Space of modular forms of level 2816 and weight 2

• Label: 2816.2
• Level: 2816
• Weight: 2
• Dimension: 135000
• Nonzero newspaces: 24
• Sturm bound: 983040
• Trace bound: 129

Defining parameters

Level:	\( N \)	=	\( 2816 = 2^{8} \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(983040\)
Trace bound:			\(129\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2816))\).

	Total	New	Old
Modular forms	249280	136872	112408
Cusp forms	242241	135000	107241
Eisenstein series	7039	1872	5167

Trace form

135000 * q - 256 * q^2 - 192 * q^3 - 256 * q^4 - 256 * q^5 - 256 * q^6 - 192 * q^7 - 256 * q^8 - 320 * q^9 - 256 * q^10 - 216 * q^11 - 576 * q^12 - 256 * q^13 - 256 * q^14 - 192 * q^15 - 256 * q^16 - 384 * q^17 - 256 * q^18 - 192 * q^19 - 256 * q^20 - 256 * q^21 - 288 * q^22 - 432 * q^23 - 256 * q^24 - 320 * q^25 - 256 * q^26 - 192 * q^27 - 256 * q^28 - 256 * q^29 - 256 * q^30 - 176 * q^31 - 256 * q^32 - 504 * q^33 - 576 * q^34 - 192 * q^35 - 256 * q^36 - 256 * q^37 - 256 * q^38 - 192 * q^39 - 256 * q^40 - 320 * q^41 - 256 * q^42 - 192 * q^43 - 288 * q^44 - 528 * q^45 - 256 * q^46 - 192 * q^47 - 256 * q^48 - 328 * q^49 - 256 * q^50 - 128 * q^51 - 256 * q^52 - 192 * q^53 - 256 * q^54 - 152 * q^55 - 576 * q^56 - 192 * q^57 - 256 * q^58 - 64 * q^59 - 256 * q^60 - 128 * q^61 - 256 * q^62 - 48 * q^63 - 256 * q^64 - 448 * q^65 - 288 * q^66 - 272 * q^67 - 256 * q^68 - 128 * q^69 - 256 * q^70 - 64 * q^71 - 256 * q^72 - 192 * q^73 - 256 * q^74 - 64 * q^75 - 256 * q^76 - 256 * q^77 - 576 * q^78 - 128 * q^79 - 256 * q^80 - 312 * q^81 - 256 * q^82 - 192 * q^83 - 256 * q^84 - 176 * q^85 - 256 * q^86 - 192 * q^87 - 288 * q^88 - 720 * q^89 - 256 * q^90 - 192 * q^91 - 256 * q^92 - 352 * q^93 - 256 * q^94 - 176 * q^95 - 256 * q^96 - 448 * q^97 - 256 * q^98 - 192 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2816))\)

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
2816.2.a	\(\chi_{2816}(1, \cdot)\)	2816.2.a.a	2	1
		2816.2.a.b	2
		2816.2.a.c	2
		2816.2.a.d	2
		2816.2.a.e	2
		2816.2.a.f	2
		2816.2.a.g	2
		2816.2.a.h	2
		2816.2.a.i	3
		2816.2.a.j	3
		2816.2.a.k	3
		2816.2.a.l	3
		2816.2.a.m	4
		2816.2.a.n	4
		2816.2.a.o	5
		2816.2.a.p	5
		2816.2.a.q	5
		2816.2.a.r	5
		2816.2.a.s	6
		2816.2.a.t	6
		2816.2.a.u	6
		2816.2.a.v	6
2816.2.c	\(\chi_{2816}(1409, \cdot)\)	2816.2.c.a	2	1
		2816.2.c.b	2
		2816.2.c.c	2
		2816.2.c.d	2
		2816.2.c.e	2
		2816.2.c.f	2
		2816.2.c.g	2
		2816.2.c.h	2
		2816.2.c.i	2
		2816.2.c.j	2
		2816.2.c.k	2
		2816.2.c.l	2
		2816.2.c.m	2
		2816.2.c.n	2
		2816.2.c.o	4
		2816.2.c.p	4
		2816.2.c.q	4
		2816.2.c.r	4
		2816.2.c.s	4
		2816.2.c.t	4
		2816.2.c.u	4
		2816.2.c.v	4
		2816.2.c.w	4
		2816.2.c.x	4
		2816.2.c.y	6
		2816.2.c.z	6
2816.2.e	\(\chi_{2816}(2815, \cdot)\)	2816.2.e.a	2	1
		2816.2.e.b	2
		2816.2.e.c	4
		2816.2.e.d	4
		2816.2.e.e	4
		2816.2.e.f	4
		2816.2.e.g	6
		2816.2.e.h	6
		2816.2.e.i	6
		2816.2.e.j	6
		2816.2.e.k	8
		2816.2.e.l	8
		2816.2.e.m	8
		2816.2.e.n	8
		2816.2.e.o	16
2816.2.g	\(\chi_{2816}(1407, \cdot)\)	2816.2.g.a	4	1
		2816.2.g.b	8
		2816.2.g.c	8
		2816.2.g.d	12
		2816.2.g.e	12
		2816.2.g.f	12
		2816.2.g.g	12
		2816.2.g.h	12
		2816.2.g.i	12
2816.2.i	\(\chi_{2816}(703, \cdot)\)	n/a	192	2
2816.2.j	\(\chi_{2816}(705, \cdot)\)	n/a	160	2
2816.2.m	\(\chi_{2816}(257, \cdot)\)	n/a	368	4
2816.2.n	\(\chi_{2816}(353, \cdot)\)	n/a	320	4
2816.2.q	\(\chi_{2816}(351, \cdot)\)	n/a	368	4
2816.2.s	\(\chi_{2816}(127, \cdot)\)	n/a	368	4
2816.2.u	\(\chi_{2816}(255, \cdot)\)	n/a	368	4
2816.2.w	\(\chi_{2816}(641, \cdot)\)	n/a	368	4
2816.2.z	\(\chi_{2816}(177, \cdot)\)	n/a	640	8
2816.2.bb	\(\chi_{2816}(175, \cdot)\)	n/a	752	8
2816.2.be	\(\chi_{2816}(449, \cdot)\)	n/a	768	8
2816.2.bf	\(\chi_{2816}(63, \cdot)\)	n/a	768	8
2816.2.bg	\(\chi_{2816}(89, \cdot)\)	None	0	16
2816.2.bh	\(\chi_{2816}(87, \cdot)\)	None	0	16
2816.2.bk	\(\chi_{2816}(95, \cdot)\)	n/a	1472	16
2816.2.bn	\(\chi_{2816}(97, \cdot)\)	n/a	1472	16
2816.2.bo	\(\chi_{2816}(45, \cdot)\)	n/a	10240	32
2816.2.bp	\(\chi_{2816}(43, \cdot)\)	n/a	12224	32
2816.2.bs	\(\chi_{2816}(79, \cdot)\)	n/a	3008	32
2816.2.bu	\(\chi_{2816}(49, \cdot)\)	n/a	3008	32
2816.2.by	\(\chi_{2816}(9, \cdot)\)	None	0	64
2816.2.bz	\(\chi_{2816}(7, \cdot)\)	None	0	64
2816.2.cc	\(\chi_{2816}(19, \cdot)\)	n/a	48896	128
2816.2.cd	\(\chi_{2816}(5, \cdot)\)	n/a	48896	128

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2816))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2816)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(256))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(352))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(704))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1408))\)\(^{\oplus 2}\)