Space of modular forms of level 2352 and weight 4

• Label: 2352.4
• Level: 2352
• Weight: 4
• Dimension: 182381
• Nonzero newspaces: 32
• Sturm bound: 1204224
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 32 \)
Sturm bound:			\(1204224\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2352))\).

	Total	New	Old
Modular forms	454944	183253	271691
Cusp forms	448224	182381	265843
Eisenstein series	6720	872	5848

Trace form

182381 * q - 50 * q^3 - 144 * q^4 + 2 * q^5 - 32 * q^6 - 108 * q^7 + 84 * q^8 + 42 * q^9 + 8 * q^10 - 60 * q^11 - 164 * q^12 - 176 * q^13 + 69 * q^15 - 424 * q^16 - 26 * q^17 - 44 * q^18 - 1138 * q^19 + 80 * q^20 - 270 * q^21 + 448 * q^22 + 256 * q^23 + 48 * q^24 + 1765 * q^25 - 20 * q^26 + 124 * q^27 - 144 * q^28 + 1258 * q^29 - 800 * q^30 + 630 * q^31 - 960 * q^32 + 281 * q^33 - 304 * q^34 - 1044 * q^35 - 604 * q^36 - 2060 * q^37 + 1256 * q^38 - 181 * q^39 + 2256 * q^40 + 414 * q^41 + 2520 * q^42 + 2662 * q^43 + 14584 * q^44 + 3819 * q^45 + 7512 * q^46 + 648 * q^47 + 852 * q^48 - 1572 * q^49 - 7692 * q^50 - 2727 * q^51 - 17368 * q^52 - 8174 * q^53 - 16168 * q^54 - 4062 * q^55 - 9240 * q^56 - 7923 * q^57 - 15072 * q^58 - 4756 * q^59 - 12244 * q^60 - 5636 * q^61 - 6612 * q^62 - 24 * q^63 + 3384 * q^64 + 7068 * q^65 + 11104 * q^66 + 782 * q^67 + 22672 * q^68 + 14011 * q^69 + 14736 * q^70 + 3152 * q^71 + 7912 * q^72 - 4852 * q^73 - 2740 * q^74 + 998 * q^75 - 2568 * q^76 - 3348 * q^78 + 5942 * q^79 + 712 * q^80 - 7162 * q^81 + 608 * q^82 + 5868 * q^83 - 72 * q^84 + 4902 * q^85 - 1712 * q^86 - 5061 * q^87 + 4808 * q^88 - 66 * q^89 + 3260 * q^90 + 10182 * q^91 - 7616 * q^92 + 3109 * q^93 - 45392 * q^94 + 47024 * q^95 - 20132 * q^96 - 902 * q^97 - 11928 * q^98 + 17216 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2352))\)

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
2352.4.a	\(\chi_{2352}(1, \cdot)\)	2352.4.a.a	1	1
		2352.4.a.b	1
		2352.4.a.c	1
		2352.4.a.d	1
		2352.4.a.e	1
		2352.4.a.f	1
		2352.4.a.g	1
		2352.4.a.h	1
		2352.4.a.i	1
		2352.4.a.j	1
		2352.4.a.k	1
		2352.4.a.l	1
		2352.4.a.m	1
		2352.4.a.n	1
		2352.4.a.o	1
		2352.4.a.p	1
		2352.4.a.q	1
		2352.4.a.r	1
		2352.4.a.s	1
		2352.4.a.t	1
		2352.4.a.u	1
		2352.4.a.v	1
		2352.4.a.w	1
		2352.4.a.x	1
		2352.4.a.y	1
		2352.4.a.z	1
		2352.4.a.ba	1
		2352.4.a.bb	1
		2352.4.a.bc	1
		2352.4.a.bd	1
		2352.4.a.be	1
		2352.4.a.bf	1
		2352.4.a.bg	1
		2352.4.a.bh	1
		2352.4.a.bi	1
		2352.4.a.bj	1
		2352.4.a.bk	1
		2352.4.a.bl	2
		2352.4.a.bm	2
		2352.4.a.bn	2
		2352.4.a.bo	2
		2352.4.a.bp	2
		2352.4.a.bq	2
		2352.4.a.br	2
		2352.4.a.bs	2
		2352.4.a.bt	2
		2352.4.a.bu	2
		2352.4.a.bv	2
		2352.4.a.bw	2
		2352.4.a.bx	2
		2352.4.a.by	2
		2352.4.a.bz	2
		2352.4.a.ca	2
		2352.4.a.cb	2
		2352.4.a.cc	2
		2352.4.a.cd	2
		2352.4.a.ce	2
		2352.4.a.cf	2
		2352.4.a.cg	3
		2352.4.a.ch	3
		2352.4.a.ci	3
		2352.4.a.cj	3
		2352.4.a.ck	4
		2352.4.a.cl	4
2352.4.a.cm	4
2352.4.a.cn	4
2352.4.a.co	4
2352.4.a.cp	4
2352.4.a.cq	4
2352.4.a.cr	4
2352.4.b	\(\chi_{2352}(1567, \cdot)\)	n/a	120	1
2352.4.c	\(\chi_{2352}(1177, \cdot)\)	None	0	1
2352.4.h	\(\chi_{2352}(2255, \cdot)\)	n/a	246	1
2352.4.i	\(\chi_{2352}(2057, \cdot)\)	None	0	1
2352.4.j	\(\chi_{2352}(1079, \cdot)\)	None	0	1
2352.4.k	\(\chi_{2352}(881, \cdot)\)	n/a	236	1
2352.4.p	\(\chi_{2352}(391, \cdot)\)	None	0	1
2352.4.q	\(\chi_{2352}(961, \cdot)\)	n/a	240	2
2352.4.s	\(\chi_{2352}(491, \cdot)\)	n/a	1948	2
2352.4.u	\(\chi_{2352}(979, \cdot)\)	n/a	960	2
2352.4.w	\(\chi_{2352}(589, \cdot)\)	n/a	984	2
2352.4.y	\(\chi_{2352}(293, \cdot)\)	n/a	1904	2
2352.4.bb	\(\chi_{2352}(1207, \cdot)\)	None	0	2
2352.4.bc	\(\chi_{2352}(1697, \cdot)\)	n/a	472	2
2352.4.bd	\(\chi_{2352}(263, \cdot)\)	None	0	2
2352.4.bi	\(\chi_{2352}(521, \cdot)\)	None	0	2
2352.4.bj	\(\chi_{2352}(863, \cdot)\)	n/a	480	2
2352.4.bk	\(\chi_{2352}(361, \cdot)\)	None	0	2
2352.4.bl	\(\chi_{2352}(31, \cdot)\)	n/a	240	2
2352.4.bo	\(\chi_{2352}(337, \cdot)\)	n/a	1008	6
2352.4.bp	\(\chi_{2352}(509, \cdot)\)	n/a	3808	4
2352.4.br	\(\chi_{2352}(373, \cdot)\)	n/a	1920	4
2352.4.bt	\(\chi_{2352}(19, \cdot)\)	n/a	1920	4
2352.4.bv	\(\chi_{2352}(275, \cdot)\)	n/a	3808	4
2352.4.bx	\(\chi_{2352}(55, \cdot)\)	None	0	6
2352.4.cc	\(\chi_{2352}(209, \cdot)\)	n/a	2004	6
2352.4.cd	\(\chi_{2352}(71, \cdot)\)	None	0	6
2352.4.ce	\(\chi_{2352}(41, \cdot)\)	None	0	6
2352.4.cf	\(\chi_{2352}(239, \cdot)\)	n/a	2016	6
2352.4.ck	\(\chi_{2352}(169, \cdot)\)	None	0	6
2352.4.cl	\(\chi_{2352}(223, \cdot)\)	n/a	1008	6
2352.4.cm	\(\chi_{2352}(193, \cdot)\)	n/a	2016	12
2352.4.cn	\(\chi_{2352}(125, \cdot)\)	n/a	16080	12
2352.4.cp	\(\chi_{2352}(85, \cdot)\)	n/a	8064	12
2352.4.cr	\(\chi_{2352}(139, \cdot)\)	n/a	8064	12
2352.4.ct	\(\chi_{2352}(155, \cdot)\)	n/a	16080	12
2352.4.cx	\(\chi_{2352}(271, \cdot)\)	n/a	2016	12
2352.4.cy	\(\chi_{2352}(25, \cdot)\)	None	0	12
2352.4.cz	\(\chi_{2352}(95, \cdot)\)	n/a	4032	12
2352.4.da	\(\chi_{2352}(89, \cdot)\)	None	0	12
2352.4.df	\(\chi_{2352}(23, \cdot)\)	None	0	12
2352.4.dg	\(\chi_{2352}(17, \cdot)\)	n/a	4008	12
2352.4.dh	\(\chi_{2352}(103, \cdot)\)	None	0	12
2352.4.dl	\(\chi_{2352}(11, \cdot)\)	n/a	32160	24
2352.4.dn	\(\chi_{2352}(115, \cdot)\)	n/a	16128	24
2352.4.dp	\(\chi_{2352}(37, \cdot)\)	n/a	16128	24
2352.4.dr	\(\chi_{2352}(5, \cdot)\)	n/a	32160	24

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2352))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2352)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 30}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 15}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 20}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(336))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(588))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(784))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1176))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2352))\)\(^{\oplus 1}\)