Space of modular forms of level 644 and weight 2

• Label: 644.2
• Level: 644
• Weight: 2
• Dimension: 6848
• Nonzero newspaces: 16
• Newform subspaces: 27
• Sturm bound: 50688
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Newform subspaces:			\( 27 \)
Sturm bound:			\(50688\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(644))\).

	Total	New	Old
Modular forms	13332	7264	6068
Cusp forms	12013	6848	5165
Eisenstein series	1319	416	903

Trace form

6848 * q - 38 * q^2 + 2 * q^3 - 38 * q^4 - 70 * q^5 - 44 * q^6 + 8 * q^7 - 104 * q^8 - 80 * q^9 - 56 * q^10 - 6 * q^11 - 68 * q^12 - 96 * q^13 - 73 * q^14 + 10 * q^15 - 62 * q^16 - 48 * q^17 - 50 * q^18 + 20 * q^19 - 44 * q^20 - 87 * q^21 - 96 * q^22 + 47 * q^23 - 64 * q^24 - 48 * q^25 - 20 * q^26 + 86 * q^27 - q^28 - 198 * q^29 - 32 * q^30 + 8 * q^31 - 38 * q^32 - 84 * q^33 - 88 * q^34 - 52 * q^35 - 238 * q^36 - 190 * q^37 - 190 * q^38 - 84 * q^39 - 244 * q^40 - 156 * q^41 - 189 * q^42 - 72 * q^43 - 234 * q^44 - 276 * q^45 - 232 * q^46 - 106 * q^47 - 220 * q^48 - 144 * q^49 - 270 * q^50 - 82 * q^51 - 264 * q^52 - 90 * q^53 - 184 * q^54 - 8 * q^55 - 128 * q^56 - 166 * q^57 - 142 * q^58 + 62 * q^59 - 64 * q^60 + 34 * q^61 - 44 * q^62 + 75 * q^63 - 128 * q^64 + 54 * q^65 + 34 * q^66 + 30 * q^67 - 66 * q^68 + 16 * q^69 - 122 * q^70 + 110 * q^71 - 80 * q^72 - 106 * q^73 + 2 * q^74 + 118 * q^75 + 66 * q^76 - 185 * q^77 + 62 * q^78 + 18 * q^79 + 202 * q^80 - 334 * q^81 + 64 * q^82 - 26 * q^83 + 99 * q^84 - 544 * q^85 + 212 * q^86 - 144 * q^87 + 96 * q^88 - 298 * q^89 + 330 * q^90 - 28 * q^91 + 94 * q^92 - 730 * q^93 + 170 * q^94 - 72 * q^95 + 422 * q^96 - 114 * q^97 - 14 * q^98 - 46 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(644))\)

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
644.2.a	\(\chi_{644}(1, \cdot)\)	644.2.a.a	1	1
		644.2.a.b	1
		644.2.a.c	5
		644.2.a.d	5
644.2.c	\(\chi_{644}(183, \cdot)\)	644.2.c.a	36	1
		644.2.c.b	36
644.2.d	\(\chi_{644}(321, \cdot)\)	644.2.d.a	16	1
644.2.f	\(\chi_{644}(139, \cdot)\)	644.2.f.a	4	1
		644.2.f.b	4
		644.2.f.c	80
644.2.i	\(\chi_{644}(93, \cdot)\)	644.2.i.a	14	2
		644.2.i.b	14
644.2.k	\(\chi_{644}(47, \cdot)\)	644.2.k.a	176	2
644.2.m	\(\chi_{644}(45, \cdot)\)	644.2.m.a	32	2
644.2.p	\(\chi_{644}(275, \cdot)\)	644.2.p.a	184	2
644.2.q	\(\chi_{644}(29, \cdot)\)	644.2.q.a	60	10
		644.2.q.b	60
644.2.t	\(\chi_{644}(27, \cdot)\)	644.2.t.a	20	10
		644.2.t.b	20
		644.2.t.c	880
644.2.v	\(\chi_{644}(97, \cdot)\)	644.2.v.a	160	10
644.2.w	\(\chi_{644}(15, \cdot)\)	644.2.w.a	360	10
		644.2.w.b	360
644.2.y	\(\chi_{644}(9, \cdot)\)	644.2.y.a	320	20
644.2.z	\(\chi_{644}(11, \cdot)\)	644.2.z.a	1840	20
644.2.bc	\(\chi_{644}(5, \cdot)\)	644.2.bc.a	320	20
644.2.be	\(\chi_{644}(3, \cdot)\)	644.2.be.a	1840	20

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(644))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(644)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(322))\)\(^{\oplus 2}\)