Space of modular forms of level 1456 and weight 4

• Label: 1456.4
• Level: 1456
• Weight: 4
• Dimension: 102590
• Nonzero newspaces: 70
• Sturm bound: 516096
• Trace bound: 25

Defining parameters

Level:	\( N \)	=	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 70 \)
Sturm bound:			\(516096\)
Trace bound:			\(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1456))\).

	Total	New	Old
Modular forms	195552	103582	91970
Cusp forms	191520	102590	88930
Eisenstein series	4032	992	3040

Trace form

102590 * q - 80 * q^2 - 46 * q^3 - 40 * q^4 - 106 * q^5 - 200 * q^6 - 120 * q^7 - 368 * q^8 - 62 * q^9 - 344 * q^10 + 194 * q^11 + 328 * q^12 - 62 * q^13 + 160 * q^14 - 672 * q^15 + 1048 * q^16 + 22 * q^17 + 624 * q^18 + 206 * q^19 - 856 * q^20 + 152 * q^21 - 2544 * q^22 - 82 * q^23 - 3464 * q^24 - 1498 * q^25 - 612 * q^26 - 1300 * q^27 + 464 * q^28 - 856 * q^29 + 4872 * q^30 + 1338 * q^31 + 3800 * q^32 + 670 * q^33 + 1672 * q^34 + 2020 * q^35 - 2576 * q^36 + 734 * q^37 - 5000 * q^38 + 3182 * q^39 - 5512 * q^40 + 2028 * q^41 - 6640 * q^42 - 2900 * q^43 - 3992 * q^44 - 5424 * q^45 + 256 * q^46 - 8786 * q^47 + 6760 * q^48 + 5700 * q^49 + 6912 * q^50 - 10510 * q^51 + 4088 * q^52 - 2690 * q^53 + 12232 * q^54 - 3412 * q^55 + 8168 * q^56 + 7408 * q^57 + 8192 * q^58 + 11866 * q^59 + 10920 * q^60 + 12830 * q^61 + 2416 * q^62 + 9540 * q^63 - 1000 * q^64 + 3722 * q^65 - 15080 * q^66 + 10994 * q^67 - 15712 * q^68 - 2964 * q^69 - 14656 * q^70 - 20 * q^71 - 7992 * q^72 + 1894 * q^73 - 1880 * q^74 - 16068 * q^75 - 4984 * q^76 - 6698 * q^77 - 1760 * q^78 - 20458 * q^79 - 10664 * q^80 - 6384 * q^81 - 2888 * q^82 - 20216 * q^83 - 4408 * q^84 - 19936 * q^85 - 23992 * q^86 - 16884 * q^87 - 26840 * q^88 - 22794 * q^89 - 36600 * q^90 - 6100 * q^91 + 200 * q^92 - 13858 * q^93 + 20008 * q^94 + 7930 * q^95 + 53768 * q^96 + 14380 * q^97 + 26856 * q^98 + 31492 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1456))\)

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
1456.4.a	\(\chi_{1456}(1, \cdot)\)	1456.4.a.a	1	1
		1456.4.a.b	1
		1456.4.a.c	1
		1456.4.a.d	1
		1456.4.a.e	1
		1456.4.a.f	1
		1456.4.a.g	1
		1456.4.a.h	2
		1456.4.a.i	2
		1456.4.a.j	2
		1456.4.a.k	2
		1456.4.a.l	2
		1456.4.a.m	2
		1456.4.a.n	3
		1456.4.a.o	3
		1456.4.a.p	3
		1456.4.a.q	4
		1456.4.a.r	4
		1456.4.a.s	4
		1456.4.a.t	5
		1456.4.a.u	5
		1456.4.a.v	5
		1456.4.a.w	5
		1456.4.a.x	5
		1456.4.a.y	6
		1456.4.a.z	7
		1456.4.a.ba	7
		1456.4.a.bb	7
		1456.4.a.bc	8
		1456.4.a.bd	8
1456.4.b	\(\chi_{1456}(727, \cdot)\)	None	0	1
1456.4.c	\(\chi_{1456}(729, \cdot)\)	None	0	1
1456.4.h	\(\chi_{1456}(391, \cdot)\)	None	0	1
1456.4.i	\(\chi_{1456}(1065, \cdot)\)	None	0	1
1456.4.j	\(\chi_{1456}(1119, \cdot)\)	n/a	144	1
1456.4.k	\(\chi_{1456}(337, \cdot)\)	n/a	126	1
1456.4.p	\(\chi_{1456}(1455, \cdot)\)	n/a	168	1
1456.4.q	\(\chi_{1456}(289, \cdot)\)	n/a	332	2
1456.4.r	\(\chi_{1456}(417, \cdot)\)	n/a	288	2
1456.4.s	\(\chi_{1456}(113, \cdot)\)	n/a	252	2
1456.4.t	\(\chi_{1456}(81, \cdot)\)	n/a	332	2
1456.4.v	\(\chi_{1456}(239, \cdot)\)	n/a	252	2
1456.4.w	\(\chi_{1456}(993, \cdot)\)	n/a	332	2
1456.4.y	\(\chi_{1456}(827, \cdot)\)	n/a	1008	2
1456.4.z	\(\chi_{1456}(125, \cdot)\)	n/a	1336	2
1456.4.bd	\(\chi_{1456}(27, \cdot)\)	n/a	1152	2
1456.4.be	\(\chi_{1456}(701, \cdot)\)	n/a	1008	2
1456.4.bh	\(\chi_{1456}(363, \cdot)\)	n/a	1336	2
1456.4.bi	\(\chi_{1456}(365, \cdot)\)	n/a	864	2
1456.4.bm	\(\chi_{1456}(99, \cdot)\)	n/a	1008	2
1456.4.bn	\(\chi_{1456}(853, \cdot)\)	n/a	1336	2
1456.4.bp	\(\chi_{1456}(967, \cdot)\)	None	0	2
1456.4.bq	\(\chi_{1456}(265, \cdot)\)	None	0	2
1456.4.bu	\(\chi_{1456}(121, \cdot)\)	None	0	2
1456.4.bv	\(\chi_{1456}(1095, \cdot)\)	None	0	2
1456.4.bw	\(\chi_{1456}(9, \cdot)\)	None	0	2
1456.4.bx	\(\chi_{1456}(647, \cdot)\)	None	0	2
1456.4.cc	\(\chi_{1456}(225, \cdot)\)	n/a	252	2
1456.4.cd	\(\chi_{1456}(783, \cdot)\)	n/a	336	2
1456.4.ce	\(\chi_{1456}(927, \cdot)\)	n/a	336	2
1456.4.cf	\(\chi_{1456}(831, \cdot)\)	n/a	336	2
1456.4.co	\(\chi_{1456}(753, \cdot)\)	n/a	332	2
1456.4.cp	\(\chi_{1456}(495, \cdot)\)	n/a	288	2
1456.4.cq	\(\chi_{1456}(159, \cdot)\)	n/a	336	2
1456.4.cr	\(\chi_{1456}(641, \cdot)\)	n/a	332	2
1456.4.cs	\(\chi_{1456}(335, \cdot)\)	n/a	336	2
1456.4.cx	\(\chi_{1456}(393, \cdot)\)	None	0	2
1456.4.cy	\(\chi_{1456}(615, \cdot)\)	None	0	2
1456.4.cz	\(\chi_{1456}(25, \cdot)\)	None	0	2
1456.4.da	\(\chi_{1456}(1223, \cdot)\)	None	0	2
1456.4.db	\(\chi_{1456}(87, \cdot)\)	None	0	2
1456.4.dc	\(\chi_{1456}(569, \cdot)\)	None	0	2
1456.4.dl	\(\chi_{1456}(199, \cdot)\)	None	0	2
1456.4.dm	\(\chi_{1456}(1017, \cdot)\)	None	0	2
1456.4.dn	\(\chi_{1456}(1145, \cdot)\)	None	0	2
1456.4.do	\(\chi_{1456}(103, \cdot)\)	None	0	2
1456.4.dp	\(\chi_{1456}(953, \cdot)\)	None	0	2
1456.4.dq	\(\chi_{1456}(55, \cdot)\)	None	0	2
1456.4.dv	\(\chi_{1456}(719, \cdot)\)	n/a	336	2
1456.4.dw	\(\chi_{1456}(849, \cdot)\)	n/a	332	2
1456.4.dx	\(\chi_{1456}(367, \cdot)\)	n/a	336	2
1456.4.eb	\(\chi_{1456}(33, \cdot)\)	n/a	664	4
1456.4.ec	\(\chi_{1456}(431, \cdot)\)	n/a	672	4
1456.4.ef	\(\chi_{1456}(487, \cdot)\)	None	0	4
1456.4.ei	\(\chi_{1456}(41, \cdot)\)	None	0	4
1456.4.ej	\(\chi_{1456}(73, \cdot)\)	None	0	4
1456.4.ek	\(\chi_{1456}(71, \cdot)\)	None	0	4
1456.4.el	\(\chi_{1456}(135, \cdot)\)	None	0	4
1456.4.eo	\(\chi_{1456}(89, \cdot)\)	None	0	4
1456.4.es	\(\chi_{1456}(349, \cdot)\)	n/a	2672	4
1456.4.et	\(\chi_{1456}(267, \cdot)\)	n/a	2016	4
1456.4.ew	\(\chi_{1456}(661, \cdot)\)	n/a	2672	4
1456.4.ex	\(\chi_{1456}(163, \cdot)\)	n/a	2672	4
1456.4.ey	\(\chi_{1456}(123, \cdot)\)	n/a	2672	4
1456.4.ez	\(\chi_{1456}(229, \cdot)\)	n/a	2672	4
1456.4.fa	\(\chi_{1456}(515, \cdot)\)	n/a	2672	4
1456.4.fb	\(\chi_{1456}(45, \cdot)\)	n/a	2672	4
1456.4.fh	\(\chi_{1456}(373, \cdot)\)	n/a	2672	4
1456.4.fi	\(\chi_{1456}(283, \cdot)\)	n/a	2672	4
1456.4.fl	\(\chi_{1456}(485, \cdot)\)	n/a	2672	4
1456.4.fm	\(\chi_{1456}(3, \cdot)\)	n/a	2672	4
1456.4.fp	\(\chi_{1456}(389, \cdot)\)	n/a	2672	4
1456.4.fq	\(\chi_{1456}(131, \cdot)\)	n/a	2304	4
1456.4.ft	\(\chi_{1456}(75, \cdot)\)	n/a	2672	4
1456.4.fv	\(\chi_{1456}(29, \cdot)\)	n/a	2016	4
1456.4.fw	\(\chi_{1456}(251, \cdot)\)	n/a	2672	4
1456.4.fy	\(\chi_{1456}(165, \cdot)\)	n/a	2672	4
1456.4.gb	\(\chi_{1456}(451, \cdot)\)	n/a	2672	4
1456.4.gd	\(\chi_{1456}(309, \cdot)\)	n/a	2016	4
1456.4.ge	\(\chi_{1456}(139, \cdot)\)	n/a	2672	4
1456.4.gg	\(\chi_{1456}(205, \cdot)\)	n/a	2672	4
1456.4.gj	\(\chi_{1456}(53, \cdot)\)	n/a	2304	4
1456.4.gk	\(\chi_{1456}(467, \cdot)\)	n/a	2672	4
1456.4.gm	\(\chi_{1456}(397, \cdot)\)	n/a	2672	4
1456.4.gn	\(\chi_{1456}(11, \cdot)\)	n/a	2672	4
1456.4.gu	\(\chi_{1456}(219, \cdot)\)	n/a	2672	4
1456.4.gv	\(\chi_{1456}(5, \cdot)\)	n/a	2672	4
1456.4.gw	\(\chi_{1456}(291, \cdot)\)	n/a	2672	4
1456.4.gx	\(\chi_{1456}(605, \cdot)\)	n/a	2672	4
1456.4.gy	\(\chi_{1456}(293, \cdot)\)	n/a	2672	4
1456.4.gz	\(\chi_{1456}(323, \cdot)\)	n/a	2016	4
1456.4.hd	\(\chi_{1456}(319, \cdot)\)	n/a	672	4
1456.4.hg	\(\chi_{1456}(97, \cdot)\)	n/a	664	4
1456.4.hh	\(\chi_{1456}(369, \cdot)\)	n/a	664	4
1456.4.hi	\(\chi_{1456}(15, \cdot)\)	n/a	504	4
1456.4.hj	\(\chi_{1456}(655, \cdot)\)	n/a	672	4
1456.4.hm	\(\chi_{1456}(145, \cdot)\)	n/a	664	4
1456.4.hp	\(\chi_{1456}(201, \cdot)\)	None	0	4
1456.4.hq	\(\chi_{1456}(375, \cdot)\)	None	0	4

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1456))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1456)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(364))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(728))\)\(^{\oplus 2}\)