Space of modular forms of level 357 and weight 2

• Label: 357.2
• Level: 357
• Weight: 2
• Dimension: 3143
• Nonzero newspaces: 20
• Newform subspaces: 47
• Sturm bound: 18432
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 20 \)
Newform subspaces:			\( 47 \)
Sturm bound:			\(18432\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(357))\).

	Total	New	Old
Modular forms	4992	3439	1553
Cusp forms	4225	3143	1082
Eisenstein series	767	296	471

Trace form

3143 * q + 9 * q^2 - 25 * q^3 - 47 * q^4 + 6 * q^5 - 35 * q^6 - 69 * q^7 + 9 * q^8 - 37 * q^9 - 74 * q^10 - 32 * q^11 - 79 * q^12 - 82 * q^13 - 35 * q^14 - 110 * q^15 - 175 * q^16 - 9 * q^17 - 119 * q^18 - 64 * q^19 - 58 * q^20 - 57 * q^21 - 164 * q^22 - 8 * q^23 - 103 * q^24 - 155 * q^25 - 102 * q^26 - 37 * q^27 - 203 * q^28 - 62 * q^29 - 154 * q^30 - 172 * q^31 - 103 * q^32 - 112 * q^33 - 275 * q^34 - 58 * q^35 - 119 * q^36 - 158 * q^37 - 88 * q^38 - 50 * q^39 - 218 * q^40 - 2 * q^41 - 19 * q^42 - 204 * q^43 - 44 * q^44 + 22 * q^45 - 56 * q^46 + 36 * q^47 + 129 * q^48 - 77 * q^49 + 99 * q^50 + 55 * q^51 - 18 * q^52 + 18 * q^53 + 9 * q^54 - 120 * q^55 - 59 * q^56 - 140 * q^57 - 186 * q^58 - 116 * q^59 - 82 * q^60 - 194 * q^61 - 200 * q^62 - 141 * q^63 - 367 * q^64 - 168 * q^65 - 156 * q^66 - 152 * q^67 - 287 * q^68 - 264 * q^69 - 298 * q^70 - 96 * q^71 - 215 * q^72 - 330 * q^73 - 198 * q^74 - 227 * q^75 - 404 * q^76 - 124 * q^77 - 386 * q^78 - 236 * q^79 - 346 * q^80 - 125 * q^81 - 406 * q^82 - 140 * q^83 - 131 * q^84 - 310 * q^85 + 16 * q^86 + 10 * q^87 - 292 * q^88 + 54 * q^89 + 142 * q^90 - 174 * q^91 - 152 * q^92 + 112 * q^93 - 200 * q^94 + 4 * q^95 + 393 * q^96 - 106 * q^97 - 19 * q^98 + 108 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(357))\)

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
357.2.a	\(\chi_{357}(1, \cdot)\)	357.2.a.a	1	1
		357.2.a.b	1
		357.2.a.c	1
		357.2.a.d	1
		357.2.a.e	2
		357.2.a.f	2
		357.2.a.g	3
		357.2.a.h	4
357.2.c	\(\chi_{357}(356, \cdot)\)	357.2.c.a	20	1
		357.2.c.b	24
357.2.d	\(\chi_{357}(188, \cdot)\)	357.2.d.a	22	1
		357.2.d.b	22
357.2.f	\(\chi_{357}(169, \cdot)\)	357.2.f.a	6	1
		357.2.f.b	10
357.2.i	\(\chi_{357}(205, \cdot)\)	357.2.i.a	2	2
		357.2.i.b	2
		357.2.i.c	2
		357.2.i.d	8
		357.2.i.e	8
		357.2.i.f	10
		357.2.i.g	12
357.2.k	\(\chi_{357}(64, \cdot)\)	357.2.k.a	12	2
		357.2.k.b	20
357.2.l	\(\chi_{357}(251, \cdot)\)	357.2.l.a	4	2
		357.2.l.b	4
		357.2.l.c	80
357.2.p	\(\chi_{357}(16, \cdot)\)	357.2.p.a	48	2
357.2.r	\(\chi_{357}(290, \cdot)\)	357.2.r.a	2	2
		357.2.r.b	2
		357.2.r.c	2
		357.2.r.d	2
		357.2.r.e	4
		357.2.r.f	4
		357.2.r.g	34
		357.2.r.h	34
357.2.s	\(\chi_{357}(101, \cdot)\)	357.2.s.a	88	2
357.2.u	\(\chi_{357}(43, \cdot)\)	357.2.u.a	32	4
		357.2.u.b	48
357.2.w	\(\chi_{357}(83, \cdot)\)	357.2.w.a	176	4
357.2.y	\(\chi_{357}(38, \cdot)\)	357.2.y.a	176	4
357.2.bb	\(\chi_{357}(4, \cdot)\)	357.2.bb.a	96	4
357.2.bc	\(\chi_{357}(97, \cdot)\)	357.2.bc.a	192	8
357.2.bf	\(\chi_{357}(29, \cdot)\)	357.2.bf.a	288	8
357.2.bh	\(\chi_{357}(25, \cdot)\)	357.2.bh.a	192	8
357.2.bj	\(\chi_{357}(26, \cdot)\)	357.2.bj.a	352	8
357.2.bl	\(\chi_{357}(10, \cdot)\)	357.2.bl.a	384	16
357.2.bm	\(\chi_{357}(11, \cdot)\)	357.2.bm.a	704	16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(357))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(357)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 2}\)