Space of modular forms of level 1856 and weight 2

• Label: 1856.2
• Level: 1856
• Weight: 2
• Dimension: 59742
• Nonzero newspaces: 28
• Sturm bound: 430080
• Trace bound: 15

Defining parameters

Level:	\( N \)	=	\( 1856 = 2^{6} \cdot 29 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 28 \)
Sturm bound:			\(430080\)
Trace bound:			\(15\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1856))\).

	Total	New	Old
Modular forms	109536	60930	48606
Cusp forms	105505	59742	45763
Eisenstein series	4031	1188	2843

Trace form

59742 * q - 208 * q^2 - 156 * q^3 - 208 * q^4 - 208 * q^5 - 208 * q^6 - 152 * q^7 - 208 * q^8 - 254 * q^9 - 208 * q^10 - 148 * q^11 - 208 * q^12 - 192 * q^13 - 208 * q^14 - 144 * q^15 - 208 * q^16 - 348 * q^17 - 208 * q^18 - 140 * q^19 - 208 * q^20 - 216 * q^21 - 224 * q^22 - 152 * q^23 - 288 * q^24 - 282 * q^25 - 288 * q^26 - 168 * q^27 - 288 * q^28 - 232 * q^29 - 592 * q^30 - 200 * q^31 - 288 * q^32 - 208 * q^33 - 288 * q^34 - 160 * q^35 - 368 * q^36 - 224 * q^37 - 288 * q^38 - 152 * q^39 - 288 * q^40 - 260 * q^41 - 288 * q^42 - 132 * q^43 - 224 * q^44 - 200 * q^45 - 208 * q^46 - 120 * q^47 - 208 * q^48 - 346 * q^49 - 160 * q^50 - 208 * q^51 - 112 * q^52 - 160 * q^53 - 80 * q^54 - 280 * q^55 - 96 * q^56 - 248 * q^57 - 144 * q^58 - 460 * q^59 - 16 * q^60 - 192 * q^61 - 144 * q^62 - 288 * q^63 - 16 * q^64 - 568 * q^65 - 48 * q^66 - 332 * q^67 - 112 * q^68 - 184 * q^69 - 16 * q^70 - 280 * q^71 - 64 * q^72 - 260 * q^73 - 96 * q^74 - 268 * q^75 - 80 * q^76 - 216 * q^77 - 160 * q^78 - 216 * q^79 - 288 * q^80 - 370 * q^81 - 368 * q^82 - 156 * q^83 - 432 * q^84 - 224 * q^85 - 416 * q^86 - 160 * q^87 - 592 * q^88 - 356 * q^89 - 496 * q^90 - 144 * q^91 - 512 * q^92 - 288 * q^93 - 400 * q^94 - 192 * q^95 - 480 * q^96 - 236 * q^97 - 480 * q^98 - 204 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1856))\)

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
1856.2.a	\(\chi_{1856}(1, \cdot)\)	1856.2.a.a	1	1
		1856.2.a.b	1
		1856.2.a.c	1
		1856.2.a.d	1
		1856.2.a.e	1
		1856.2.a.f	1
		1856.2.a.g	1
		1856.2.a.h	1
		1856.2.a.i	1
		1856.2.a.j	1
		1856.2.a.k	1
		1856.2.a.l	1
		1856.2.a.m	1
		1856.2.a.n	1
		1856.2.a.o	1
		1856.2.a.p	1
		1856.2.a.q	2
		1856.2.a.r	2
		1856.2.a.s	2
		1856.2.a.t	2
		1856.2.a.u	2
		1856.2.a.v	2
		1856.2.a.w	2
		1856.2.a.x	3
		1856.2.a.y	3
		1856.2.a.z	4
		1856.2.a.ba	5
		1856.2.a.bb	5
		1856.2.a.bc	6
1856.2.c	\(\chi_{1856}(929, \cdot)\)	1856.2.c.a	8	1
		1856.2.c.b	8
		1856.2.c.c	20
		1856.2.c.d	20
1856.2.e	\(\chi_{1856}(1217, \cdot)\)	1856.2.e.a	2	1
		1856.2.e.b	2
		1856.2.e.c	2
		1856.2.e.d	2
		1856.2.e.e	2
		1856.2.e.f	2
		1856.2.e.g	2
		1856.2.e.h	4
		1856.2.e.i	8
		1856.2.e.j	8
		1856.2.e.k	12
		1856.2.e.l	12
1856.2.g	\(\chi_{1856}(289, \cdot)\)	1856.2.g.a	4	1
		1856.2.g.b	16
		1856.2.g.c	40
1856.2.j	\(\chi_{1856}(911, \cdot)\)	n/a	116	2
1856.2.k	\(\chi_{1856}(191, \cdot)\)	n/a	116	2
1856.2.m	\(\chi_{1856}(753, \cdot)\)	n/a	116	2
1856.2.n	\(\chi_{1856}(465, \cdot)\)	n/a	112	2
1856.2.q	\(\chi_{1856}(1119, \cdot)\)	n/a	120	2
1856.2.t	\(\chi_{1856}(655, \cdot)\)	n/a	116	2
1856.2.u	\(\chi_{1856}(65, \cdot)\)	n/a	348	6
1856.2.v	\(\chi_{1856}(233, \cdot)\)	None	0	4
1856.2.x	\(\chi_{1856}(679, \cdot)\)	None	0	4
1856.2.ba	\(\chi_{1856}(215, \cdot)\)	None	0	4
1856.2.bc	\(\chi_{1856}(57, \cdot)\)	None	0	4
1856.2.be	\(\chi_{1856}(33, \cdot)\)	n/a	360	6
1856.2.bg	\(\chi_{1856}(129, \cdot)\)	n/a	348	6
1856.2.bi	\(\chi_{1856}(161, \cdot)\)	n/a	360	6
1856.2.bl	\(\chi_{1856}(307, \cdot)\)	n/a	1904	8
1856.2.bn	\(\chi_{1856}(117, \cdot)\)	n/a	1792	8
1856.2.bp	\(\chi_{1856}(173, \cdot)\)	n/a	1904	8
1856.2.bq	\(\chi_{1856}(75, \cdot)\)	n/a	1904	8
1856.2.bs	\(\chi_{1856}(47, \cdot)\)	n/a	696	12
1856.2.bv	\(\chi_{1856}(31, \cdot)\)	n/a	720	12
1856.2.by	\(\chi_{1856}(49, \cdot)\)	n/a	696	12
1856.2.bz	\(\chi_{1856}(209, \cdot)\)	n/a	696	12
1856.2.cb	\(\chi_{1856}(127, \cdot)\)	n/a	696	12
1856.2.cc	\(\chi_{1856}(15, \cdot)\)	n/a	696	12
1856.2.cf	\(\chi_{1856}(9, \cdot)\)	None	0	24
1856.2.ch	\(\chi_{1856}(55, \cdot)\)	None	0	24
1856.2.ci	\(\chi_{1856}(39, \cdot)\)	None	0	24
1856.2.ck	\(\chi_{1856}(25, \cdot)\)	None	0	24
1856.2.cm	\(\chi_{1856}(11, \cdot)\)	n/a	11424	48
1856.2.co	\(\chi_{1856}(5, \cdot)\)	n/a	11424	48
1856.2.cq	\(\chi_{1856}(45, \cdot)\)	n/a	11424	48
1856.2.ct	\(\chi_{1856}(3, \cdot)\)	n/a	11424	48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1856))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1856)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(232))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(464))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(928))\)\(^{\oplus 2}\)