Space of modular forms of level 820 and weight 2

• Label: 820.2
• Level: 820
• Weight: 2
• Dimension: 10534
• Nonzero newspaces: 28
• Newform subspaces: 72
• Sturm bound: 80640
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 28 \)
Newform subspaces:			\( 72 \)
Sturm bound:			\(80640\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(820))\).

	Total	New	Old
Modular forms	20960	10998	9962
Cusp forms	19361	10534	8827
Eisenstein series	1599	464	1135

Trace form

10534 * q - 36 * q^2 + 4 * q^3 - 40 * q^4 - 110 * q^5 - 120 * q^6 - 4 * q^7 - 48 * q^8 - 82 * q^9 - 72 * q^10 - 40 * q^12 - 80 * q^13 - 40 * q^14 - 4 * q^15 - 104 * q^16 - 80 * q^17 - 28 * q^18 + 8 * q^19 - 52 * q^20 - 232 * q^21 - 40 * q^22 - 12 * q^23 - 40 * q^24 - 134 * q^25 - 128 * q^26 - 8 * q^27 - 40 * q^28 - 92 * q^29 - 60 * q^30 + 48 * q^31 - 56 * q^32 + 40 * q^33 - 40 * q^34 + 44 * q^35 - 144 * q^36 + 64 * q^37 - 40 * q^38 + 168 * q^39 - 72 * q^40 - 190 * q^41 - 80 * q^42 + 60 * q^43 - 40 * q^44 - 50 * q^45 - 120 * q^46 + 132 * q^47 - 40 * q^48 + 6 * q^49 - 32 * q^50 + 96 * q^51 - 32 * q^52 - 64 * q^53 - 40 * q^54 - 120 * q^56 - 96 * q^57 - 56 * q^58 - 24 * q^59 - 60 * q^60 - 292 * q^61 - 40 * q^62 - 4 * q^63 - 40 * q^64 - 130 * q^65 - 280 * q^66 - 124 * q^67 - 216 * q^68 - 216 * q^69 - 260 * q^70 - 136 * q^71 - 376 * q^72 - 200 * q^73 - 280 * q^74 - 156 * q^75 - 720 * q^76 - 240 * q^77 - 440 * q^78 - 176 * q^79 - 292 * q^80 - 602 * q^81 - 536 * q^82 - 172 * q^83 - 520 * q^84 - 266 * q^85 - 520 * q^86 - 136 * q^87 - 440 * q^88 - 228 * q^89 - 372 * q^90 - 328 * q^91 - 280 * q^92 - 256 * q^93 - 400 * q^94 - 88 * q^95 - 520 * q^96 - 296 * q^97 - 268 * q^98 - 120 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(820))\)

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
820.2.a	\(\chi_{820}(1, \cdot)\)	820.2.a.a	2	1
		820.2.a.b	2
		820.2.a.c	4
		820.2.a.d	4
820.2.b	\(\chi_{820}(81, \cdot)\)	820.2.b.a	6	1
		820.2.b.b	8
820.2.d	\(\chi_{820}(329, \cdot)\)	820.2.d.a	6	1
		820.2.d.b	14
820.2.g	\(\chi_{820}(409, \cdot)\)	820.2.g.a	4	1
		820.2.g.b	16
820.2.j	\(\chi_{820}(483, \cdot)\)	820.2.j.a	2	2
		820.2.j.b	2
		820.2.j.c	240
820.2.k	\(\chi_{820}(83, \cdot)\)	820.2.k.a	4	2
		820.2.k.b	8
		820.2.k.c	108
		820.2.k.d	120
820.2.n	\(\chi_{820}(9, \cdot)\)	820.2.n.a	44	2
820.2.p	\(\chi_{820}(401, \cdot)\)	820.2.p.a	2	2
		820.2.p.b	2
		820.2.p.c	2
		820.2.p.d	8
		820.2.p.e	14
820.2.r	\(\chi_{820}(163, \cdot)\)	820.2.r.a	2	2
		820.2.r.b	2
		820.2.r.c	16
		820.2.r.d	16
		820.2.r.e	208
820.2.s	\(\chi_{820}(583, \cdot)\)	820.2.s.a	2	2
		820.2.s.b	2
		820.2.s.c	240
820.2.u	\(\chi_{820}(141, \cdot)\)	820.2.u.a	24	4
		820.2.u.b	32
820.2.w	\(\chi_{820}(79, \cdot)\)	820.2.w.a	4	4
		820.2.w.b	4
		820.2.w.c	8
		820.2.w.d	8
		820.2.w.e	464
820.2.x	\(\chi_{820}(273, \cdot)\)	820.2.x.a	84	4
820.2.y	\(\chi_{820}(137, \cdot)\)	820.2.y.a	84	4
820.2.bc	\(\chi_{820}(191, \cdot)\)	820.2.bc.a	168	4
		820.2.bc.b	168
820.2.be	\(\chi_{820}(469, \cdot)\)	820.2.be.a	80	4
820.2.bg	\(\chi_{820}(441, \cdot)\)	820.2.bg.a	24	4
		820.2.bg.b	32
820.2.bi	\(\chi_{820}(189, \cdot)\)	820.2.bi.a	80	4
820.2.bk	\(\chi_{820}(43, \cdot)\)	820.2.bk.a	8	8
		820.2.bk.b	8
		820.2.bk.c	960
820.2.bm	\(\chi_{820}(23, \cdot)\)	820.2.bm.a	8	8
		820.2.bm.b	8
		820.2.bm.c	960
820.2.bo	\(\chi_{820}(21, \cdot)\)	820.2.bo.a	48	8
		820.2.bo.b	64
820.2.bq	\(\chi_{820}(49, \cdot)\)	820.2.bq.a	176	8
820.2.bt	\(\chi_{820}(223, \cdot)\)	820.2.bt.a	8	8
		820.2.bt.b	8
		820.2.bt.c	960
820.2.bv	\(\chi_{820}(103, \cdot)\)	820.2.bv.a	8	8
		820.2.bv.b	8
		820.2.bv.c	960
820.2.bw	\(\chi_{820}(11, \cdot)\)	820.2.bw.a	672	16
		820.2.bw.b	672
820.2.ca	\(\chi_{820}(13, \cdot)\)	820.2.ca.a	336	16
820.2.cb	\(\chi_{820}(157, \cdot)\)	820.2.cb.a	336	16
820.2.cc	\(\chi_{820}(19, \cdot)\)	820.2.cc.a	16	16
		820.2.cc.b	16
		820.2.cc.c	16
		820.2.cc.d	16
		820.2.cc.e	16
		820.2.cc.f	16
		820.2.cc.g	1856

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(820))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(820)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(164))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(205))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(410))\)\(^{\oplus 2}\)