Space of modular forms of level 702 and weight 2

• Label: 702.2
• Level: 702
• Weight: 2
• Dimension: 3540
• Nonzero newspaces: 24
• Newform subspaces: 78
• Sturm bound: 54432
• Trace bound: 27

Defining parameters

Level:	\( N \)	=	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Newform subspaces:			\( 78 \)
Sturm bound:			\(54432\)
Trace bound:			\(27\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(702))\).

	Total	New	Old
Modular forms	14328	3540	10788
Cusp forms	12889	3540	9349
Eisenstein series	1439	0	1439

Trace form

3540 * q - 2 * q^2 - 2 * q^4 + 12 * q^5 + 12 * q^6 + 8 * q^7 + 10 * q^8 + 24 * q^9 + 12 * q^10 + 36 * q^11 + 6 * q^12 + 10 * q^13 + 8 * q^14 + 36 * q^15 - 2 * q^16 + 12 * q^17 - 12 * q^18 - 4 * q^19 - 24 * q^20 - 48 * q^21 - 36 * q^23 + 10 * q^25 - 32 * q^26 - 54 * q^27 + 4 * q^28 - 24 * q^29 - 72 * q^30 + 64 * q^31 - 2 * q^32 - 54 * q^33 + 60 * q^34 + 108 * q^35 - 12 * q^36 + 64 * q^37 + 98 * q^38 + 42 * q^39 + 12 * q^40 + 108 * q^41 + 48 * q^42 + 112 * q^43 + 48 * q^44 + 48 * q^46 + 84 * q^47 + 12 * q^48 + 110 * q^49 + 130 * q^50 + 18 * q^52 + 96 * q^53 + 72 * q^54 + 36 * q^55 + 8 * q^56 + 18 * q^57 + 36 * q^58 - 18 * q^59 + 36 * q^60 + 20 * q^61 + 32 * q^62 + 12 * q^63 + 10 * q^64 + 66 * q^65 - 52 * q^67 + 30 * q^68 - 36 * q^69 - 84 * q^70 - 48 * q^72 + 116 * q^73 - 52 * q^74 - 24 * q^75 - 46 * q^76 + 24 * q^77 - 36 * q^78 - 136 * q^79 - 24 * q^80 - 60 * q^82 + 96 * q^83 - 48 * q^85 - 52 * q^86 - 72 * q^87 - 54 * q^88 + 102 * q^89 - 36 * q^90 + 50 * q^91 + 12 * q^93 - 60 * q^94 + 36 * q^95 - 12 * q^96 - 128 * q^97 - 222 * q^98 - 144 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(702))\)

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
702.2.a	\(\chi_{702}(1, \cdot)\)	702.2.a.a	1	1
		702.2.a.b	1
		702.2.a.c	1
		702.2.a.d	1
		702.2.a.e	1
		702.2.a.f	1
		702.2.a.g	1
		702.2.a.h	1
		702.2.a.i	1
		702.2.a.j	1
		702.2.a.k	1
		702.2.a.l	1
		702.2.a.m	1
		702.2.a.n	1
		702.2.a.o	1
		702.2.a.p	1
702.2.b	\(\chi_{702}(649, \cdot)\)	702.2.b.a	2	1
		702.2.b.b	2
		702.2.b.c	2
		702.2.b.d	2
		702.2.b.e	4
		702.2.b.f	4
		702.2.b.g	4
702.2.e	\(\chi_{702}(235, \cdot)\)	702.2.e.a	2	2
		702.2.e.b	4
		702.2.e.c	4
		702.2.e.d	6
		702.2.e.e	8
702.2.f	\(\chi_{702}(289, \cdot)\)	702.2.f.a	2	2
		702.2.f.b	2
		702.2.f.c	12
		702.2.f.d	12
702.2.g	\(\chi_{702}(451, \cdot)\)	702.2.g.a	2	2
		702.2.g.b	2
		702.2.g.c	12
		702.2.g.d	12
702.2.h	\(\chi_{702}(55, \cdot)\)	702.2.h.a	2	2
		702.2.h.b	2
		702.2.h.c	2
		702.2.h.d	2
		702.2.h.e	2
		702.2.h.f	2
		702.2.h.g	4
		702.2.h.h	4
		702.2.h.i	4
		702.2.h.j	4
		702.2.h.k	4
		702.2.h.l	4
702.2.j	\(\chi_{702}(161, \cdot)\)	702.2.j.a	16	2
		702.2.j.b	24
702.2.l	\(\chi_{702}(433, \cdot)\)	702.2.l.a	8	2
		702.2.l.b	8
		702.2.l.c	8
		702.2.l.d	12
702.2.p	\(\chi_{702}(361, \cdot)\)	702.2.p.a	28	2
702.2.s	\(\chi_{702}(127, \cdot)\)	702.2.s.a	28	2
702.2.t	\(\chi_{702}(181, \cdot)\)	702.2.t.a	28	2
702.2.w	\(\chi_{702}(79, \cdot)\)	702.2.w.a	42	6
		702.2.w.b	48
		702.2.w.c	60
		702.2.w.d	66
702.2.x	\(\chi_{702}(61, \cdot)\)	702.2.x.a	126	6
		702.2.x.b	126
702.2.y	\(\chi_{702}(133, \cdot)\)	702.2.y.a	126	6
		702.2.y.b	126
702.2.ba	\(\chi_{702}(215, \cdot)\)	702.2.ba.a	16	4
		702.2.ba.b	16
		702.2.ba.c	16
		702.2.ba.d	24
702.2.bb	\(\chi_{702}(71, \cdot)\)	702.2.bb.a	56	4
702.2.bc	\(\chi_{702}(305, \cdot)\)	702.2.bc.a	56	4
702.2.bg	\(\chi_{702}(125, \cdot)\)	702.2.bg.a	56	4
702.2.bj	\(\chi_{702}(43, \cdot)\)	702.2.bj.a	252	6
702.2.bk	\(\chi_{702}(25, \cdot)\)	702.2.bk.a	252	6
702.2.bp	\(\chi_{702}(121, \cdot)\)	702.2.bp.a	252	6
702.2.br	\(\chi_{702}(41, \cdot)\)	702.2.br.a	504	12
702.2.bs	\(\chi_{702}(5, \cdot)\)	702.2.bs.a	504	12
702.2.bv	\(\chi_{702}(11, \cdot)\)	702.2.bv.a	504	12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(702))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(702)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(234))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(351))\)\(^{\oplus 2}\)