Space of modular forms of level 429 and weight 2

• Label: 429.2
• Level: 429
• Weight: 2
• Dimension: 4703
• Nonzero newspaces: 24
• Newform subspaces: 53
• Sturm bound: 26880
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Newform subspaces:			\( 53 \)
Sturm bound:			\(26880\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(429))\).

	Total	New	Old
Modular forms	7200	5095	2105
Cusp forms	6241	4703	1538
Eisenstein series	959	392	567

Trace form

4703 * q + 9 * q^2 - 35 * q^3 - 55 * q^4 + 18 * q^5 - 39 * q^6 - 80 * q^7 - 31 * q^8 - 59 * q^9 - 142 * q^10 - 9 * q^11 - 159 * q^12 - 117 * q^13 - 36 * q^14 - 84 * q^15 - 183 * q^16 - 42 * q^17 - 107 * q^18 - 156 * q^19 - 106 * q^20 - 116 * q^21 - 199 * q^22 - 16 * q^23 - 115 * q^24 - 147 * q^25 - 89 * q^26 - 125 * q^27 - 176 * q^28 - 10 * q^29 - 42 * q^30 - 68 * q^31 + 29 * q^32 - 7 * q^33 - 190 * q^34 + 16 * q^35 + 33 * q^36 - 54 * q^37 + 80 * q^38 - 9 * q^39 - 218 * q^40 - 78 * q^41 - 72 * q^42 - 212 * q^43 - 119 * q^44 - 136 * q^45 - 360 * q^46 - 92 * q^47 - 167 * q^48 - 301 * q^49 - 169 * q^50 - 202 * q^51 - 327 * q^52 - 170 * q^53 - 155 * q^54 - 242 * q^55 - 240 * q^56 - 116 * q^57 - 286 * q^58 - 48 * q^59 - 166 * q^60 - 218 * q^61 - 96 * q^62 - 36 * q^63 - 243 * q^64 - 78 * q^65 - 31 * q^66 - 200 * q^67 - 2 * q^68 + 2 * q^69 - 208 * q^70 + 48 * q^71 + 29 * q^72 - 114 * q^73 + 6 * q^74 - 39 * q^75 - 260 * q^76 - 68 * q^77 + 41 * q^78 - 336 * q^79 - 138 * q^80 + 13 * q^81 - 122 * q^82 - 80 * q^83 - 100 * q^84 - 192 * q^85 - 76 * q^86 - 126 * q^87 - 267 * q^88 - 130 * q^89 - 174 * q^90 - 276 * q^91 - 172 * q^92 - 226 * q^93 - 376 * q^94 - 276 * q^95 - 207 * q^96 - 286 * q^97 - 239 * q^98 - 159 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(429))\)

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
429.2.a	\(\chi_{429}(1, \cdot)\)	429.2.a.a	1	1
		429.2.a.b	1
		429.2.a.c	2
		429.2.a.d	2
		429.2.a.e	3
		429.2.a.f	3
		429.2.a.g	3
		429.2.a.h	4
429.2.b	\(\chi_{429}(298, \cdot)\)	429.2.b.a	10	1
		429.2.b.b	14
429.2.e	\(\chi_{429}(428, \cdot)\)	429.2.e.a	8	1
		429.2.e.b	8
		429.2.e.c	16
		429.2.e.d	20
429.2.f	\(\chi_{429}(131, \cdot)\)	429.2.f.a	48	1
429.2.i	\(\chi_{429}(100, \cdot)\)	429.2.i.a	2	2
		429.2.i.b	2
		429.2.i.c	10
		429.2.i.d	10
		429.2.i.e	10
		429.2.i.f	10
429.2.j	\(\chi_{429}(122, \cdot)\)	429.2.j.a	96	2
429.2.m	\(\chi_{429}(109, \cdot)\)	429.2.m.a	28	2
		429.2.m.b	28
429.2.n	\(\chi_{429}(157, \cdot)\)	429.2.n.a	12	4
		429.2.n.b	20
		429.2.n.c	28
		429.2.n.d	36
429.2.p	\(\chi_{429}(230, \cdot)\)	429.2.p.a	8	2
		429.2.p.b	96
429.2.s	\(\chi_{429}(166, \cdot)\)	429.2.s.a	24	2
		429.2.s.b	28
429.2.t	\(\chi_{429}(296, \cdot)\)	429.2.t.a	104	2
429.2.x	\(\chi_{429}(248, \cdot)\)	429.2.x.a	192	4
429.2.y	\(\chi_{429}(116, \cdot)\)	429.2.y.a	32	4
		429.2.y.b	176
429.2.bb	\(\chi_{429}(25, \cdot)\)	429.2.bb.a	56	4
		429.2.bb.b	56
429.2.bd	\(\chi_{429}(76, \cdot)\)	429.2.bd.a	56	4
		429.2.bd.b	56
429.2.be	\(\chi_{429}(89, \cdot)\)	429.2.be.a	184	4
429.2.bg	\(\chi_{429}(16, \cdot)\)	429.2.bg.a	112	8
		429.2.bg.b	112
429.2.bi	\(\chi_{429}(5, \cdot)\)	429.2.bi.a	416	8
429.2.bj	\(\chi_{429}(73, \cdot)\)	429.2.bj.a	112	8
		429.2.bj.b	112
429.2.bm	\(\chi_{429}(17, \cdot)\)	429.2.bm.a	416	8
429.2.bn	\(\chi_{429}(4, \cdot)\)	429.2.bn.a	112	8
		429.2.bn.b	112
429.2.bq	\(\chi_{429}(29, \cdot)\)	429.2.bq.a	416	8
429.2.bs	\(\chi_{429}(7, \cdot)\)	429.2.bs.a	224	16
		429.2.bs.b	224
429.2.bv	\(\chi_{429}(20, \cdot)\)	429.2.bv.a	832	16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(429))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(429)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(143))\)\(^{\oplus 2}\)