Space of modular forms of level 1078 and weight 2

• Label: 1078.2
• Level: 1078
• Weight: 2
• Dimension: 11095
• Nonzero newspaces: 16
• Sturm bound: 141120
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(141120\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1078))\).

	Total	New	Old
Modular forms	36480	11095	25385
Cusp forms	34081	11095	22986
Eisenstein series	2399	0	2399

Trace form

11095 * q - 2 * q^2 + 6 * q^4 + 12 * q^5 + 21 * q^6 + 16 * q^7 - 2 * q^8 + 50 * q^9 + 22 * q^10 + 22 * q^11 + 10 * q^12 + 22 * q^13 + 12 * q^14 + 78 * q^15 + 6 * q^16 + 80 * q^17 + 27 * q^18 + 63 * q^19 + 12 * q^20 + 52 * q^21 + 12 * q^22 + 68 * q^23 + 21 * q^24 + 82 * q^25 + 64 * q^26 + 141 * q^27 + 16 * q^28 + 76 * q^29 + 78 * q^30 + 78 * q^31 + 3 * q^32 + 103 * q^33 + 32 * q^34 + 84 * q^35 + 35 * q^36 - 8 * q^37 - 22 * q^38 - 2 * q^39 - 62 * q^40 - 20 * q^41 - 108 * q^42 + 2 * q^43 - 15 * q^44 - 214 * q^45 - 184 * q^46 - 80 * q^47 - 28 * q^48 - 236 * q^49 - 66 * q^50 - 175 * q^51 + 4 * q^52 + 14 * q^53 - 148 * q^54 - 68 * q^55 - 72 * q^56 + 61 * q^57 - 44 * q^58 - 7 * q^59 - 16 * q^60 - 90 * q^61 - 94 * q^62 - 108 * q^63 + 6 * q^64 - 92 * q^65 - 372 * q^66 - 30 * q^67 - 40 * q^68 - 298 * q^69 - 96 * q^70 - 256 * q^71 - 198 * q^72 - 144 * q^73 - 152 * q^74 - 557 * q^75 - 62 * q^76 - 96 * q^77 - 360 * q^78 - 118 * q^79 - 98 * q^80 - 795 * q^81 - 145 * q^82 - 319 * q^83 - 68 * q^84 - 322 * q^85 - 239 * q^86 - 548 * q^87 - 98 * q^88 - 172 * q^89 - 234 * q^90 - 160 * q^91 + 78 * q^92 - 446 * q^93 + 84 * q^94 - 106 * q^95 + 16 * q^96 + 83 * q^97 + 96 * q^98 + 118 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1078))\)

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
1078.2.a	\(\chi_{1078}(1, \cdot)\)	1078.2.a.a	1	1
		1078.2.a.b	1
		1078.2.a.c	1
		1078.2.a.d	1
		1078.2.a.e	1
		1078.2.a.f	1
		1078.2.a.g	1
		1078.2.a.h	1
		1078.2.a.i	1
		1078.2.a.j	1
		1078.2.a.k	1
		1078.2.a.l	1
		1078.2.a.m	1
		1078.2.a.n	2
		1078.2.a.o	2
		1078.2.a.p	2
		1078.2.a.q	2
		1078.2.a.r	2
		1078.2.a.s	2
		1078.2.a.t	2
		1078.2.a.u	2
		1078.2.a.v	2
		1078.2.a.w	2
		1078.2.a.x	2
1078.2.c	\(\chi_{1078}(1077, \cdot)\)	1078.2.c.a	8	1
		1078.2.c.b	16
		1078.2.c.c	16
1078.2.e	\(\chi_{1078}(67, \cdot)\)	1078.2.e.a	2	2
		1078.2.e.b	2
		1078.2.e.c	2
		1078.2.e.d	2
		1078.2.e.e	2
		1078.2.e.f	2
		1078.2.e.g	2
		1078.2.e.h	2
		1078.2.e.i	2
		1078.2.e.j	2
		1078.2.e.k	2
		1078.2.e.l	2
		1078.2.e.m	4
		1078.2.e.n	4
		1078.2.e.o	4
		1078.2.e.p	4
		1078.2.e.q	4
		1078.2.e.r	4
		1078.2.e.s	4
		1078.2.e.t	4
		1078.2.e.u	4
		1078.2.e.v	4
1078.2.f	\(\chi_{1078}(295, \cdot)\)	n/a	164	4
1078.2.i	\(\chi_{1078}(901, \cdot)\)	1078.2.i.a	16	2
		1078.2.i.b	16
		1078.2.i.c	16
		1078.2.i.d	32
1078.2.j	\(\chi_{1078}(155, \cdot)\)	n/a	264	6
1078.2.l	\(\chi_{1078}(195, \cdot)\)	n/a	160	4
1078.2.o	\(\chi_{1078}(153, \cdot)\)	n/a	336	6
1078.2.q	\(\chi_{1078}(361, \cdot)\)	n/a	320	8
1078.2.r	\(\chi_{1078}(23, \cdot)\)	n/a	576	12
1078.2.s	\(\chi_{1078}(19, \cdot)\)	n/a	320	8
1078.2.v	\(\chi_{1078}(15, \cdot)\)	n/a	1344	24
1078.2.w	\(\chi_{1078}(87, \cdot)\)	n/a	672	12
1078.2.ba	\(\chi_{1078}(13, \cdot)\)	n/a	1344	24
1078.2.bc	\(\chi_{1078}(9, \cdot)\)	n/a	2688	48
1078.2.bf	\(\chi_{1078}(17, \cdot)\)	n/a	2688	48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1078))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1078)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(539))\)\(^{\oplus 2}\)