Space of modular forms of level 1776 and weight 2

• Label: 1776.2
• Level: 1776
• Weight: 2
• Dimension: 36566
• Nonzero newspaces: 42
• Sturm bound: 350208
• Trace bound: 32

Defining parameters

Level:	\( N \)	=	\( 1776 = 2^{4} \cdot 3 \cdot 37 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 42 \)
Sturm bound:			\(350208\)
Trace bound:			\(32\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1776))\).

	Total	New	Old
Modular forms	89568	37198	52370
Cusp forms	85537	36566	48971
Eisenstein series	4031	632	3399

Trace form

36566 * q - 52 * q^3 - 128 * q^4 + 4 * q^5 - 56 * q^6 - 92 * q^7 + 24 * q^8 - 8 * q^9 - 128 * q^10 + 24 * q^11 - 72 * q^12 - 160 * q^13 - 24 * q^14 - 34 * q^15 - 176 * q^16 - 4 * q^17 - 88 * q^18 - 76 * q^19 - 32 * q^20 - 98 * q^21 - 176 * q^22 - 16 * q^23 - 128 * q^24 - 54 * q^25 - 40 * q^26 - 76 * q^27 - 144 * q^28 + 20 * q^29 - 112 * q^30 - 140 * q^31 - 146 * q^33 - 128 * q^34 - 48 * q^35 - 104 * q^36 - 146 * q^37 + 16 * q^38 - 90 * q^39 - 96 * q^40 + 12 * q^41 + 16 * q^42 - 108 * q^43 + 80 * q^44 - 62 * q^45 - 48 * q^46 + 56 * q^48 - 234 * q^49 + 72 * q^50 - 122 * q^51 - 80 * q^52 - 28 * q^53 + 24 * q^54 - 172 * q^55 - 2 * q^57 - 176 * q^58 - 56 * q^59 - 88 * q^60 - 288 * q^61 + 24 * q^62 - 70 * q^63 - 272 * q^64 + 24 * q^65 - 176 * q^66 - 140 * q^67 - 64 * q^68 - 146 * q^69 - 288 * q^70 + 16 * q^71 - 144 * q^72 - 60 * q^73 - 52 * q^74 - 70 * q^75 - 272 * q^76 - 32 * q^77 - 168 * q^78 - 76 * q^79 - 16 * q^80 - 176 * q^81 - 192 * q^82 + 72 * q^83 - 56 * q^84 - 204 * q^85 + 32 * q^86 + 54 * q^87 - 80 * q^88 + 12 * q^89 - 24 * q^90 + 20 * q^91 + 32 * q^92 - 58 * q^93 - 64 * q^94 + 112 * q^95 + 40 * q^96 - 256 * q^97 + 80 * q^98 + 74 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1776))\)

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
1776.2.a	\(\chi_{1776}(1, \cdot)\)	1776.2.a.a	1	1
		1776.2.a.b	1
		1776.2.a.c	1
		1776.2.a.d	1
		1776.2.a.e	1
		1776.2.a.f	1
		1776.2.a.g	1
		1776.2.a.h	1
		1776.2.a.i	1
		1776.2.a.j	1
		1776.2.a.k	1
		1776.2.a.l	2
		1776.2.a.m	2
		1776.2.a.n	2
		1776.2.a.o	2
		1776.2.a.p	2
		1776.2.a.q	2
		1776.2.a.r	3
		1776.2.a.s	3
		1776.2.a.t	3
		1776.2.a.u	4
1776.2.c	\(\chi_{1776}(887, \cdot)\)	None	0	1
1776.2.e	\(\chi_{1776}(815, \cdot)\)	1776.2.e.a	2	1
		1776.2.e.b	2
		1776.2.e.c	2
		1776.2.e.d	2
		1776.2.e.e	8
		1776.2.e.f	12
		1776.2.e.g	12
		1776.2.e.h	16
		1776.2.e.i	16
1776.2.f	\(\chi_{1776}(889, \cdot)\)	None	0	1
1776.2.h	\(\chi_{1776}(961, \cdot)\)	1776.2.h.a	2	1
		1776.2.h.b	2
		1776.2.h.c	2
		1776.2.h.d	4
		1776.2.h.e	4
		1776.2.h.f	4
		1776.2.h.g	4
		1776.2.h.h	6
		1776.2.h.i	10
1776.2.j	\(\chi_{1776}(1703, \cdot)\)	None	0	1
1776.2.l	\(\chi_{1776}(1775, \cdot)\)	1776.2.l.a	2	1
		1776.2.l.b	2
		1776.2.l.c	24
		1776.2.l.d	48
1776.2.o	\(\chi_{1776}(73, \cdot)\)	None	0	1
1776.2.q	\(\chi_{1776}(433, \cdot)\)	1776.2.q.a	2	2
		1776.2.q.b	2
		1776.2.q.c	2
		1776.2.q.d	2
		1776.2.q.e	2
		1776.2.q.f	2
		1776.2.q.g	2
		1776.2.q.h	4
		1776.2.q.i	4
		1776.2.q.j	6
		1776.2.q.k	6
		1776.2.q.l	6
		1776.2.q.m	6
		1776.2.q.n	6
		1776.2.q.o	6
		1776.2.q.p	8
		1776.2.q.q	10
1776.2.r	\(\chi_{1776}(413, \cdot)\)	n/a	600	2
1776.2.u	\(\chi_{1776}(43, \cdot)\)	n/a	304	2
1776.2.v	\(\chi_{1776}(487, \cdot)\)	None	0	2
1776.2.x	\(\chi_{1776}(517, \cdot)\)	n/a	304	2
1776.2.ba	\(\chi_{1776}(445, \cdot)\)	n/a	288	2
1776.2.bb	\(\chi_{1776}(31, \cdot)\)	1776.2.bb.a	14	2
		1776.2.bb.b	14
		1776.2.bb.c	24
		1776.2.bb.d	24
1776.2.be	\(\chi_{1776}(857, \cdot)\)	None	0	2
1776.2.bf	\(\chi_{1776}(371, \cdot)\)	n/a	576	2
1776.2.bi	\(\chi_{1776}(443, \cdot)\)	n/a	600	2
1776.2.bk	\(\chi_{1776}(401, \cdot)\)	n/a	148	2
1776.2.bm	\(\chi_{1776}(845, \cdot)\)	n/a	600	2
1776.2.bn	\(\chi_{1776}(475, \cdot)\)	n/a	304	2
1776.2.bp	\(\chi_{1776}(841, \cdot)\)	None	0	2
1776.2.bt	\(\chi_{1776}(359, \cdot)\)	None	0	2
1776.2.bv	\(\chi_{1776}(767, \cdot)\)	n/a	152	2
1776.2.bx	\(\chi_{1776}(121, \cdot)\)	None	0	2
1776.2.bz	\(\chi_{1776}(529, \cdot)\)	1776.2.bz.a	2	2
		1776.2.bz.b	2
		1776.2.bz.c	2
		1776.2.bz.d	4
		1776.2.bz.e	4
		1776.2.bz.f	4
		1776.2.bz.g	6
		1776.2.bz.h	8
		1776.2.bz.i	8
		1776.2.bz.j	8
		1776.2.bz.k	8
		1776.2.bz.l	20
1776.2.ca	\(\chi_{1776}(455, \cdot)\)	None	0	2
1776.2.cc	\(\chi_{1776}(47, \cdot)\)	n/a	152	2
1776.2.ce	\(\chi_{1776}(49, \cdot)\)	n/a	228	6
1776.2.cg	\(\chi_{1776}(1435, \cdot)\)	n/a	608	4
1776.2.ch	\(\chi_{1776}(29, \cdot)\)	n/a	1200	4
1776.2.cj	\(\chi_{1776}(473, \cdot)\)	None	0	4
1776.2.cm	\(\chi_{1776}(11, \cdot)\)	n/a	1200	4
1776.2.cn	\(\chi_{1776}(491, \cdot)\)	n/a	1200	4
1776.2.cp	\(\chi_{1776}(689, \cdot)\)	n/a	296	4
1776.2.cs	\(\chi_{1776}(103, \cdot)\)	None	0	4
1776.2.cu	\(\chi_{1776}(565, \cdot)\)	n/a	608	4
1776.2.cv	\(\chi_{1776}(85, \cdot)\)	n/a	608	4
1776.2.cy	\(\chi_{1776}(319, \cdot)\)	n/a	152	4
1776.2.cz	\(\chi_{1776}(547, \cdot)\)	n/a	608	4
1776.2.dc	\(\chi_{1776}(917, \cdot)\)	n/a	1200	4
1776.2.de	\(\chi_{1776}(527, \cdot)\)	n/a	456	6
1776.2.dh	\(\chi_{1776}(95, \cdot)\)	n/a	456	6
1776.2.di	\(\chi_{1776}(289, \cdot)\)	n/a	228	6
1776.2.dl	\(\chi_{1776}(71, \cdot)\)	None	0	6
1776.2.dm	\(\chi_{1776}(601, \cdot)\)	None	0	6
1776.2.dp	\(\chi_{1776}(25, \cdot)\)	None	0	6
1776.2.dq	\(\chi_{1776}(215, \cdot)\)	None	0	6
1776.2.du	\(\chi_{1776}(17, \cdot)\)	n/a	888	12
1776.2.dv	\(\chi_{1776}(79, \cdot)\)	n/a	456	12
1776.2.dw	\(\chi_{1776}(373, \cdot)\)	n/a	1824	12
1776.2.dy	\(\chi_{1776}(299, \cdot)\)	n/a	3600	12
1776.2.ea	\(\chi_{1776}(5, \cdot)\)	n/a	3600	12
1776.2.eb	\(\chi_{1776}(19, \cdot)\)	n/a	1824	12
1776.2.eg	\(\chi_{1776}(461, \cdot)\)	n/a	3600	12
1776.2.eh	\(\chi_{1776}(91, \cdot)\)	n/a	1824	12
1776.2.ei	\(\chi_{1776}(83, \cdot)\)	n/a	3600	12
1776.2.ek	\(\chi_{1776}(157, \cdot)\)	n/a	1824	12
1776.2.eo	\(\chi_{1776}(55, \cdot)\)	None	0	12
1776.2.ep	\(\chi_{1776}(89, \cdot)\)	None	0	12

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1776))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1776)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(148))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(222))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(296))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(444))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(592))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(888))\)\(^{\oplus 2}\)