Space of modular forms of level 435 and weight 2

• Label: 435.2
• Level: 435
• Weight: 2
• Dimension: 4451
• Nonzero newspaces: 20
• Newform subspaces: 59
• Sturm bound: 26880
• Trace bound: 6

Defining parameters

Level:	\( N \)	=	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 20 \)
Newform subspaces:			\( 59 \)
Sturm bound:			\(26880\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(435))\).

	Total	New	Old
Modular forms	7168	4771	2397
Cusp forms	6273	4451	1822
Eisenstein series	895	320	575

Trace form

4451 * q + 5 * q^2 - 25 * q^3 - 47 * q^4 - q^5 - 83 * q^6 - 48 * q^7 + 9 * q^8 - 29 * q^9 - 79 * q^10 + 20 * q^11 - 23 * q^12 - 38 * q^13 + 24 * q^14 - 39 * q^15 - 135 * q^16 + 14 * q^17 - 23 * q^18 - 44 * q^19 - 33 * q^20 - 132 * q^21 - 140 * q^22 - 32 * q^23 - 175 * q^24 - 141 * q^25 - 102 * q^26 - 109 * q^27 - 280 * q^28 - 81 * q^29 - 167 * q^30 - 248 * q^31 - 151 * q^32 - 108 * q^33 - 138 * q^34 - 48 * q^35 - 243 * q^36 - 54 * q^37 - 44 * q^38 - 74 * q^39 - 117 * q^40 + 22 * q^41 - 4 * q^42 - 20 * q^43 + 20 * q^44 - 57 * q^45 - 376 * q^46 - 80 * q^47 - 223 * q^48 - 209 * q^49 - 191 * q^50 - 174 * q^51 - 410 * q^52 - 178 * q^53 - 27 * q^54 - 288 * q^55 - 272 * q^56 - 140 * q^57 - 643 * q^58 - 44 * q^59 - 233 * q^60 - 326 * q^61 - 296 * q^62 - 76 * q^63 - 447 * q^64 - 108 * q^65 - 264 * q^66 - 236 * q^67 - 262 * q^68 - 116 * q^69 - 284 * q^70 - 24 * q^71 + 93 * q^72 - 142 * q^73 + 38 * q^74 + 31 * q^75 - 20 * q^76 + 96 * q^77 + 242 * q^78 + 24 * q^79 + 33 * q^80 + 139 * q^81 + 90 * q^82 + 60 * q^83 + 280 * q^84 - 70 * q^85 + 140 * q^86 + 139 * q^87 + 92 * q^88 + 102 * q^89 + 103 * q^90 - 56 * q^91 + 168 * q^92 + 116 * q^93 + 104 * q^94 + 12 * q^95 + 277 * q^96 - 158 * q^97 - 123 * q^98 - 92 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(435))\)

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
435.2.a	\(\chi_{435}(1, \cdot)\)	435.2.a.a	1	1
		435.2.a.b	1
		435.2.a.c	1
		435.2.a.d	1
		435.2.a.e	2
		435.2.a.f	2
		435.2.a.g	2
		435.2.a.h	2
		435.2.a.i	3
		435.2.a.j	4
435.2.c	\(\chi_{435}(349, \cdot)\)	435.2.c.a	2	1
		435.2.c.b	2
		435.2.c.c	4
		435.2.c.d	10
		435.2.c.e	10
435.2.d	\(\chi_{435}(376, \cdot)\)	435.2.d.a	10	1
		435.2.d.b	10
435.2.f	\(\chi_{435}(289, \cdot)\)	435.2.f.a	2	1
		435.2.f.b	2
		435.2.f.c	2
		435.2.f.d	2
		435.2.f.e	12
		435.2.f.f	12
435.2.j	\(\chi_{435}(133, \cdot)\)	435.2.j.a	2	2
		435.2.j.b	4
		435.2.j.c	24
		435.2.j.d	30
435.2.l	\(\chi_{435}(104, \cdot)\)	435.2.l.a	112	2
435.2.m	\(\chi_{435}(233, \cdot)\)	435.2.m.a	4	2
		435.2.m.b	4
		435.2.m.c	52
		435.2.m.d	52
435.2.p	\(\chi_{435}(173, \cdot)\)	435.2.p.a	112	2
435.2.q	\(\chi_{435}(41, \cdot)\)	435.2.q.a	4	2
		435.2.q.b	4
		435.2.q.c	36
		435.2.q.d	36
435.2.s	\(\chi_{435}(307, \cdot)\)	435.2.s.a	2	2
		435.2.s.b	4
		435.2.s.c	24
		435.2.s.d	30
435.2.u	\(\chi_{435}(16, \cdot)\)	435.2.u.a	30	6
		435.2.u.b	30
		435.2.u.c	30
		435.2.u.d	30
435.2.x	\(\chi_{435}(4, \cdot)\)	435.2.x.a	96	6
		435.2.x.b	96
435.2.z	\(\chi_{435}(91, \cdot)\)	435.2.z.a	60	6
		435.2.z.b	60
435.2.ba	\(\chi_{435}(49, \cdot)\)	435.2.ba.a	168	6
435.2.bd	\(\chi_{435}(73, \cdot)\)	435.2.bd.a	180	12
		435.2.bd.b	180
435.2.bf	\(\chi_{435}(11, \cdot)\)	435.2.bf.a	240	12
		435.2.bf.b	240
435.2.bg	\(\chi_{435}(38, \cdot)\)	435.2.bg.a	672	12
435.2.bj	\(\chi_{435}(23, \cdot)\)	435.2.bj.a	672	12
435.2.bk	\(\chi_{435}(14, \cdot)\)	435.2.bk.a	672	12
435.2.bm	\(\chi_{435}(37, \cdot)\)	435.2.bm.a	180	12
		435.2.bm.b	180

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(435))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(435)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(145))\)\(^{\oplus 2}\)