Space of modular forms of level 704 and weight 2

• Label: 704.2
• Level: 704
• Weight: 2
• Dimension: 8298
• Nonzero newspaces: 16
• Newform subspaces: 61
• Sturm bound: 61440
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 704 = 2^{6} \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Newform subspaces:			\( 61 \)
Sturm bound:			\(61440\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(704))\).

	Total	New	Old
Modular forms	16080	8694	7386
Cusp forms	14641	8298	6343
Eisenstein series	1439	396	1043

Trace form

8298 * q - 64 * q^2 - 48 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 44 * q^7 - 64 * q^8 - 74 * q^9 - 64 * q^10 - 50 * q^11 - 144 * q^12 - 48 * q^13 - 64 * q^14 - 36 * q^15 - 64 * q^16 - 96 * q^17 - 64 * q^18 - 32 * q^19 - 64 * q^20 - 72 * q^21 - 80 * q^22 - 104 * q^23 - 144 * q^24 - 102 * q^25 - 144 * q^26 - 60 * q^27 - 144 * q^28 - 96 * q^29 - 224 * q^30 - 92 * q^31 - 144 * q^32 - 80 * q^33 - 224 * q^34 - 52 * q^35 - 224 * q^36 - 80 * q^37 - 144 * q^38 - 44 * q^39 - 144 * q^40 - 80 * q^41 - 144 * q^42 - 24 * q^43 - 80 * q^44 - 136 * q^45 - 64 * q^46 - 12 * q^47 - 64 * q^48 - 94 * q^49 - 16 * q^50 - 100 * q^51 + 32 * q^52 - 16 * q^53 + 64 * q^54 - 116 * q^55 - 32 * q^56 - 68 * q^57 + 80 * q^58 - 184 * q^59 + 128 * q^60 - 48 * q^61 - 180 * q^63 + 128 * q^64 - 172 * q^65 + 8 * q^66 - 284 * q^67 + 32 * q^68 - 40 * q^69 + 128 * q^70 - 172 * q^71 + 80 * q^72 - 80 * q^73 + 48 * q^74 - 160 * q^75 + 64 * q^76 - 76 * q^77 - 96 * q^78 - 108 * q^79 - 144 * q^80 - 118 * q^81 - 224 * q^82 - 48 * q^83 - 288 * q^84 - 80 * q^85 - 272 * q^86 - 64 * q^87 - 152 * q^88 - 276 * q^89 - 352 * q^90 - 36 * q^91 - 368 * q^92 - 144 * q^93 - 256 * q^94 - 84 * q^95 - 336 * q^96 - 128 * q^97 - 336 * q^98 - 78 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(704))\)

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
704.2.a	\(\chi_{704}(1, \cdot)\)	704.2.a.a	1	1
		704.2.a.b	1
		704.2.a.c	1
		704.2.a.d	1
		704.2.a.e	1
		704.2.a.f	1
		704.2.a.g	1
		704.2.a.h	1
		704.2.a.i	1
		704.2.a.j	1
		704.2.a.k	1
		704.2.a.l	1
		704.2.a.m	2
		704.2.a.n	2
		704.2.a.o	2
		704.2.a.p	2
704.2.c	\(\chi_{704}(353, \cdot)\)	704.2.c.a	4	1
		704.2.c.b	4
		704.2.c.c	12
704.2.e	\(\chi_{704}(703, \cdot)\)	704.2.e.a	2	1
		704.2.e.b	4
		704.2.e.c	4
		704.2.e.d	12
704.2.g	\(\chi_{704}(351, \cdot)\)	704.2.g.a	4	1
		704.2.g.b	4
		704.2.g.c	8
		704.2.g.d	8
704.2.i	\(\chi_{704}(175, \cdot)\)	704.2.i.a	44	2
704.2.j	\(\chi_{704}(177, \cdot)\)	704.2.j.a	40	2
704.2.m	\(\chi_{704}(257, \cdot)\)	704.2.m.a	4	4
		704.2.m.b	4
		704.2.m.c	4
		704.2.m.d	4
		704.2.m.e	4
		704.2.m.f	4
		704.2.m.g	4
		704.2.m.h	4
		704.2.m.i	8
		704.2.m.j	8
		704.2.m.k	8
		704.2.m.l	8
		704.2.m.m	12
		704.2.m.n	12
704.2.n	\(\chi_{704}(89, \cdot)\)	None	0	4
704.2.q	\(\chi_{704}(87, \cdot)\)	None	0	4
704.2.s	\(\chi_{704}(95, \cdot)\)	704.2.s.a	8	4
		704.2.s.b	8
		704.2.s.c	8
		704.2.s.d	8
		704.2.s.e	64
704.2.u	\(\chi_{704}(63, \cdot)\)	704.2.u.a	8	4
		704.2.u.b	16
		704.2.u.c	16
		704.2.u.d	48
704.2.w	\(\chi_{704}(97, \cdot)\)	704.2.w.a	16	4
		704.2.w.b	16
		704.2.w.c	64
704.2.z	\(\chi_{704}(45, \cdot)\)	704.2.z.a	640	8
704.2.bb	\(\chi_{704}(43, \cdot)\)	704.2.bb.a	752	8
704.2.be	\(\chi_{704}(49, \cdot)\)	704.2.be.a	176	8
704.2.bf	\(\chi_{704}(79, \cdot)\)	704.2.bf.a	176	8
704.2.bg	\(\chi_{704}(7, \cdot)\)	None	0	16
704.2.bj	\(\chi_{704}(9, \cdot)\)	None	0	16
704.2.bk	\(\chi_{704}(19, \cdot)\)	704.2.bk.a	3008	32
704.2.bm	\(\chi_{704}(5, \cdot)\)	704.2.bm.a	3008	32

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(704))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(704)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(352))\)\(^{\oplus 2}\)