Space of modular forms of level 1710 and weight 4

• Label: 1710.4
• Level: 1710
• Weight: 4
• Dimension: 56116
• Nonzero newspaces: 48
• Sturm bound: 622080
• Trace bound: 17

Defining parameters

Level:	\( N \)	=	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 48 \)
Sturm bound:			\(622080\)
Trace bound:			\(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1710))\).

	Total	New	Old
Modular forms	235584	56116	179468
Cusp forms	230976	56116	174860
Eisenstein series	4608	0	4608

Trace form

56116 * q + 12 * q^2 + 12 * q^3 - 24 * q^4 + 34 * q^5 - 72 * q^6 - 8 * q^7 - 48 * q^8 - 164 * q^9 + 68 * q^10 + 68 * q^11 - 32 * q^12 - 1172 * q^13 - 472 * q^14 - 492 * q^15 - 224 * q^16 - 132 * q^17 + 560 * q^18 + 2144 * q^19 + 776 * q^20 + 1440 * q^21 + 1452 * q^22 + 624 * q^23 - 96 * q^24 - 1306 * q^25 - 2496 * q^26 - 1104 * q^27 - 1472 * q^28 - 5016 * q^29 - 576 * q^30 - 2076 * q^31 + 192 * q^32 - 572 * q^33 + 1648 * q^34 + 860 * q^35 + 1168 * q^36 + 6064 * q^37 + 972 * q^38 + 1864 * q^39 - 240 * q^40 + 5156 * q^41 + 1600 * q^42 + 2596 * q^43 + 4120 * q^44 + 13844 * q^45 + 8240 * q^46 + 13404 * q^47 + 1024 * q^48 - 4026 * q^49 - 1556 * q^50 - 9300 * q^51 - 416 * q^52 - 20916 * q^53 - 11400 * q^54 - 11168 * q^55 - 13184 * q^56 - 24410 * q^57 - 8328 * q^58 - 29596 * q^59 - 2864 * q^60 - 6040 * q^61 - 8520 * q^62 - 8824 * q^63 + 1920 * q^64 + 5826 * q^65 + 10752 * q^66 + 23260 * q^67 + 3144 * q^68 + 23144 * q^69 + 6552 * q^70 + 35940 * q^71 + 6528 * q^72 + 8266 * q^73 - 4360 * q^74 - 9480 * q^75 - 4408 * q^76 - 7740 * q^77 - 4432 * q^78 + 4 * q^79 - 1184 * q^80 - 1684 * q^81 - 8088 * q^82 + 9372 * q^83 + 3744 * q^84 - 3380 * q^85 + 13384 * q^86 + 16720 * q^87 + 4512 * q^88 + 22144 * q^89 + 13888 * q^90 + 15920 * q^91 - 3552 * q^92 + 11672 * q^93 - 6928 * q^94 + 9036 * q^95 + 1024 * q^96 + 18448 * q^97 - 12684 * q^98 + 19420 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1710))\)

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
1710.4.a	\(\chi_{1710}(1, \cdot)\)	1710.4.a.a	1	1
		1710.4.a.b	1
		1710.4.a.c	1
		1710.4.a.d	1
		1710.4.a.e	1
		1710.4.a.f	1
		1710.4.a.g	1
		1710.4.a.h	1
		1710.4.a.i	1
		1710.4.a.j	1
		1710.4.a.k	2
		1710.4.a.l	2
		1710.4.a.m	2
		1710.4.a.n	2
		1710.4.a.o	2
		1710.4.a.p	2
		1710.4.a.q	2
		1710.4.a.r	2
		1710.4.a.s	2
		1710.4.a.t	2
		1710.4.a.u	2
		1710.4.a.v	3
		1710.4.a.w	3
		1710.4.a.x	3
		1710.4.a.y	3
		1710.4.a.z	3
		1710.4.a.ba	3
		1710.4.a.bb	4
		1710.4.a.bc	4
		1710.4.a.bd	4
		1710.4.a.be	4
		1710.4.a.bf	4
		1710.4.a.bg	5
		1710.4.a.bh	5
		1710.4.a.bi	5
		1710.4.a.bj	5
1710.4.c	\(\chi_{1710}(1709, \cdot)\)	n/a	120	1
1710.4.d	\(\chi_{1710}(1369, \cdot)\)	n/a	134	1
1710.4.f	\(\chi_{1710}(341, \cdot)\)	1710.4.f.a	40	1
		1710.4.f.b	40
1710.4.i	\(\chi_{1710}(121, \cdot)\)	n/a	480	2
1710.4.j	\(\chi_{1710}(571, \cdot)\)	n/a	432	2
1710.4.k	\(\chi_{1710}(391, \cdot)\)	n/a	480	2
1710.4.l	\(\chi_{1710}(1261, \cdot)\)	n/a	200	2
1710.4.n	\(\chi_{1710}(647, \cdot)\)	n/a	216	2
1710.4.p	\(\chi_{1710}(37, \cdot)\)	n/a	300	2
1710.4.q	\(\chi_{1710}(179, \cdot)\)	n/a	240	2
1710.4.t	\(\chi_{1710}(919, \cdot)\)	n/a	300	2
1710.4.x	\(\chi_{1710}(1361, \cdot)\)	n/a	480	2
1710.4.ba	\(\chi_{1710}(911, \cdot)\)	n/a	480	2
1710.4.bb	\(\chi_{1710}(221, \cdot)\)	n/a	480	2
1710.4.bd	\(\chi_{1710}(49, \cdot)\)	n/a	720	2
1710.4.bg	\(\chi_{1710}(229, \cdot)\)	n/a	648	2
1710.4.bh	\(\chi_{1710}(619, \cdot)\)	n/a	720	2
1710.4.bk	\(\chi_{1710}(749, \cdot)\)	n/a	720	2
1710.4.bl	\(\chi_{1710}(569, \cdot)\)	n/a	720	2
1710.4.bo	\(\chi_{1710}(1019, \cdot)\)	n/a	720	2
1710.4.bq	\(\chi_{1710}(521, \cdot)\)	n/a	160	2
1710.4.bs	\(\chi_{1710}(271, \cdot)\)	n/a	600	6
1710.4.bt	\(\chi_{1710}(61, \cdot)\)	n/a	1440	6
1710.4.bu	\(\chi_{1710}(481, \cdot)\)	n/a	1440	6
1710.4.bv	\(\chi_{1710}(197, \cdot)\)	n/a	480	4
1710.4.by	\(\chi_{1710}(493, \cdot)\)	n/a	1440	4
1710.4.bz	\(\chi_{1710}(103, \cdot)\)	n/a	1440	4
1710.4.cc	\(\chi_{1710}(373, \cdot)\)	n/a	1440	4
1710.4.ce	\(\chi_{1710}(77, \cdot)\)	n/a	1296	4
1710.4.cf	\(\chi_{1710}(83, \cdot)\)	n/a	1440	4
1710.4.ci	\(\chi_{1710}(353, \cdot)\)	n/a	1440	4
1710.4.cj	\(\chi_{1710}(217, \cdot)\)	n/a	600	4
1710.4.cl	\(\chi_{1710}(139, \cdot)\)	n/a	2160	6
1710.4.co	\(\chi_{1710}(299, \cdot)\)	n/a	2160	6
1710.4.cp	\(\chi_{1710}(41, \cdot)\)	n/a	1440	6
1710.4.ct	\(\chi_{1710}(71, \cdot)\)	n/a	480	6
1710.4.cv	\(\chi_{1710}(29, \cdot)\)	n/a	2160	6
1710.4.cx	\(\chi_{1710}(199, \cdot)\)	n/a	900	6
1710.4.da	\(\chi_{1710}(89, \cdot)\)	n/a	720	6
1710.4.dc	\(\chi_{1710}(499, \cdot)\)	n/a	2160	6
1710.4.df	\(\chi_{1710}(641, \cdot)\)	n/a	1440	6
1710.4.dh	\(\chi_{1710}(47, \cdot)\)	n/a	4320	12
1710.4.dk	\(\chi_{1710}(13, \cdot)\)	n/a	4320	12
1710.4.dl	\(\chi_{1710}(127, \cdot)\)	n/a	1800	12
1710.4.dm	\(\chi_{1710}(23, \cdot)\)	n/a	4320	12
1710.4.dn	\(\chi_{1710}(17, \cdot)\)	n/a	1440	12
1710.4.dq	\(\chi_{1710}(193, \cdot)\)	n/a	4320	12

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1710))\) into lower level spaces

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