Space of modular forms of level 507 and weight 2

• Label: 507.2
• Level: 507
• Weight: 2
• Dimension: 6811
• Nonzero newspaces: 12
• Newform subspaces: 69
• Sturm bound: 37856
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 69 \)
Sturm bound:			\(37856\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(507))\).

	Total	New	Old
Modular forms	9920	7219	2701
Cusp forms	9009	6811	2198
Eisenstein series	911	408	503

Trace form

6811 * q + 3 * q^2 - 65 * q^3 - 125 * q^4 + 6 * q^5 - 63 * q^6 - 132 * q^7 - 21 * q^8 - 69 * q^9 - 174 * q^10 - 12 * q^11 - 111 * q^12 - 168 * q^13 - 24 * q^14 - 84 * q^15 - 181 * q^16 - 18 * q^17 - 111 * q^18 - 192 * q^19 - 90 * q^20 - 110 * q^21 - 216 * q^22 - 24 * q^23 - 123 * q^24 - 185 * q^25 - 60 * q^26 - 197 * q^27 - 244 * q^28 - 30 * q^29 - 96 * q^30 - 148 * q^31 - 57 * q^32 - 66 * q^33 - 174 * q^34 + q^36 - 106 * q^37 + 60 * q^38 - 56 * q^39 - 258 * q^40 - 42 * q^41 - 78 * q^42 - 216 * q^43 - 36 * q^44 - 36 * q^45 - 300 * q^46 - 48 * q^47 - 107 * q^48 - 251 * q^49 - 135 * q^50 - 156 * q^51 - 294 * q^52 - 138 * q^53 - 159 * q^54 - 324 * q^55 - 240 * q^56 - 194 * q^57 - 342 * q^58 - 108 * q^59 - 228 * q^60 - 298 * q^61 - 168 * q^62 - 110 * q^63 - 353 * q^64 - 90 * q^65 - 114 * q^66 - 192 * q^67 - 54 * q^68 - 54 * q^69 - 252 * q^70 + 24 * q^71 - 39 * q^72 - 138 * q^73 - 42 * q^74 - 39 * q^75 - 216 * q^76 - 48 * q^77 - 18 * q^78 - 316 * q^79 - 90 * q^80 + 3 * q^81 - 210 * q^82 + 12 * q^83 - 110 * q^84 - 204 * q^85 - 60 * q^86 - 84 * q^87 - 360 * q^88 - 150 * q^89 - 108 * q^90 - 292 * q^91 - 168 * q^92 - 158 * q^93 - 420 * q^94 - 216 * q^95 - 231 * q^96 - 298 * q^97 - 141 * q^98 - 210 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(507))\)

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
507.2.a	\(\chi_{507}(1, \cdot)\)	507.2.a.a	1	1
		507.2.a.b	1
		507.2.a.c	1
		507.2.a.d	2
		507.2.a.e	2
		507.2.a.f	2
		507.2.a.g	2
		507.2.a.h	2
		507.2.a.i	3
		507.2.a.j	3
		507.2.a.k	3
		507.2.a.l	3
507.2.b	\(\chi_{507}(337, \cdot)\)	507.2.b.a	2	1
		507.2.b.b	2
		507.2.b.c	2
		507.2.b.d	4
		507.2.b.e	4
		507.2.b.f	6
		507.2.b.g	6
507.2.e	\(\chi_{507}(22, \cdot)\)	507.2.e.a	2	2
		507.2.e.b	2
		507.2.e.c	2
		507.2.e.d	4
		507.2.e.e	4
		507.2.e.f	4
		507.2.e.g	4
		507.2.e.h	4
		507.2.e.i	6
		507.2.e.j	6
		507.2.e.k	6
		507.2.e.l	6
507.2.f	\(\chi_{507}(239, \cdot)\)	507.2.f.a	4	2
		507.2.f.b	4
		507.2.f.c	4
		507.2.f.d	8
		507.2.f.e	8
		507.2.f.f	8
		507.2.f.g	48
507.2.j	\(\chi_{507}(316, \cdot)\)	507.2.j.a	2	2
		507.2.j.b	2
		507.2.j.c	2
		507.2.j.d	4
		507.2.j.e	4
		507.2.j.f	8
		507.2.j.g	8
		507.2.j.h	12
		507.2.j.i	12
507.2.k	\(\chi_{507}(80, \cdot)\)	507.2.k.a	4	4
		507.2.k.b	4
		507.2.k.c	4
		507.2.k.d	8
		507.2.k.e	8
		507.2.k.f	8
		507.2.k.g	8
		507.2.k.h	8
		507.2.k.i	8
		507.2.k.j	8
		507.2.k.k	96
507.2.m	\(\chi_{507}(40, \cdot)\)	507.2.m.a	180	12
		507.2.m.b	204
507.2.p	\(\chi_{507}(25, \cdot)\)	507.2.p.a	168	12
		507.2.p.b	192
507.2.q	\(\chi_{507}(16, \cdot)\)	507.2.q.a	360	24
		507.2.q.b	384
507.2.s	\(\chi_{507}(5, \cdot)\)	507.2.s.a	1392	24
507.2.t	\(\chi_{507}(4, \cdot)\)	507.2.t.a	336	24
		507.2.t.b	360
507.2.x	\(\chi_{507}(2, \cdot)\)	507.2.x.a	48	48
		507.2.x.b	2784

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(507))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(507)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 2}\)