Space of modular forms of level 2352 and weight 2

• Label: 2352.2
• Level: 2352
• Weight: 2
• Dimension: 60503
• Nonzero newspaces: 32
• Sturm bound: 602112
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 32 \)
Sturm bound:			\(602112\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2352))\).

	Total	New	Old
Modular forms	153888	61375	92513
Cusp forms	147169	60503	86666
Eisenstein series	6719	872	5847

Trace form

60503 * q - 46 * q^3 - 128 * q^4 - 2 * q^5 - 68 * q^6 - 108 * q^7 - 12 * q^8 - 20 * q^9 - 128 * q^10 - 12 * q^11 - 60 * q^12 - 172 * q^13 - 91 * q^15 - 104 * q^16 + 2 * q^17 - 52 * q^18 - 130 * q^19 + 16 * q^20 - 102 * q^21 - 200 * q^22 - 64 * q^23 - 32 * q^24 - 117 * q^25 + 20 * q^26 - 40 * q^27 - 144 * q^28 - 58 * q^29 - 40 * q^30 - 170 * q^31 - 191 * q^33 - 128 * q^34 - 36 * q^35 - 92 * q^36 - 232 * q^37 - 8 * q^38 - 21 * q^39 - 144 * q^40 - 6 * q^41 - 138 * q^43 + 152 * q^44 + 7 * q^45 + 72 * q^46 + 72 * q^47 + 116 * q^48 - 228 * q^49 + 300 * q^50 + 49 * q^51 + 280 * q^52 + 206 * q^53 + 228 * q^54 + 98 * q^55 + 168 * q^56 + 157 * q^57 + 232 * q^58 + 124 * q^59 + 284 * q^60 + 96 * q^61 + 420 * q^62 - 24 * q^63 + 184 * q^64 + 180 * q^65 + 232 * q^66 - 2 * q^67 + 272 * q^68 + 91 * q^69 - 48 * q^70 + 16 * q^71 + 168 * q^72 + 52 * q^74 + 74 * q^75 - 56 * q^76 - 60 * q^78 - 106 * q^79 + 8 * q^80 - 32 * q^81 - 96 * q^82 - 36 * q^83 - 72 * q^84 - 258 * q^85 - 16 * q^86 + 27 * q^87 - 152 * q^88 - 6 * q^89 - 84 * q^90 + 102 * q^91 - 64 * q^92 + 29 * q^93 - 448 * q^94 + 304 * q^95 - 356 * q^96 - 274 * q^97 - 168 * q^98 - 16 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2352))\)

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
2352.2.a	\(\chi_{2352}(1, \cdot)\)	2352.2.a.a	1	1
		2352.2.a.b	1
		2352.2.a.c	1
		2352.2.a.d	1
		2352.2.a.e	1
		2352.2.a.f	1
		2352.2.a.g	1
		2352.2.a.h	1
		2352.2.a.i	1
		2352.2.a.j	1
		2352.2.a.k	1
		2352.2.a.l	1
		2352.2.a.m	1
		2352.2.a.n	1
		2352.2.a.o	1
		2352.2.a.p	1
		2352.2.a.q	1
		2352.2.a.r	1
		2352.2.a.s	1
		2352.2.a.t	1
		2352.2.a.u	1
		2352.2.a.v	1
		2352.2.a.w	1
		2352.2.a.x	1
		2352.2.a.y	1
		2352.2.a.z	2
		2352.2.a.ba	2
		2352.2.a.bb	2
		2352.2.a.bc	2
		2352.2.a.bd	2
		2352.2.a.be	2
		2352.2.a.bf	2
		2352.2.a.bg	2
2352.2.b	\(\chi_{2352}(1567, \cdot)\)	2352.2.b.a	2	1
		2352.2.b.b	2
		2352.2.b.c	2
		2352.2.b.d	2
		2352.2.b.e	2
		2352.2.b.f	2
		2352.2.b.g	2
		2352.2.b.h	2
		2352.2.b.i	4
		2352.2.b.j	4
		2352.2.b.k	8
		2352.2.b.l	8
2352.2.c	\(\chi_{2352}(1177, \cdot)\)	None	0	1
2352.2.h	\(\chi_{2352}(2255, \cdot)\)	2352.2.h.a	2	1
		2352.2.h.b	2
		2352.2.h.c	2
		2352.2.h.d	2
		2352.2.h.e	2
		2352.2.h.f	4
		2352.2.h.g	4
		2352.2.h.h	4
		2352.2.h.i	4
		2352.2.h.j	4
		2352.2.h.k	4
		2352.2.h.l	8
		2352.2.h.m	8
		2352.2.h.n	8
		2352.2.h.o	8
		2352.2.h.p	16
2352.2.i	\(\chi_{2352}(2057, \cdot)\)	None	0	1
2352.2.j	\(\chi_{2352}(1079, \cdot)\)	None	0	1
2352.2.k	\(\chi_{2352}(881, \cdot)\)	2352.2.k.a	2	1
		2352.2.k.b	2
		2352.2.k.c	2
		2352.2.k.d	2
		2352.2.k.e	4
		2352.2.k.f	8
		2352.2.k.g	8
		2352.2.k.h	8
		2352.2.k.i	16
		2352.2.k.j	24
2352.2.p	\(\chi_{2352}(391, \cdot)\)	None	0	1
2352.2.q	\(\chi_{2352}(961, \cdot)\)	2352.2.q.a	2	2
		2352.2.q.b	2
		2352.2.q.c	2
		2352.2.q.d	2
		2352.2.q.e	2
		2352.2.q.f	2
		2352.2.q.g	2
		2352.2.q.h	2
		2352.2.q.i	2
		2352.2.q.j	2
		2352.2.q.k	2
		2352.2.q.l	2
		2352.2.q.m	2
		2352.2.q.n	2
		2352.2.q.o	2
		2352.2.q.p	2
		2352.2.q.q	2
		2352.2.q.r	2
		2352.2.q.s	2
		2352.2.q.t	2
		2352.2.q.u	2
		2352.2.q.v	2
		2352.2.q.w	2
		2352.2.q.x	2
		2352.2.q.y	2
		2352.2.q.z	2
		2352.2.q.ba	4
		2352.2.q.bb	4
		2352.2.q.bc	4
		2352.2.q.bd	4
		2352.2.q.be	4
		2352.2.q.bf	4
		2352.2.q.bg	4
2352.2.s	\(\chi_{2352}(491, \cdot)\)	n/a	636	2
2352.2.u	\(\chi_{2352}(979, \cdot)\)	n/a	320	2
2352.2.w	\(\chi_{2352}(589, \cdot)\)	n/a	328	2
2352.2.y	\(\chi_{2352}(293, \cdot)\)	n/a	624	2
2352.2.bb	\(\chi_{2352}(1207, \cdot)\)	None	0	2
2352.2.bc	\(\chi_{2352}(1697, \cdot)\)	n/a	152	2
2352.2.bd	\(\chi_{2352}(263, \cdot)\)	None	0	2
2352.2.bi	\(\chi_{2352}(521, \cdot)\)	None	0	2
2352.2.bj	\(\chi_{2352}(863, \cdot)\)	n/a	160	2
2352.2.bk	\(\chi_{2352}(361, \cdot)\)	None	0	2
2352.2.bl	\(\chi_{2352}(31, \cdot)\)	2352.2.bl.a	2	2
		2352.2.bl.b	2
		2352.2.bl.c	2
		2352.2.bl.d	2
		2352.2.bl.e	2
		2352.2.bl.f	2
		2352.2.bl.g	2
		2352.2.bl.h	2
		2352.2.bl.i	2
		2352.2.bl.j	2
		2352.2.bl.k	2
		2352.2.bl.l	2
		2352.2.bl.m	4
		2352.2.bl.n	4
		2352.2.bl.o	8
		2352.2.bl.p	8
		2352.2.bl.q	8
		2352.2.bl.r	8
		2352.2.bl.s	8
		2352.2.bl.t	8
2352.2.bo	\(\chi_{2352}(337, \cdot)\)	n/a	336	6
2352.2.bp	\(\chi_{2352}(509, \cdot)\)	n/a	1248	4
2352.2.br	\(\chi_{2352}(373, \cdot)\)	n/a	640	4
2352.2.bt	\(\chi_{2352}(19, \cdot)\)	n/a	640	4
2352.2.bv	\(\chi_{2352}(275, \cdot)\)	n/a	1248	4
2352.2.bx	\(\chi_{2352}(55, \cdot)\)	None	0	6
2352.2.cc	\(\chi_{2352}(209, \cdot)\)	n/a	660	6
2352.2.cd	\(\chi_{2352}(71, \cdot)\)	None	0	6
2352.2.ce	\(\chi_{2352}(41, \cdot)\)	None	0	6
2352.2.cf	\(\chi_{2352}(239, \cdot)\)	n/a	672	6
2352.2.ck	\(\chi_{2352}(169, \cdot)\)	None	0	6
2352.2.cl	\(\chi_{2352}(223, \cdot)\)	n/a	336	6
2352.2.cm	\(\chi_{2352}(193, \cdot)\)	n/a	672	12
2352.2.cn	\(\chi_{2352}(125, \cdot)\)	n/a	5328	12
2352.2.cp	\(\chi_{2352}(85, \cdot)\)	n/a	2688	12
2352.2.cr	\(\chi_{2352}(139, \cdot)\)	n/a	2688	12
2352.2.ct	\(\chi_{2352}(155, \cdot)\)	n/a	5328	12
2352.2.cx	\(\chi_{2352}(271, \cdot)\)	n/a	672	12
2352.2.cy	\(\chi_{2352}(25, \cdot)\)	None	0	12
2352.2.cz	\(\chi_{2352}(95, \cdot)\)	n/a	1344	12
2352.2.da	\(\chi_{2352}(89, \cdot)\)	None	0	12
2352.2.df	\(\chi_{2352}(23, \cdot)\)	None	0	12
2352.2.dg	\(\chi_{2352}(17, \cdot)\)	n/a	1320	12
2352.2.dh	\(\chi_{2352}(103, \cdot)\)	None	0	12
2352.2.dl	\(\chi_{2352}(11, \cdot)\)	n/a	10656	24
2352.2.dn	\(\chi_{2352}(115, \cdot)\)	n/a	5376	24
2352.2.dp	\(\chi_{2352}(37, \cdot)\)	n/a	5376	24
2352.2.dr	\(\chi_{2352}(5, \cdot)\)	n/a	10656	24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2352))\) into lower level spaces

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