Space of modular forms of level 728 and weight 2

• Label: 728.2
• Level: 728
• Weight: 2
• Dimension: 8370
• Nonzero newspaces: 45
• Newform subspaces: 94
• Sturm bound: 64512
• Trace bound: 11

Defining parameters

Level:	\( N \)	=	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 45 \)
Newform subspaces:			\( 94 \)
Sturm bound:			\(64512\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(728))\).

	Total	New	Old
Modular forms	16992	8810	8182
Cusp forms	15265	8370	6895
Eisenstein series	1727	440	1287

Trace form

8370 * q - 36 * q^2 - 36 * q^3 - 36 * q^4 - 36 * q^6 - 48 * q^7 - 96 * q^8 - 60 * q^9 - 36 * q^10 - 24 * q^11 - 36 * q^12 + 6 * q^13 - 108 * q^14 - 72 * q^15 - 36 * q^16 - 54 * q^17 - 72 * q^18 - 12 * q^19 - 72 * q^20 + 24 * q^21 - 156 * q^22 - 48 * q^23 - 108 * q^24 - 78 * q^25 - 72 * q^26 - 72 * q^27 - 144 * q^28 + 30 * q^29 - 132 * q^30 - 48 * q^31 - 96 * q^32 - 36 * q^33 - 108 * q^34 - 36 * q^35 - 228 * q^36 + 18 * q^37 - 72 * q^38 - 72 * q^39 - 240 * q^40 - 42 * q^41 - 48 * q^42 - 192 * q^43 - 108 * q^44 - 78 * q^45 - 216 * q^46 - 144 * q^47 - 108 * q^48 - 120 * q^49 - 228 * q^50 - 288 * q^51 - 204 * q^52 - 84 * q^53 - 108 * q^54 - 240 * q^55 - 72 * q^56 - 264 * q^57 - 168 * q^58 - 180 * q^59 - 144 * q^60 - 90 * q^61 - 48 * q^62 - 144 * q^63 - 156 * q^64 - 30 * q^65 - 132 * q^66 - 48 * q^67 - 36 * q^68 + 48 * q^69 - 156 * q^70 - 72 * q^71 - 72 * q^72 + 60 * q^73 - 204 * q^74 - 108 * q^75 - 180 * q^76 + 12 * q^77 - 192 * q^78 - 72 * q^79 - 264 * q^80 - 24 * q^81 - 180 * q^82 + 12 * q^83 - 180 * q^84 + 78 * q^85 - 156 * q^86 - 168 * q^87 - 60 * q^88 - 84 * q^89 + 120 * q^90 - 114 * q^91 - 228 * q^92 - 84 * q^93 + 84 * q^94 - 216 * q^95 + 348 * q^96 - 240 * q^97 + 12 * q^98 - 336 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(728))\)

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
728.2.a	\(\chi_{728}(1, \cdot)\)	728.2.a.a	1	1
		728.2.a.b	1
		728.2.a.c	1
		728.2.a.d	1
		728.2.a.e	2
		728.2.a.f	2
		728.2.a.g	2
		728.2.a.h	4
		728.2.a.i	4
728.2.b	\(\chi_{728}(363, \cdot)\)	728.2.b.a	12	1
		728.2.b.b	96
728.2.c	\(\chi_{728}(365, \cdot)\)	728.2.c.a	34	1
		728.2.c.b	38
728.2.h	\(\chi_{728}(27, \cdot)\)	728.2.h.a	48	1
		728.2.h.b	48
728.2.i	\(\chi_{728}(701, \cdot)\)	728.2.i.a	84	1
728.2.j	\(\chi_{728}(391, \cdot)\)	None	0	1
728.2.k	\(\chi_{728}(337, \cdot)\)	728.2.k.a	8	1
		728.2.k.b	12
728.2.p	\(\chi_{728}(727, \cdot)\)	None	0	1
728.2.q	\(\chi_{728}(289, \cdot)\)	728.2.q.a	2	2
		728.2.q.b	6
		728.2.q.c	8
		728.2.q.d	18
		728.2.q.e	22
728.2.r	\(\chi_{728}(417, \cdot)\)	728.2.r.a	2	2
		728.2.r.b	2
		728.2.r.c	2
		728.2.r.d	4
		728.2.r.e	8
		728.2.r.f	14
		728.2.r.g	16
728.2.s	\(\chi_{728}(113, \cdot)\)	728.2.s.a	2	2
		728.2.s.b	4
		728.2.s.c	4
		728.2.s.d	4
		728.2.s.e	8
		728.2.s.f	8
		728.2.s.g	14
728.2.t	\(\chi_{728}(9, \cdot)\)	728.2.t.a	2	2
		728.2.t.b	6
		728.2.t.c	8
		728.2.t.d	18
		728.2.t.e	22
728.2.v	\(\chi_{728}(239, \cdot)\)	None	0	2
728.2.w	\(\chi_{728}(265, \cdot)\)	728.2.w.a	56	2
728.2.z	\(\chi_{728}(99, \cdot)\)	728.2.z.a	168	2
728.2.ba	\(\chi_{728}(125, \cdot)\)	728.2.ba.a	4	2
		728.2.ba.b	4
		728.2.ba.c	8
		728.2.ba.d	8
		728.2.ba.e	192
728.2.be	\(\chi_{728}(485, \cdot)\)	728.2.be.a	216	2
728.2.bf	\(\chi_{728}(3, \cdot)\)	728.2.bf.a	4	2
		728.2.bf.b	212
728.2.bg	\(\chi_{728}(373, \cdot)\)	728.2.bg.a	8	2
		728.2.bg.b	12
		728.2.bg.c	196
728.2.bh	\(\chi_{728}(283, \cdot)\)	728.2.bh.a	216	2
728.2.bm	\(\chi_{728}(225, \cdot)\)	728.2.bm.a	4	2
		728.2.bm.b	12
		728.2.bm.c	24
728.2.bn	\(\chi_{728}(55, \cdot)\)	None	0	2
728.2.bo	\(\chi_{728}(199, \cdot)\)	None	0	2
728.2.bp	\(\chi_{728}(103, \cdot)\)	None	0	2
728.2.by	\(\chi_{728}(25, \cdot)\)	728.2.by.a	56	2
728.2.bz	\(\chi_{728}(495, \cdot)\)	None	0	2
728.2.ca	\(\chi_{728}(87, \cdot)\)	None	0	2
728.2.cb	\(\chi_{728}(569, \cdot)\)	728.2.cb.a	56	2
728.2.cc	\(\chi_{728}(335, \cdot)\)	None	0	2
728.2.ch	\(\chi_{728}(29, \cdot)\)	728.2.ch.a	84	2
		728.2.ch.b	84
728.2.ci	\(\chi_{728}(251, \cdot)\)	728.2.ci.a	216	2
728.2.cj	\(\chi_{728}(389, \cdot)\)	728.2.cj.a	216	2
728.2.ck	\(\chi_{728}(131, \cdot)\)	728.2.ck.a	96	2
		728.2.ck.b	96
728.2.cl	\(\chi_{728}(451, \cdot)\)	728.2.cl.a	4	2
		728.2.cl.b	212
728.2.cm	\(\chi_{728}(205, \cdot)\)	728.2.cm.a	216	2
728.2.cv	\(\chi_{728}(75, \cdot)\)	728.2.cv.a	216	2
728.2.cw	\(\chi_{728}(165, \cdot)\)	728.2.cw.a	8	2
		728.2.cw.b	12
		728.2.cw.c	196
728.2.cx	\(\chi_{728}(53, \cdot)\)	728.2.cx.a	192	2
728.2.cy	\(\chi_{728}(467, \cdot)\)	728.2.cy.a	24	2
		728.2.cy.b	192
728.2.cz	\(\chi_{728}(309, \cdot)\)	728.2.cz.a	168	2
728.2.da	\(\chi_{728}(139, \cdot)\)	728.2.da.a	216	2
728.2.df	\(\chi_{728}(647, \cdot)\)	None	0	2
728.2.dg	\(\chi_{728}(121, \cdot)\)	728.2.dg.a	56	2
728.2.dh	\(\chi_{728}(367, \cdot)\)	None	0	2
728.2.dl	\(\chi_{728}(33, \cdot)\)	728.2.dl.a	112	4
728.2.dm	\(\chi_{728}(375, \cdot)\)	None	0	4
728.2.dp	\(\chi_{728}(123, \cdot)\)	728.2.dp.a	432	4
728.2.ds	\(\chi_{728}(293, \cdot)\)	728.2.ds.a	16	4
		728.2.ds.b	16
		728.2.ds.c	400
728.2.dt	\(\chi_{728}(5, \cdot)\)	728.2.dt.a	432	4
728.2.du	\(\chi_{728}(267, \cdot)\)	728.2.du.a	336	4
728.2.dv	\(\chi_{728}(291, \cdot)\)	728.2.dv.a	432	4
728.2.dy	\(\chi_{728}(45, \cdot)\)	728.2.dy.a	432	4
728.2.eb	\(\chi_{728}(319, \cdot)\)	None	0	4
728.2.ee	\(\chi_{728}(41, \cdot)\)	728.2.ee.a	112	4
728.2.ef	\(\chi_{728}(73, \cdot)\)	728.2.ef.a	112	4
728.2.eg	\(\chi_{728}(15, \cdot)\)	None	0	4
728.2.eh	\(\chi_{728}(135, \cdot)\)	None	0	4
728.2.ek	\(\chi_{728}(89, \cdot)\)	728.2.ek.a	112	4
728.2.en	\(\chi_{728}(397, \cdot)\)	728.2.en.a	432	4
728.2.eo	\(\chi_{728}(11, \cdot)\)	728.2.eo.a	432	4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(728))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(728)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(364))\)\(^{\oplus 2}\)