Space of modular forms of level 1824 and weight 2

• Label: 1824.2
• Level: 1824
• Weight: 2
• Dimension: 38324
• Nonzero newspaces: 36
• Sturm bound: 368640
• Trace bound: 49

Defining parameters

Level:	\( N \)	=	\( 1824 = 2^{5} \cdot 3 \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 36 \)
Sturm bound:			\(368640\)
Trace bound:			\(49\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1824))\).

	Total	New	Old
Modular forms	94464	39004	55460
Cusp forms	89857	38324	51533
Eisenstein series	4607	680	3927

Trace form

38324 * q - 50 * q^3 - 128 * q^4 - 8 * q^5 - 64 * q^6 - 100 * q^7 - 104 * q^9 - 96 * q^10 - 32 * q^12 - 104 * q^13 + 64 * q^14 - 30 * q^15 - 48 * q^16 + 32 * q^17 - 48 * q^18 - 96 * q^19 + 64 * q^20 - 32 * q^21 - 80 * q^22 + 48 * q^23 - 88 * q^24 - 156 * q^25 - 80 * q^26 + 22 * q^27 - 208 * q^28 - 8 * q^29 - 160 * q^30 - 4 * q^31 - 80 * q^32 - 164 * q^33 - 176 * q^34 + 96 * q^35 - 168 * q^36 - 168 * q^37 - 40 * q^38 - 68 * q^39 - 208 * q^40 - 16 * q^41 - 184 * q^42 - 100 * q^43 - 16 * q^44 - 136 * q^45 - 128 * q^46 - 48 * q^47 - 168 * q^48 - 148 * q^49 - 48 * q^50 - 86 * q^51 - 224 * q^52 + 24 * q^53 - 168 * q^54 - 220 * q^55 - 112 * q^56 - 124 * q^57 - 416 * q^58 - 128 * q^59 - 184 * q^60 - 8 * q^61 - 96 * q^62 - 78 * q^63 - 272 * q^64 - 16 * q^65 - 112 * q^66 - 196 * q^67 + 16 * q^68 + 64 * q^69 - 176 * q^70 - 80 * q^71 + 56 * q^72 - 112 * q^73 + 64 * q^74 - 112 * q^75 - 136 * q^76 + 128 * q^77 + 64 * q^78 - 100 * q^79 + 112 * q^80 + 40 * q^81 + 32 * q^82 + 200 * q^84 + 128 * q^86 - 182 * q^87 + 48 * q^88 + 200 * q^90 - 92 * q^91 + 160 * q^92 - 88 * q^93 + 48 * q^94 - 16 * q^95 + 144 * q^96 - 304 * q^97 + 160 * q^98 - 206 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1824))\)

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
1824.2.a	\(\chi_{1824}(1, \cdot)\)	1824.2.a.a	1	1
		1824.2.a.b	1
		1824.2.a.c	1
		1824.2.a.d	1
		1824.2.a.e	1
		1824.2.a.f	1
		1824.2.a.g	1
		1824.2.a.h	1
		1824.2.a.i	1
		1824.2.a.j	1
		1824.2.a.k	1
		1824.2.a.l	1
		1824.2.a.m	2
		1824.2.a.n	2
		1824.2.a.o	2
		1824.2.a.p	2
		1824.2.a.q	2
		1824.2.a.r	2
		1824.2.a.s	3
		1824.2.a.t	3
		1824.2.a.u	3
		1824.2.a.v	3
1824.2.d	\(\chi_{1824}(191, \cdot)\)	1824.2.d.a	4	1
		1824.2.d.b	4
		1824.2.d.c	4
		1824.2.d.d	4
		1824.2.d.e	4
		1824.2.d.f	20
		1824.2.d.g	32
1824.2.e	\(\chi_{1824}(1519, \cdot)\)	1824.2.e.a	40	1
1824.2.f	\(\chi_{1824}(1025, \cdot)\)	1824.2.f.a	4	1
		1824.2.f.b	4
		1824.2.f.c	4
		1824.2.f.d	4
		1824.2.f.e	16
		1824.2.f.f	16
		1824.2.f.g	16
		1824.2.f.h	16
1824.2.g	\(\chi_{1824}(913, \cdot)\)	1824.2.g.a	18	1
		1824.2.g.b	18
1824.2.j	\(\chi_{1824}(1103, \cdot)\)	1824.2.j.a	4	1
		1824.2.j.b	8
		1824.2.j.c	12
		1824.2.j.d	24
		1824.2.j.e	24
1824.2.k	\(\chi_{1824}(607, \cdot)\)	1824.2.k.a	20	1
		1824.2.k.b	20
1824.2.p	\(\chi_{1824}(113, \cdot)\)	1824.2.p.a	12	1
		1824.2.p.b	64
1824.2.q	\(\chi_{1824}(577, \cdot)\)	1824.2.q.a	2	2
		1824.2.q.b	2
		1824.2.q.c	2
		1824.2.q.d	2
		1824.2.q.e	2
		1824.2.q.f	2
		1824.2.q.g	2
		1824.2.q.h	2
		1824.2.q.i	4
		1824.2.q.j	4
		1824.2.q.k	6
		1824.2.q.l	6
		1824.2.q.m	6
		1824.2.q.n	6
		1824.2.q.o	6
		1824.2.q.p	6
		1824.2.q.q	10
		1824.2.q.r	10
1824.2.r	\(\chi_{1824}(569, \cdot)\)	None	0	2
1824.2.u	\(\chi_{1824}(457, \cdot)\)	None	0	2
1824.2.v	\(\chi_{1824}(647, \cdot)\)	None	0	2
1824.2.y	\(\chi_{1824}(151, \cdot)\)	None	0	2
1824.2.bb	\(\chi_{1824}(31, \cdot)\)	1824.2.bb.a	40	2
		1824.2.bb.b	40
1824.2.bc	\(\chi_{1824}(239, \cdot)\)	n/a	152	2
1824.2.bd	\(\chi_{1824}(977, \cdot)\)	n/a	152	2
1824.2.bg	\(\chi_{1824}(559, \cdot)\)	1824.2.bg.a	80	2
1824.2.bh	\(\chi_{1824}(767, \cdot)\)	n/a	160	2
1824.2.bm	\(\chi_{1824}(49, \cdot)\)	1824.2.bm.a	80	2
1824.2.bn	\(\chi_{1824}(65, \cdot)\)	n/a	160	2
1824.2.bq	\(\chi_{1824}(229, \cdot)\)	n/a	576	4
1824.2.br	\(\chi_{1824}(379, \cdot)\)	n/a	640	4
1824.2.bs	\(\chi_{1824}(419, \cdot)\)	n/a	1152	4
1824.2.bt	\(\chi_{1824}(341, \cdot)\)	n/a	1264	4
1824.2.bw	\(\chi_{1824}(289, \cdot)\)	n/a	240	6
1824.2.by	\(\chi_{1824}(121, \cdot)\)	None	0	4
1824.2.bz	\(\chi_{1824}(521, \cdot)\)	None	0	4
1824.2.cc	\(\chi_{1824}(103, \cdot)\)	None	0	4
1824.2.cd	\(\chi_{1824}(311, \cdot)\)	None	0	4
1824.2.ch	\(\chi_{1824}(401, \cdot)\)	n/a	456	6
1824.2.ci	\(\chi_{1824}(529, \cdot)\)	n/a	240	6
1824.2.ck	\(\chi_{1824}(257, \cdot)\)	n/a	480	6
1824.2.cn	\(\chi_{1824}(79, \cdot)\)	n/a	240	6
1824.2.cp	\(\chi_{1824}(479, \cdot)\)	n/a	480	6
1824.2.cq	\(\chi_{1824}(127, \cdot)\)	n/a	240	6
1824.2.cs	\(\chi_{1824}(47, \cdot)\)	n/a	456	6
1824.2.cu	\(\chi_{1824}(221, \cdot)\)	n/a	2528	8
1824.2.cv	\(\chi_{1824}(11, \cdot)\)	n/a	2528	8
1824.2.da	\(\chi_{1824}(259, \cdot)\)	n/a	1280	8
1824.2.db	\(\chi_{1824}(277, \cdot)\)	n/a	1280	8
1824.2.dd	\(\chi_{1824}(295, \cdot)\)	None	0	12
1824.2.df	\(\chi_{1824}(23, \cdot)\)	None	0	12
1824.2.dg	\(\chi_{1824}(25, \cdot)\)	None	0	12
1824.2.di	\(\chi_{1824}(41, \cdot)\)	None	0	12
1824.2.dl	\(\chi_{1824}(61, \cdot)\)	n/a	3840	24
1824.2.dm	\(\chi_{1824}(67, \cdot)\)	n/a	3840	24
1824.2.do	\(\chi_{1824}(29, \cdot)\)	n/a	7584	24
1824.2.dr	\(\chi_{1824}(35, \cdot)\)	n/a	7584	24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1824))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1824)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(304))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(456))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(608))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(912))\)\(^{\oplus 2}\)