Space of modular forms of level 425 and weight 2

• Label: 425.2
• Level: 425
• Weight: 2
• Dimension: 6284
• Nonzero newspaces: 20
• Newform subspaces: 62
• Sturm bound: 28800
• Trace bound: 8

Defining parameters

Level:	\( N \)	=	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 20 \)
Newform subspaces:			\( 62 \)
Sturm bound:			\(28800\)
Trace bound:			\(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(425))\).

	Total	New	Old
Modular forms	7648	6898	750
Cusp forms	6753	6284	469
Eisenstein series	895	614	281

Trace form

6284 * q - 90 * q^2 - 92 * q^3 - 98 * q^4 - 118 * q^5 - 156 * q^6 - 100 * q^7 - 114 * q^8 - 110 * q^9 - 138 * q^10 - 164 * q^11 - 164 * q^12 - 120 * q^13 - 148 * q^14 - 148 * q^15 - 198 * q^16 - 110 * q^17 - 248 * q^18 - 92 * q^19 - 108 * q^20 - 180 * q^21 - 92 * q^22 - 100 * q^23 - 104 * q^24 - 98 * q^25 - 352 * q^26 - 128 * q^27 - 124 * q^28 - 124 * q^29 - 148 * q^30 - 188 * q^31 - 196 * q^32 - 180 * q^33 - 187 * q^34 - 296 * q^35 - 282 * q^36 - 182 * q^37 - 192 * q^38 - 164 * q^39 - 158 * q^40 - 220 * q^41 - 172 * q^42 - 132 * q^43 - 208 * q^44 - 78 * q^45 - 204 * q^46 - 140 * q^47 - 136 * q^48 - 120 * q^49 - 78 * q^50 - 344 * q^51 - 228 * q^52 - 146 * q^53 - 184 * q^54 - 148 * q^55 - 308 * q^56 - 180 * q^57 - 212 * q^58 - 168 * q^59 - 108 * q^60 - 240 * q^61 - 160 * q^62 - 232 * q^63 + 26 * q^64 - 138 * q^65 - 332 * q^66 - 180 * q^67 - 104 * q^68 - 224 * q^69 - 60 * q^70 - 116 * q^71 + 150 * q^72 + 68 * q^73 + 112 * q^74 - 20 * q^75 + 64 * q^76 + 60 * q^77 + 184 * q^78 + 28 * q^79 + 182 * q^80 + 58 * q^81 + 340 * q^82 + 96 * q^83 + 516 * q^84 + 99 * q^85 - 180 * q^86 + 224 * q^87 + 564 * q^88 + 106 * q^89 + 194 * q^90 + 116 * q^91 + 308 * q^92 + 80 * q^93 + 300 * q^94 - 20 * q^95 + 52 * q^96 + 192 * q^97 + 10 * q^98 + 32 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(425))\)

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
425.2.a	\(\chi_{425}(1, \cdot)\)	425.2.a.a	1	1
		425.2.a.b	1
		425.2.a.c	1
		425.2.a.d	1
		425.2.a.e	2
		425.2.a.f	2
		425.2.a.g	4
		425.2.a.h	4
		425.2.a.i	5
		425.2.a.j	5
425.2.b	\(\chi_{425}(324, \cdot)\)	425.2.b.a	2	1
		425.2.b.b	2
		425.2.b.c	2
		425.2.b.d	4
		425.2.b.e	4
		425.2.b.f	10
425.2.c	\(\chi_{425}(424, \cdot)\)	425.2.c.a	6	1
		425.2.c.b	6
		425.2.c.c	12
425.2.d	\(\chi_{425}(101, \cdot)\)	425.2.d.a	6	1
		425.2.d.b	6
		425.2.d.c	6
		425.2.d.d	8
425.2.e	\(\chi_{425}(251, \cdot)\)	425.2.e.a	2	2
		425.2.e.b	2
		425.2.e.c	12
		425.2.e.d	12
		425.2.e.e	12
		425.2.e.f	12
425.2.j	\(\chi_{425}(149, \cdot)\)	425.2.j.a	12	2
		425.2.j.b	12
		425.2.j.c	12
		425.2.j.d	12
425.2.k	\(\chi_{425}(86, \cdot)\)	425.2.k.a	4	4
		425.2.k.b	76
		425.2.k.c	80
425.2.m	\(\chi_{425}(26, \cdot)\)	425.2.m.a	4	4
		425.2.m.b	24
		425.2.m.c	24
		425.2.m.d	24
		425.2.m.e	24
425.2.n	\(\chi_{425}(49, \cdot)\)	425.2.n.a	4	4
		425.2.n.b	4
		425.2.n.c	24
		425.2.n.d	24
		425.2.n.e	24
		425.2.n.f	24
425.2.p	\(\chi_{425}(16, \cdot)\)	425.2.p.a	168	4
425.2.q	\(\chi_{425}(84, \cdot)\)	425.2.q.a	176	4
425.2.r	\(\chi_{425}(69, \cdot)\)	425.2.r.a	160	4
425.2.s	\(\chi_{425}(7, \cdot)\)	425.2.s.a	48	8
		425.2.s.b	56
		425.2.s.c	96
425.2.v	\(\chi_{425}(82, \cdot)\)	425.2.v.a	48	8
		425.2.v.b	56
		425.2.v.c	96
425.2.w	\(\chi_{425}(4, \cdot)\)	425.2.w.a	352	8
425.2.bb	\(\chi_{425}(21, \cdot)\)	425.2.bb.a	336	8
425.2.bd	\(\chi_{425}(9, \cdot)\)	425.2.bd.a	672	16
425.2.be	\(\chi_{425}(36, \cdot)\)	425.2.be.a	704	16
425.2.bg	\(\chi_{425}(12, \cdot)\)	425.2.bg.a	1376	32
425.2.bj	\(\chi_{425}(3, \cdot)\)	425.2.bj.a	1376	32

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(425))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(425)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(425))\)\(^{\oplus 1}\)