Space of modular forms of level 621 and weight 2

• Label: 621.2
• Level: 621
• Weight: 2
• Dimension: 10886
• Nonzero newspaces: 12
• Newform subspaces: 32
• Sturm bound: 57024
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 621 = 3^{3} \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 32 \)
Sturm bound:			\(57024\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(621))\).

	Total	New	Old
Modular forms	14916	11558	3358
Cusp forms	13597	10886	2711
Eisenstein series	1319	672	647

Trace form

10886 * q - 76 * q^2 - 120 * q^3 - 138 * q^4 - 82 * q^5 - 132 * q^6 - 140 * q^7 - 100 * q^8 - 132 * q^9 - 148 * q^10 - 94 * q^11 - 156 * q^12 - 152 * q^13 - 118 * q^14 - 150 * q^15 - 162 * q^16 - 106 * q^17 - 150 * q^18 - 134 * q^19 - 82 * q^20 - 108 * q^21 - 160 * q^22 - 76 * q^23 - 228 * q^24 - 150 * q^25 - 28 * q^26 - 114 * q^27 - 332 * q^28 - 76 * q^29 - 114 * q^30 - 152 * q^31 - 88 * q^32 - 132 * q^33 - 172 * q^34 - 112 * q^35 - 168 * q^36 - 170 * q^37 - 172 * q^38 - 198 * q^39 - 196 * q^40 - 118 * q^41 - 168 * q^42 - 176 * q^43 - 138 * q^44 - 114 * q^45 - 151 * q^46 - 146 * q^47 - 102 * q^48 - 166 * q^49 - 22 * q^50 - 96 * q^51 - 152 * q^52 - 52 * q^53 - 24 * q^54 - 372 * q^55 - 154 * q^56 - 126 * q^57 - 284 * q^58 - 152 * q^59 - 132 * q^60 - 264 * q^61 - 196 * q^62 - 150 * q^63 - 338 * q^64 - 248 * q^65 - 114 * q^66 - 178 * q^67 - 392 * q^68 - 141 * q^69 - 454 * q^70 - 252 * q^71 - 168 * q^72 - 196 * q^73 - 330 * q^74 - 210 * q^75 - 262 * q^76 - 228 * q^77 - 168 * q^78 - 192 * q^79 - 392 * q^80 - 204 * q^81 - 416 * q^82 - 232 * q^83 - 144 * q^84 - 144 * q^85 - 234 * q^86 - 150 * q^87 - 94 * q^88 - 106 * q^89 - 168 * q^90 - 156 * q^91 - 49 * q^92 - 186 * q^93 - 124 * q^94 - 22 * q^95 - 132 * q^96 - 122 * q^97 + 2 * q^98 - 78 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(621))\)

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
621.2.a	\(\chi_{621}(1, \cdot)\)	621.2.a.a	1	1
		621.2.a.b	1
		621.2.a.c	2
		621.2.a.d	2
		621.2.a.e	2
		621.2.a.f	2
		621.2.a.g	2
		621.2.a.h	2
		621.2.a.i	2
		621.2.a.j	2
		621.2.a.k	6
		621.2.a.l	6
621.2.c	\(\chi_{621}(620, \cdot)\)	621.2.c.a	16	1
		621.2.c.b	16
621.2.e	\(\chi_{621}(208, \cdot)\)	621.2.e.a	16	2
		621.2.e.b	28
621.2.g	\(\chi_{621}(206, \cdot)\)	621.2.g.a	12	2
		621.2.g.b	32
621.2.i	\(\chi_{621}(70, \cdot)\)	621.2.i.a	180	6
		621.2.i.b	216
621.2.j	\(\chi_{621}(55, \cdot)\)	621.2.j.a	80	10
		621.2.j.b	80
		621.2.j.c	80
		621.2.j.d	80
621.2.m	\(\chi_{621}(68, \cdot)\)	621.2.m.a	36	6
		621.2.m.b	384
621.2.o	\(\chi_{621}(53, \cdot)\)	621.2.o.a	160	10
		621.2.o.b	160
621.2.q	\(\chi_{621}(64, \cdot)\)	621.2.q.a	440	20
621.2.s	\(\chi_{621}(17, \cdot)\)	621.2.s.a	440	20
621.2.u	\(\chi_{621}(4, \cdot)\)	621.2.u.a	4200	60
621.2.v	\(\chi_{621}(5, \cdot)\)	621.2.v.a	4200	60

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(621))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(621)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(207))\)\(^{\oplus 2}\)