + 8 * q^69 + 44 * q^70 - 64 * q^71 + 84 * q^72 + 20 * q^73 - 32 * q^74 + 20 * q^75 + 36 * q^76 + 36 * q^77 + 56 * q^78 + 12 * q^79 + 40 * q^81 + 60 * q^82 + 56 * q^83 + 110 * q^84 + 80 * q^85 + 16 * q^86 + 96 * q^87 - 44 * q^88 + 76 * q^89 + 116 * q^90 + 96 * q^91 + 12 * q^92 + 82 * q^93 + 12 * q^94 + 136 * q^95 + 90 * q^96 - 64 * q^97 + 64 * q^98 + 120 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(168))\)

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
168.2.a	\(\chi_{168}(1, \cdot)\)	168.2.a.a	1	1
		168.2.a.b	1
168.2.b	\(\chi_{168}(55, \cdot)\)	None	0	1
168.2.c	\(\chi_{168}(85, \cdot)\)	168.2.c.a	4	1
		168.2.c.b	8
168.2.h	\(\chi_{168}(71, \cdot)\)	None	0	1
168.2.i	\(\chi_{168}(125, \cdot)\)	168.2.i.a	4	1
		168.2.i.b	4
		168.2.i.c	4
		168.2.i.d	8
		168.2.i.e	8
168.2.j	\(\chi_{168}(155, \cdot)\)	168.2.j.a	4	1
		168.2.j.b	4
		168.2.j.c	4
		168.2.j.d	12
168.2.k	\(\chi_{168}(41, \cdot)\)	168.2.k.a	8	1
168.2.p	\(\chi_{168}(139, \cdot)\)	168.2.p.a	16	1
168.2.q	\(\chi_{168}(25, \cdot)\)	168.2.q.a	2	2
		168.2.q.b	2
		168.2.q.c	4
168.2.t	\(\chi_{168}(19, \cdot)\)	168.2.t.a	32	2
168.2.u	\(\chi_{168}(17, \cdot)\)	168.2.u.a	16	2
168.2.v	\(\chi_{168}(11, \cdot)\)	168.2.v.a	56	2
168.2.ba	\(\chi_{168}(5, \cdot)\)	168.2.ba.a	4	2
		168.2.ba.b	4
		168.2.ba.c	48
168.2.bb	\(\chi_{168}(23, \cdot)\)	None	0	2
168.2.bc	\(\chi_{168}(37, \cdot)\)	168.2.bc.a	32	2
168.2.bd	\(\chi_{168}(31, \cdot)\)	None	0	2

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(168))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(168)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 2}\)