Space of modular forms of level 1710 and weight 2

• Label: 1710.2
• Level: 1710
• Weight: 2
• Dimension: 18704
• Nonzero newspaces: 48
• Sturm bound: 311040
• Trace bound: 17

Defining parameters

Level:	\( N \)	=	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 48 \)
Sturm bound:			\(311040\)
Trace bound:			\(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1710))\).

	Total	New	Old
Modular forms	80064	18704	61360
Cusp forms	75457	18704	56753
Eisenstein series	4607	0	4607

Trace form

18704 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 10 * q^5 + 12 * q^6 - 24 * q^7 + 6 * q^8 + 28 * q^9 + 22 * q^10 + 52 * q^11 + 16 * q^12 - 20 * q^13 + 4 * q^14 + 48 * q^15 - 6 * q^16 + 8 * q^18 - 76 * q^19 + 4 * q^20 + 72 * q^21 - 34 * q^22 + 36 * q^23 - 12 * q^24 - 2 * q^25 - 48 * q^26 + 48 * q^27 - 12 * q^28 - 24 * q^29 - 20 * q^31 - 6 * q^32 - 20 * q^33 - 8 * q^34 - 68 * q^35 - 20 * q^36 + 16 * q^37 - 42 * q^38 - 128 * q^39 + 6 * q^40 - 188 * q^41 - 128 * q^42 - 56 * q^43 - 10 * q^44 - 52 * q^45 + 216 * q^46 + 168 * q^47 + 16 * q^48 + 210 * q^49 + 122 * q^50 + 300 * q^51 + 16 * q^52 + 372 * q^53 + 156 * q^54 + 256 * q^55 + 176 * q^56 + 334 * q^57 + 148 * q^58 + 520 * q^59 + 88 * q^60 + 392 * q^61 + 324 * q^62 + 368 * q^63 + 42 * q^64 + 336 * q^65 + 384 * q^66 + 216 * q^67 + 126 * q^68 + 344 * q^69 + 156 * q^70 + 432 * q^71 + 48 * q^72 + 98 * q^73 + 100 * q^74 - 12 * q^75 + 46 * q^76 + 24 * q^77 + 56 * q^78 + 52 * q^79 - 10 * q^80 - 4 * q^81 + 188 * q^82 + 24 * q^84 + 276 * q^85 + 212 * q^86 + 40 * q^87 + 20 * q^88 + 164 * q^89 + 112 * q^90 + 224 * q^91 + 144 * q^92 - 64 * q^93 + 200 * q^94 + 258 * q^95 + 16 * q^96 + 412 * q^97 + 198 * q^98 + 292 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1710))\)

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
1710.2.a	\(\chi_{1710}(1, \cdot)\)	1710.2.a.a	1	1
		1710.2.a.b	1
		1710.2.a.c	1
		1710.2.a.d	1
		1710.2.a.e	1
		1710.2.a.f	1
		1710.2.a.g	1
		1710.2.a.h	1
		1710.2.a.i	1
		1710.2.a.j	1
		1710.2.a.k	1
		1710.2.a.l	1
		1710.2.a.m	1
		1710.2.a.n	1
		1710.2.a.o	1
		1710.2.a.p	1
		1710.2.a.q	1
		1710.2.a.r	1
		1710.2.a.s	1
		1710.2.a.t	1
		1710.2.a.u	2
		1710.2.a.v	2
		1710.2.a.w	2
		1710.2.a.x	2
		1710.2.a.y	2
1710.2.c	\(\chi_{1710}(1709, \cdot)\)	1710.2.c.a	4	1
		1710.2.c.b	4
		1710.2.c.c	8
		1710.2.c.d	24
1710.2.d	\(\chi_{1710}(1369, \cdot)\)	1710.2.d.a	2	1
		1710.2.d.b	2
		1710.2.d.c	4
		1710.2.d.d	6
		1710.2.d.e	6
		1710.2.d.f	6
		1710.2.d.g	8
		1710.2.d.h	12
1710.2.f	\(\chi_{1710}(341, \cdot)\)	1710.2.f.a	16	1
		1710.2.f.b	16
1710.2.i	\(\chi_{1710}(121, \cdot)\)	n/a	160	2
1710.2.j	\(\chi_{1710}(571, \cdot)\)	n/a	144	2
1710.2.k	\(\chi_{1710}(391, \cdot)\)	n/a	160	2
1710.2.l	\(\chi_{1710}(1261, \cdot)\)	1710.2.l.a	2	2
		1710.2.l.b	2
		1710.2.l.c	2
		1710.2.l.d	2
		1710.2.l.e	2
		1710.2.l.f	2
		1710.2.l.g	2
		1710.2.l.h	2
		1710.2.l.i	2
		1710.2.l.j	4
		1710.2.l.k	4
		1710.2.l.l	4
		1710.2.l.m	4
		1710.2.l.n	4
		1710.2.l.o	6
		1710.2.l.p	6
		1710.2.l.q	6
		1710.2.l.r	8
		1710.2.l.s	8
1710.2.n	\(\chi_{1710}(647, \cdot)\)	1710.2.n.a	4	2
		1710.2.n.b	4
		1710.2.n.c	4
		1710.2.n.d	4
		1710.2.n.e	4
		1710.2.n.f	8
		1710.2.n.g	8
		1710.2.n.h	16
		1710.2.n.i	20
1710.2.p	\(\chi_{1710}(37, \cdot)\)	1710.2.p.a	4	2
		1710.2.p.b	16
		1710.2.p.c	20
		1710.2.p.d	20
		1710.2.p.e	40
1710.2.q	\(\chi_{1710}(179, \cdot)\)	1710.2.q.a	16	2
		1710.2.q.b	64
1710.2.t	\(\chi_{1710}(919, \cdot)\)	1710.2.t.a	8	2
		1710.2.t.b	12
		1710.2.t.c	20
		1710.2.t.d	20
		1710.2.t.e	40
1710.2.x	\(\chi_{1710}(1361, \cdot)\)	n/a	160	2
1710.2.ba	\(\chi_{1710}(911, \cdot)\)	n/a	160	2
1710.2.bb	\(\chi_{1710}(221, \cdot)\)	n/a	160	2
1710.2.bd	\(\chi_{1710}(49, \cdot)\)	n/a	240	2
1710.2.bg	\(\chi_{1710}(229, \cdot)\)	n/a	216	2
1710.2.bh	\(\chi_{1710}(619, \cdot)\)	n/a	240	2
1710.2.bk	\(\chi_{1710}(749, \cdot)\)	n/a	240	2
1710.2.bl	\(\chi_{1710}(569, \cdot)\)	n/a	240	2
1710.2.bo	\(\chi_{1710}(1019, \cdot)\)	n/a	240	2
1710.2.bq	\(\chi_{1710}(521, \cdot)\)	1710.2.bq.a	32	2
		1710.2.bq.b	32
1710.2.bs	\(\chi_{1710}(271, \cdot)\)	n/a	192	6
1710.2.bt	\(\chi_{1710}(61, \cdot)\)	n/a	480	6
1710.2.bu	\(\chi_{1710}(481, \cdot)\)	n/a	480	6
1710.2.bv	\(\chi_{1710}(197, \cdot)\)	n/a	160	4
1710.2.by	\(\chi_{1710}(493, \cdot)\)	n/a	480	4
1710.2.bz	\(\chi_{1710}(103, \cdot)\)	n/a	480	4
1710.2.cc	\(\chi_{1710}(373, \cdot)\)	n/a	480	4
1710.2.ce	\(\chi_{1710}(77, \cdot)\)	n/a	432	4
1710.2.cf	\(\chi_{1710}(83, \cdot)\)	n/a	480	4
1710.2.ci	\(\chi_{1710}(353, \cdot)\)	n/a	480	4
1710.2.cj	\(\chi_{1710}(217, \cdot)\)	n/a	200	4
1710.2.cl	\(\chi_{1710}(139, \cdot)\)	n/a	720	6
1710.2.co	\(\chi_{1710}(299, \cdot)\)	n/a	720	6
1710.2.cp	\(\chi_{1710}(41, \cdot)\)	n/a	480	6
1710.2.ct	\(\chi_{1710}(71, \cdot)\)	n/a	144	6
1710.2.cv	\(\chi_{1710}(29, \cdot)\)	n/a	720	6
1710.2.cx	\(\chi_{1710}(199, \cdot)\)	n/a	300	6
1710.2.da	\(\chi_{1710}(89, \cdot)\)	n/a	240	6
1710.2.dc	\(\chi_{1710}(499, \cdot)\)	n/a	720	6
1710.2.df	\(\chi_{1710}(641, \cdot)\)	n/a	480	6
1710.2.dh	\(\chi_{1710}(47, \cdot)\)	n/a	1440	12
1710.2.dk	\(\chi_{1710}(13, \cdot)\)	n/a	1440	12
1710.2.dl	\(\chi_{1710}(127, \cdot)\)	n/a	600	12
1710.2.dm	\(\chi_{1710}(23, \cdot)\)	n/a	1440	12
1710.2.dn	\(\chi_{1710}(17, \cdot)\)	n/a	480	12
1710.2.dq	\(\chi_{1710}(193, \cdot)\)	n/a	1440	12

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1710))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1710)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(190))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(285))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(342))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(570))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(855))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1710))\)\(^{\oplus 1}\)