Space of modular forms of level 1638 and weight 4

• Label: 1638.4
• Level: 1638
• Weight: 4
• Dimension: 54406
• Nonzero newspaces: 84
• Sturm bound: 580608
• Trace bound: 18

Defining parameters

Level:	\( N \)	=	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 84 \)
Sturm bound:			\(580608\)
Trace bound:			\(18\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1638))\).

	Total	New	Old
Modular forms	220032	54406	165626
Cusp forms	215424	54406	161018
Eisenstein series	4608	0	4608

Trace form

54406 * q + 16 * q^2 + 12 * q^3 - 32 * q^4 + 96 * q^5 - 72 * q^6 + 16 * q^7 - 80 * q^8 - 420 * q^9 + 60 * q^10 + 264 * q^11 + 96 * q^12 + 826 * q^13 + 1048 * q^14 + 840 * q^15 - 128 * q^16 - 1134 * q^17 - 48 * q^18 - 2344 * q^19 - 792 * q^20 - 1512 * q^21 - 1464 * q^22 - 2700 * q^23 - 288 * q^24 - 902 * q^25 - 500 * q^26 + 1584 * q^27 + 880 * q^28 + 10206 * q^29 + 3792 * q^30 + 6860 * q^31 + 256 * q^32 + 3396 * q^33 - 408 * q^34 - 1620 * q^35 - 1008 * q^36 - 7006 * q^37 - 6976 * q^38 - 9720 * q^39 - 480 * q^40 - 16854 * q^41 - 3504 * q^42 - 6100 * q^43 - 2928 * q^44 - 4632 * q^45 + 3600 * q^46 + 4284 * q^47 - 576 * q^48 + 12676 * q^49 + 9844 * q^50 + 4164 * q^51 + 3664 * q^52 + 2004 * q^53 + 2376 * q^54 - 1800 * q^55 + 352 * q^56 + 10092 * q^57 - 2076 * q^58 + 10188 * q^59 + 4320 * q^60 - 10114 * q^61 + 2528 * q^62 + 23628 * q^63 + 1408 * q^64 + 29514 * q^65 + 10752 * q^66 + 18104 * q^67 + 6456 * q^68 + 13104 * q^69 + 2832 * q^70 - 5808 * q^71 - 96 * q^72 - 7468 * q^73 + 4724 * q^74 - 27468 * q^75 + 6560 * q^76 - 15084 * q^77 - 8280 * q^78 - 18508 * q^79 - 2976 * q^80 - 13068 * q^81 - 14940 * q^82 - 32340 * q^83 + 1488 * q^84 - 35610 * q^85 + 2264 * q^86 - 888 * q^87 + 4704 * q^88 + 2316 * q^89 + 8448 * q^90 - 8870 * q^91 - 9504 * q^92 + 17976 * q^93 - 12720 * q^94 + 16788 * q^95 + 768 * q^96 + 5252 * q^97 - 26696 * q^98 - 56784 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1638))\)

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
1638.4.a	\(\chi_{1638}(1, \cdot)\)	1638.4.a.a	1	1
		1638.4.a.b	1
		1638.4.a.c	1
		1638.4.a.d	1
		1638.4.a.e	1
		1638.4.a.f	1
		1638.4.a.g	1
		1638.4.a.h	1
		1638.4.a.i	1
		1638.4.a.j	1
		1638.4.a.k	1
		1638.4.a.l	2
		1638.4.a.m	2
		1638.4.a.n	2
		1638.4.a.o	2
		1638.4.a.p	2
		1638.4.a.q	2
		1638.4.a.r	2
		1638.4.a.s	2
		1638.4.a.t	2
		1638.4.a.u	2
		1638.4.a.v	3
		1638.4.a.w	3
		1638.4.a.x	3
		1638.4.a.y	3
		1638.4.a.z	3
		1638.4.a.ba	3
		1638.4.a.bb	3
		1638.4.a.bc	3
		1638.4.a.bd	3
		1638.4.a.be	4
		1638.4.a.bf	4
		1638.4.a.bg	4
		1638.4.a.bh	5
		1638.4.a.bi	5
		1638.4.a.bj	5
		1638.4.a.bk	5
1638.4.c	\(\chi_{1638}(883, \cdot)\)	n/a	104	1
1638.4.e	\(\chi_{1638}(1637, \cdot)\)	n/a	112	1
1638.4.g	\(\chi_{1638}(755, \cdot)\)	1638.4.g.a	48	1
		1638.4.g.b	48
1638.4.i	\(\chi_{1638}(625, \cdot)\)	n/a	576	2
1638.4.j	\(\chi_{1638}(235, \cdot)\)	n/a	240	2
1638.4.k	\(\chi_{1638}(211, \cdot)\)	n/a	504	2
1638.4.l	\(\chi_{1638}(373, \cdot)\)	n/a	672	2
1638.4.m	\(\chi_{1638}(289, \cdot)\)	n/a	280	2
1638.4.n	\(\chi_{1638}(547, \cdot)\)	n/a	432	2
1638.4.o	\(\chi_{1638}(841, \cdot)\)	n/a	504	2
1638.4.p	\(\chi_{1638}(919, \cdot)\)	n/a	280	2
1638.4.q	\(\chi_{1638}(529, \cdot)\)	n/a	672	2
1638.4.r	\(\chi_{1638}(757, \cdot)\)	n/a	212	2
1638.4.s	\(\chi_{1638}(445, \cdot)\)	n/a	672	2
1638.4.t	\(\chi_{1638}(835, \cdot)\)	n/a	672	2
1638.4.u	\(\chi_{1638}(79, \cdot)\)	n/a	576	2
1638.4.x	\(\chi_{1638}(307, \cdot)\)	n/a	280	2
1638.4.y	\(\chi_{1638}(827, \cdot)\)	n/a	168	2
1638.4.z	\(\chi_{1638}(571, \cdot)\)	n/a	672	2
1638.4.bc	\(\chi_{1638}(251, \cdot)\)	n/a	224	2
1638.4.bd	\(\chi_{1638}(173, \cdot)\)	n/a	672	2
1638.4.bg	\(\chi_{1638}(563, \cdot)\)	n/a	672	2
1638.4.bi	\(\chi_{1638}(1213, \cdot)\)	n/a	672	2
1638.4.bj	\(\chi_{1638}(127, \cdot)\)	n/a	208	2
1638.4.bm	\(\chi_{1638}(205, \cdot)\)	n/a	672	2
1638.4.bn	\(\chi_{1638}(311, \cdot)\)	n/a	672	2
1638.4.bq	\(\chi_{1638}(971, \cdot)\)	n/a	224	2
1638.4.br	\(\chi_{1638}(965, \cdot)\)	n/a	672	2
1638.4.bu	\(\chi_{1638}(887, \cdot)\)	n/a	672	2
1638.4.cd	\(\chi_{1638}(731, \cdot)\)	n/a	672	2
1638.4.ce	\(\chi_{1638}(419, \cdot)\)	n/a	672	2
1638.4.cf	\(\chi_{1638}(521, \cdot)\)	n/a	192	2
1638.4.cg	\(\chi_{1638}(131, \cdot)\)	n/a	576	2
1638.4.cl	\(\chi_{1638}(209, \cdot)\)	n/a	576	2
1638.4.cm	\(\chi_{1638}(269, \cdot)\)	n/a	224	2
1638.4.cr	\(\chi_{1638}(361, \cdot)\)	n/a	280	2
1638.4.cs	\(\chi_{1638}(589, \cdot)\)	n/a	504	2
1638.4.cv	\(\chi_{1638}(277, \cdot)\)	n/a	672	2
1638.4.cy	\(\chi_{1638}(1343, \cdot)\)	n/a	672	2
1638.4.cz	\(\chi_{1638}(467, \cdot)\)	n/a	224	2
1638.4.da	\(\chi_{1638}(857, \cdot)\)	n/a	672	2
1638.4.db	\(\chi_{1638}(101, \cdot)\)	n/a	672	2
1638.4.dg	\(\chi_{1638}(17, \cdot)\)	n/a	224	2
1638.4.dh	\(\chi_{1638}(545, \cdot)\)	n/a	672	2
1638.4.dk	\(\chi_{1638}(121, \cdot)\)	n/a	672	2
1638.4.dl	\(\chi_{1638}(25, \cdot)\)	n/a	672	2
1638.4.dm	\(\chi_{1638}(415, \cdot)\)	n/a	280	2
1638.4.dn	\(\chi_{1638}(43, \cdot)\)	n/a	504	2
1638.4.ds	\(\chi_{1638}(337, \cdot)\)	n/a	504	2
1638.4.dt	\(\chi_{1638}(1297, \cdot)\)	n/a	280	2
1638.4.dv	\(\chi_{1638}(335, \cdot)\)	n/a	672	2
1638.4.dw	\(\chi_{1638}(647, \cdot)\)	n/a	224	2
1638.4.dz	\(\chi_{1638}(257, \cdot)\)	n/a	672	2
1638.4.ea	\(\chi_{1638}(677, \cdot)\)	n/a	576	2
1638.4.eg	\(\chi_{1638}(185, \cdot)\)	n/a	672	2
1638.4.eh	\(\chi_{1638}(503, \cdot)\)	n/a	224	2
1638.4.ek	\(\chi_{1638}(815, \cdot)\)	n/a	672	2
1638.4.eu	\(\chi_{1638}(31, \cdot)\)	n/a	1344	4
1638.4.ev	\(\chi_{1638}(97, \cdot)\)	n/a	1344	4
1638.4.ew	\(\chi_{1638}(115, \cdot)\)	n/a	1344	4
1638.4.ex	\(\chi_{1638}(695, \cdot)\)	n/a	1344	4
1638.4.ey	\(\chi_{1638}(71, \cdot)\)	n/a	336	4
1638.4.ez	\(\chi_{1638}(359, \cdot)\)	n/a	448	4
1638.4.fa	\(\chi_{1638}(617, \cdot)\)	n/a	1008	4
1638.4.fb	\(\chi_{1638}(431, \cdot)\)	n/a	448	4
1638.4.fc	\(\chi_{1638}(515, \cdot)\)	n/a	1344	4
1638.4.fd	\(\chi_{1638}(535, \cdot)\)	n/a	1344	4
1638.4.fe	\(\chi_{1638}(1189, \cdot)\)	n/a	560	4
1638.4.ff	\(\chi_{1638}(229, \cdot)\)	n/a	1344	4
1638.4.fg	\(\chi_{1638}(19, \cdot)\)	n/a	560	4
1638.4.fh	\(\chi_{1638}(73, \cdot)\)	n/a	560	4
1638.4.fi	\(\chi_{1638}(223, \cdot)\)	n/a	1344	4
1638.4.fj	\(\chi_{1638}(317, \cdot)\)	n/a	1344	4
1638.4.fk	\(\chi_{1638}(11, \cdot)\)	n/a	1344	4
1638.4.fl	\(\chi_{1638}(743, \cdot)\)	n/a	1008	4
1638.4.ge	\(\chi_{1638}(145, \cdot)\)	n/a	560	4
1638.4.gf	\(\chi_{1638}(821, \cdot)\)	n/a	1344	4
1638.4.gg	\(\chi_{1638}(137, \cdot)\)	n/a	1344	4
1638.4.gh	\(\chi_{1638}(239, \cdot)\)	n/a	1008	4
1638.4.gi	\(\chi_{1638}(409, \cdot)\)	n/a	1344	4
1638.4.gj	\(\chi_{1638}(241, \cdot)\)	n/a	1344	4
1638.4.gk	\(\chi_{1638}(265, \cdot)\)	n/a	1344	4
1638.4.gl	\(\chi_{1638}(305, \cdot)\)	n/a	448	4

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1638))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1638)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(234))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(273))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(546))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(819))\)\(^{\oplus 2}\)