Space of modular forms of level 1656 and weight 4

• Label: 1656.4
• Level: 1656
• Weight: 4
• Dimension: 100810
• Nonzero newspaces: 24
• Sturm bound: 608256
• Trace bound: 6

Defining parameters

Level:	\( N \)	=	\( 1656 = 2^{3} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(608256\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1656))\).

	Total	New	Old
Modular forms	230208	101566	128642
Cusp forms	225984	100810	125174
Eisenstein series	4224	756	3468

Trace form

100810 * q - 58 * q^2 - 82 * q^3 - 38 * q^4 + 44 * q^5 - 48 * q^6 + 18 * q^7 - 118 * q^8 - 218 * q^9 - 358 * q^10 - 280 * q^11 - 300 * q^12 - 128 * q^13 - 358 * q^14 - 136 * q^15 - 334 * q^16 + 152 * q^17 + 152 * q^18 + 174 * q^19 + 842 * q^20 - 456 * q^21 + 1178 * q^22 - 312 * q^23 + 352 * q^24 - 150 * q^25 - 130 * q^26 - 664 * q^27 + 106 * q^28 + 384 * q^29 - 324 * q^30 - 2 * q^31 - 398 * q^32 + 762 * q^33 - 2830 * q^34 - 608 * q^35 + 1444 * q^36 - 852 * q^37 - 854 * q^38 + 464 * q^39 - 1686 * q^40 + 1812 * q^41 + 148 * q^42 + 4664 * q^43 + 2010 * q^44 - 892 * q^45 + 2498 * q^46 + 4412 * q^47 + 1504 * q^48 + 640 * q^49 + 6170 * q^50 - 778 * q^51 + 3058 * q^52 - 4122 * q^53 - 1336 * q^54 - 5778 * q^55 - 5314 * q^56 - 3250 * q^57 - 9662 * q^58 - 11778 * q^59 - 1684 * q^60 + 1204 * q^61 - 8666 * q^62 - 2456 * q^63 - 3998 * q^64 + 160 * q^65 - 5088 * q^66 + 1560 * q^67 + 3654 * q^68 + 3710 * q^69 + 12672 * q^70 + 11998 * q^71 - 1996 * q^72 + 2424 * q^73 + 7660 * q^74 + 11670 * q^75 + 18808 * q^76 + 2520 * q^77 - 7980 * q^78 - 3368 * q^79 - 8268 * q^80 - 4050 * q^81 - 18138 * q^82 - 16064 * q^83 - 392 * q^84 - 5722 * q^85 - 13778 * q^86 - 14188 * q^87 - 22830 * q^88 - 14974 * q^89 - 3828 * q^90 - 8012 * q^91 - 17130 * q^92 - 7492 * q^93 - 6792 * q^94 - 478 * q^95 + 7976 * q^96 - 3036 * q^97 + 11962 * q^98 + 14828 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1656))\)

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
1656.4.a	\(\chi_{1656}(1, \cdot)\)	1656.4.a.a	1	1
		1656.4.a.b	1
		1656.4.a.c	1
		1656.4.a.d	1
		1656.4.a.e	2
		1656.4.a.f	2
		1656.4.a.g	2
		1656.4.a.h	2
		1656.4.a.i	3
		1656.4.a.j	3
		1656.4.a.k	4
		1656.4.a.l	4
		1656.4.a.m	4
		1656.4.a.n	4
		1656.4.a.o	5
		1656.4.a.p	5
		1656.4.a.q	6
		1656.4.a.r	7
		1656.4.a.s	7
		1656.4.a.t	9
		1656.4.a.u	9
1656.4.b	\(\chi_{1656}(413, \cdot)\)	n/a	288	1
1656.4.e	\(\chi_{1656}(1151, \cdot)\)	None	0	1
1656.4.f	\(\chi_{1656}(829, \cdot)\)	n/a	330	1
1656.4.i	\(\chi_{1656}(919, \cdot)\)	None	0	1
1656.4.j	\(\chi_{1656}(323, \cdot)\)	n/a	264	1
1656.4.m	\(\chi_{1656}(1241, \cdot)\)	1656.4.m.a	72	1
1656.4.n	\(\chi_{1656}(91, \cdot)\)	n/a	358	1
1656.4.q	\(\chi_{1656}(553, \cdot)\)	n/a	396	2
1656.4.t	\(\chi_{1656}(643, \cdot)\)	n/a	1720	2
1656.4.u	\(\chi_{1656}(137, \cdot)\)	n/a	432	2
1656.4.x	\(\chi_{1656}(875, \cdot)\)	n/a	1584	2
1656.4.y	\(\chi_{1656}(367, \cdot)\)	None	0	2
1656.4.bb	\(\chi_{1656}(277, \cdot)\)	n/a	1584	2
1656.4.bc	\(\chi_{1656}(47, \cdot)\)	None	0	2
1656.4.bf	\(\chi_{1656}(965, \cdot)\)	n/a	1720	2
1656.4.bg	\(\chi_{1656}(73, \cdot)\)	n/a	900	10
1656.4.bj	\(\chi_{1656}(19, \cdot)\)	n/a	3580	10
1656.4.bk	\(\chi_{1656}(17, \cdot)\)	n/a	720	10
1656.4.bn	\(\chi_{1656}(35, \cdot)\)	n/a	2880	10
1656.4.bo	\(\chi_{1656}(199, \cdot)\)	None	0	10
1656.4.br	\(\chi_{1656}(325, \cdot)\)	n/a	3580	10
1656.4.bs	\(\chi_{1656}(71, \cdot)\)	None	0	10
1656.4.bv	\(\chi_{1656}(53, \cdot)\)	n/a	2880	10
1656.4.bw	\(\chi_{1656}(25, \cdot)\)	n/a	4320	20
1656.4.bx	\(\chi_{1656}(5, \cdot)\)	n/a	17200	20
1656.4.ca	\(\chi_{1656}(95, \cdot)\)	None	0	20
1656.4.cb	\(\chi_{1656}(13, \cdot)\)	n/a	17200	20
1656.4.ce	\(\chi_{1656}(7, \cdot)\)	None	0	20
1656.4.cf	\(\chi_{1656}(59, \cdot)\)	n/a	17200	20
1656.4.ci	\(\chi_{1656}(65, \cdot)\)	n/a	4320	20
1656.4.cj	\(\chi_{1656}(43, \cdot)\)	n/a	17200	20

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1656))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1656)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(207))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(276))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(414))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(552))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(828))\)\(^{\oplus 2}\)