Space of modular forms of level 2088 and weight 4

• Label: 2088.4
• Level: 2088
• Weight: 4
• Dimension: 160723
• Nonzero newspaces: 36
• Sturm bound: 967680
• Trace bound: 22

Defining parameters

Level:	\( N \)	=	\( 2088 = 2^{3} \cdot 3^{2} \cdot 29 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 36 \)
Sturm bound:			\(967680\)
Trace bound:			\(22\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2088))\).

	Total	New	Old
Modular forms	365568	161695	203873
Cusp forms	360192	160723	199469
Eisenstein series	5376	972	4404

Trace form

160723 * q - 76 * q^2 - 106 * q^3 - 56 * q^4 + 44 * q^5 - 72 * q^6 - 136 * q^8 - 266 * q^9 - 412 * q^10 - 298 * q^11 - 324 * q^12 - 128 * q^13 - 376 * q^14 - 160 * q^15 - 352 * q^16 + 116 * q^17 + 128 * q^18 + 120 * q^19 + 824 * q^20 - 456 * q^21 + 1160 * q^22 - 576 * q^23 + 416 * q^24 - 186 * q^25 - 148 * q^26 - 688 * q^27 + 52 * q^28 + 192 * q^29 - 460 * q^30 - 20 * q^31 - 416 * q^32 + 714 * q^33 - 2848 * q^34 + 804 * q^35 + 1420 * q^36 + 336 * q^37 - 872 * q^38 + 440 * q^39 - 1704 * q^40 + 1226 * q^41 + 124 * q^42 + 2930 * q^43 + 1992 * q^44 - 892 * q^45 + 5140 * q^46 + 1084 * q^47 + 1480 * q^48 - 2414 * q^49 + 6152 * q^50 - 802 * q^51 + 3040 * q^52 - 1549 * q^53 - 1360 * q^54 + 1860 * q^55 - 5332 * q^56 - 3298 * q^57 - 4882 * q^58 - 7326 * q^59 - 1708 * q^60 + 3724 * q^61 - 8684 * q^62 - 2480 * q^63 - 4052 * q^64 + 187 * q^65 - 5112 * q^66 - 306 * q^67 + 3636 * q^68 + 7420 * q^69 + 12720 * q^70 + 8480 * q^71 - 2020 * q^72 - 4089 * q^73 + 2912 * q^74 + 11646 * q^75 + 2400 * q^76 + 2520 * q^77 - 8004 * q^78 - 7676 * q^79 - 16404 * q^80 - 4098 * q^81 - 18060 * q^82 - 14828 * q^83 - 416 * q^84 - 2488 * q^85 - 376 * q^86 - 7162 * q^87 - 9028 * q^88 - 9400 * q^89 - 3852 * q^90 + 3924 * q^91 + 1824 * q^92 - 7492 * q^93 + 10020 * q^94 + 9932 * q^95 + 7952 * q^96 + 5721 * q^97 + 47308 * q^98 + 14804 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2088))\)

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
2088.4.a	\(\chi_{2088}(1, \cdot)\)	2088.4.a.a	3	1
		2088.4.a.b	3
		2088.4.a.c	4
		2088.4.a.d	4
		2088.4.a.e	4
		2088.4.a.f	5
		2088.4.a.g	5
		2088.4.a.h	5
		2088.4.a.i	6
		2088.4.a.j	6
		2088.4.a.k	6
		2088.4.a.l	6
		2088.4.a.m	6
		2088.4.a.n	10
		2088.4.a.o	10
		2088.4.a.p	11
		2088.4.a.q	11
2088.4.c	\(\chi_{2088}(2087, \cdot)\)	None	0	1
2088.4.e	\(\chi_{2088}(1799, \cdot)\)	None	0	1
2088.4.f	\(\chi_{2088}(1045, \cdot)\)	n/a	420	1
2088.4.h	\(\chi_{2088}(1333, \cdot)\)	n/a	448	1
2088.4.j	\(\chi_{2088}(755, \cdot)\)	n/a	336	1
2088.4.l	\(\chi_{2088}(1043, \cdot)\)	n/a	360	1
2088.4.o	\(\chi_{2088}(289, \cdot)\)	n/a	112	1
2088.4.q	\(\chi_{2088}(697, \cdot)\)	n/a	504	2
2088.4.r	\(\chi_{2088}(1351, \cdot)\)	None	0	2
2088.4.u	\(\chi_{2088}(1061, \cdot)\)	n/a	720	2
2088.4.w	\(\chi_{2088}(307, \cdot)\)	n/a	896	2
2088.4.x	\(\chi_{2088}(17, \cdot)\)	n/a	180	2
2088.4.ba	\(\chi_{2088}(985, \cdot)\)	n/a	540	2
2088.4.bd	\(\chi_{2088}(347, \cdot)\)	n/a	2152	2
2088.4.bf	\(\chi_{2088}(59, \cdot)\)	n/a	2016	2
2088.4.bh	\(\chi_{2088}(637, \cdot)\)	n/a	2152	2
2088.4.bj	\(\chi_{2088}(349, \cdot)\)	n/a	2016	2
2088.4.bk	\(\chi_{2088}(407, \cdot)\)	None	0	2
2088.4.bm	\(\chi_{2088}(695, \cdot)\)	None	0	2
2088.4.bo	\(\chi_{2088}(721, \cdot)\)	n/a	678	6
2088.4.bq	\(\chi_{2088}(41, \cdot)\)	n/a	1080	4
2088.4.br	\(\chi_{2088}(331, \cdot)\)	n/a	4304	4
2088.4.bt	\(\chi_{2088}(365, \cdot)\)	n/a	4304	4
2088.4.bw	\(\chi_{2088}(655, \cdot)\)	None	0	4
2088.4.by	\(\chi_{2088}(361, \cdot)\)	n/a	672	6
2088.4.cb	\(\chi_{2088}(35, \cdot)\)	n/a	2160	6
2088.4.cd	\(\chi_{2088}(107, \cdot)\)	n/a	2160	6
2088.4.cf	\(\chi_{2088}(109, \cdot)\)	n/a	2688	6
2088.4.ch	\(\chi_{2088}(181, \cdot)\)	n/a	2688	6
2088.4.ci	\(\chi_{2088}(431, \cdot)\)	None	0	6
2088.4.ck	\(\chi_{2088}(71, \cdot)\)	None	0	6
2088.4.cm	\(\chi_{2088}(25, \cdot)\)	n/a	3240	12
2088.4.co	\(\chi_{2088}(89, \cdot)\)	n/a	1080	12
2088.4.cp	\(\chi_{2088}(19, \cdot)\)	n/a	5376	12
2088.4.cr	\(\chi_{2088}(269, \cdot)\)	n/a	4320	12
2088.4.cu	\(\chi_{2088}(55, \cdot)\)	None	0	12
2088.4.cw	\(\chi_{2088}(167, \cdot)\)	None	0	12
2088.4.cy	\(\chi_{2088}(23, \cdot)\)	None	0	12
2088.4.cz	\(\chi_{2088}(277, \cdot)\)	n/a	12912	12
2088.4.db	\(\chi_{2088}(13, \cdot)\)	n/a	12912	12
2088.4.dd	\(\chi_{2088}(83, \cdot)\)	n/a	12912	12
2088.4.df	\(\chi_{2088}(299, \cdot)\)	n/a	12912	12
2088.4.di	\(\chi_{2088}(121, \cdot)\)	n/a	3240	12
2088.4.dk	\(\chi_{2088}(31, \cdot)\)	None	0	24
2088.4.dn	\(\chi_{2088}(77, \cdot)\)	n/a	25824	24
2088.4.dp	\(\chi_{2088}(43, \cdot)\)	n/a	25824	24
2088.4.dq	\(\chi_{2088}(113, \cdot)\)	n/a	6480	24

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2088))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2088)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(174))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(232))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(261))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(348))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(522))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(696))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1044))\)\(^{\oplus 2}\)