Space of modular forms of level 795 and weight 2

• Label: 795.2
• Level: 795
• Weight: 2
• Dimension: 15131
• Nonzero newspaces: 20
• Newform subspaces: 54
• Sturm bound: 89856
• Trace bound: 10

Defining parameters

Level:	\( N \)	=	\( 795 = 3 \cdot 5 \cdot 53 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 20 \)
Newform subspaces:			\( 54 \)
Sturm bound:			\(89856\)
Trace bound:			\(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(795))\).

	Total	New	Old
Modular forms	23296	15739	7557
Cusp forms	21633	15131	6502
Eisenstein series	1663	608	1055

Trace form

15131 * q + 5 * q^2 - 49 * q^3 - 95 * q^4 - q^5 - 155 * q^6 - 96 * q^7 + 9 * q^8 - 53 * q^9 - 151 * q^10 + 20 * q^11 - 47 * q^12 - 86 * q^13 + 24 * q^14 - 75 * q^15 - 279 * q^16 + 14 * q^17 - 47 * q^18 - 92 * q^19 + 9 * q^20 - 148 * q^21 - 76 * q^22 + 24 * q^23 - 31 * q^24 - 157 * q^25 + 38 * q^26 - 49 * q^27 - 48 * q^28 + 34 * q^29 - 77 * q^30 - 280 * q^31 + 73 * q^32 - 48 * q^33 - 46 * q^34 + 8 * q^35 - 147 * q^36 - 46 * q^37 + 68 * q^38 - 42 * q^39 - 225 * q^40 - 82 * q^41 - 236 * q^42 - 276 * q^43 - 340 * q^44 - 209 * q^45 - 448 * q^46 - 72 * q^47 - 543 * q^48 - 241 * q^49 - 229 * q^50 - 342 * q^51 - 738 * q^52 - 249 * q^53 - 415 * q^54 - 292 * q^55 - 504 * q^56 - 232 * q^57 - 486 * q^58 - 140 * q^59 - 333 * q^60 - 350 * q^61 - 112 * q^62 - 304 * q^63 - 407 * q^64 - 86 * q^65 - 320 * q^66 - 164 * q^67 - 26 * q^68 - 28 * q^69 - 132 * q^70 + 88 * q^71 - 43 * q^72 - 50 * q^73 + 94 * q^74 - 75 * q^75 - 164 * q^76 + 96 * q^77 - 6 * q^78 - 24 * q^79 + 33 * q^80 - 157 * q^81 + 42 * q^82 + 60 * q^83 + 4 * q^84 - 142 * q^85 + 140 * q^86 - 130 * q^87 - 420 * q^88 - 158 * q^89 - 125 * q^90 - 616 * q^91 - 768 * q^92 - 228 * q^93 - 1192 * q^94 - 196 * q^95 - 623 * q^96 - 894 * q^97 - 675 * q^98 - 240 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(795))\)

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
795.2.a	\(\chi_{795}(1, \cdot)\)	795.2.a.a	1	1
		795.2.a.b	1
		795.2.a.c	1
		795.2.a.d	1
		795.2.a.e	3
		795.2.a.f	3
		795.2.a.g	3
		795.2.a.h	3
		795.2.a.i	4
		795.2.a.j	4
		795.2.a.k	5
		795.2.a.l	6
795.2.c	\(\chi_{795}(319, \cdot)\)	795.2.c.a	2	1
		795.2.c.b	2
		795.2.c.c	4
		795.2.c.d	14
		795.2.c.e	30
795.2.e	\(\chi_{795}(211, \cdot)\)	795.2.e.a	16	1
		795.2.e.b	20
795.2.g	\(\chi_{795}(529, \cdot)\)	795.2.g.a	2	1
		795.2.g.b	2
		795.2.g.c	2
		795.2.g.d	2
		795.2.g.e	24
		795.2.g.f	24
795.2.i	\(\chi_{795}(553, \cdot)\)	795.2.i.a	54	2
		795.2.i.b	54
795.2.l	\(\chi_{795}(341, \cdot)\)	795.2.l.a	144	2
795.2.m	\(\chi_{795}(158, \cdot)\)	795.2.m.a	40	2
		795.2.m.b	168
795.2.n	\(\chi_{795}(107, \cdot)\)	795.2.n.a	4	2
		795.2.n.b	204
795.2.r	\(\chi_{795}(659, \cdot)\)	795.2.r.a	8	2
		795.2.r.b	200
795.2.s	\(\chi_{795}(613, \cdot)\)	795.2.s.a	54	2
		795.2.s.b	54
795.2.u	\(\chi_{795}(16, \cdot)\)	795.2.u.a	96	12
		795.2.u.b	96
		795.2.u.c	120
		795.2.u.d	120
795.2.w	\(\chi_{795}(4, \cdot)\)	795.2.w.a	336	12
		795.2.w.b	336
795.2.y	\(\chi_{795}(91, \cdot)\)	795.2.y.a	192	12
		795.2.y.b	240
795.2.ba	\(\chi_{795}(49, \cdot)\)	795.2.ba.a	624	12
795.2.bd	\(\chi_{795}(22, \cdot)\)	795.2.bd.a	648	24
		795.2.bd.b	648
795.2.be	\(\chi_{795}(14, \cdot)\)	795.2.be.a	96	24
		795.2.be.b	2400
795.2.bi	\(\chi_{795}(47, \cdot)\)	795.2.bi.a	2496	24
795.2.bj	\(\chi_{795}(17, \cdot)\)	795.2.bj.a	2496	24
795.2.bk	\(\chi_{795}(26, \cdot)\)	795.2.bk.a	1728	24
795.2.bn	\(\chi_{795}(58, \cdot)\)	795.2.bn.a	648	24
		795.2.bn.b	648

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(795))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(795)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(53))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(159))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(265))\)\(^{\oplus 2}\)