Space of modular forms of level 507 and weight 4

• Label: 507.4
• Level: 507
• Weight: 4
• Dimension: 20838
• Nonzero newspaces: 12
• Sturm bound: 75712
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(75712\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(507))\).

	Total	New	Old
Modular forms	28848	21246	7602
Cusp forms	27936	20838	7098
Eisenstein series	912	408	504

Trace form

20838 * q - 66 * q^3 - 132 * q^4 - 66 * q^6 - 276 * q^7 - 288 * q^8 - 66 * q^9 + 228 * q^10 + 240 * q^11 + 402 * q^12 + 144 * q^13 + 480 * q^14 + 78 * q^15 - 132 * q^16 - 756 * q^17 - 1398 * q^18 - 1908 * q^19 - 2064 * q^20 - 66 * q^21 + 1428 * q^22 + 912 * q^23 + 2238 * q^24 + 1344 * q^25 + 1500 * q^26 + 1530 * q^27 + 1956 * q^28 + 780 * q^29 + 2046 * q^30 - 372 * q^31 - 2040 * q^32 - 1842 * q^33 - 4644 * q^34 - 3120 * q^35 - 6198 * q^36 - 1416 * q^37 - 1824 * q^39 - 8028 * q^40 - 4956 * q^41 - 5070 * q^42 - 2820 * q^43 - 600 * q^44 + 498 * q^45 + 4908 * q^46 + 2976 * q^47 + 6654 * q^48 + 7788 * q^49 + 8832 * q^50 + 4818 * q^51 + 1500 * q^52 + 3792 * q^53 - 3474 * q^54 + 5484 * q^55 + 5544 * q^56 + 2262 * q^57 + 3972 * q^58 + 1968 * q^59 + 5250 * q^60 - 4656 * q^61 + 1272 * q^62 + 10230 * q^63 - 3756 * q^64 - 2430 * q^65 + 4794 * q^66 - 612 * q^67 + 9360 * q^68 + 3270 * q^69 + 1764 * q^70 + 1056 * q^71 - 6246 * q^72 - 2436 * q^73 - 11544 * q^74 - 15870 * q^75 - 25092 * q^76 - 13248 * q^77 - 14682 * q^78 - 11292 * q^79 - 18624 * q^80 - 11298 * q^81 + 420 * q^82 + 2448 * q^83 - 7278 * q^84 - 96 * q^85 - 12768 * q^86 - 5370 * q^87 + 7620 * q^88 - 6960 * q^89 + 4242 * q^90 - 552 * q^91 + 12720 * q^92 + 15030 * q^93 + 21084 * q^94 + 14160 * q^95 + 34410 * q^96 + 21900 * q^97 + 19032 * q^98 + 22710 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(507))\)

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
507.4.a	\(\chi_{507}(1, \cdot)\)	507.4.a.a	1	1
		507.4.a.b	1
		507.4.a.c	1
		507.4.a.d	1
		507.4.a.e	1
		507.4.a.f	2
		507.4.a.g	2
		507.4.a.h	3
		507.4.a.i	4
		507.4.a.j	4
		507.4.a.k	4
		507.4.a.l	4
		507.4.a.m	4
		507.4.a.n	9
		507.4.a.o	9
		507.4.a.p	9
		507.4.a.q	9
		507.4.a.r	10
507.4.b	\(\chi_{507}(337, \cdot)\)	507.4.b.a	2	1
		507.4.b.b	2
		507.4.b.c	2
		507.4.b.d	2
		507.4.b.e	4
		507.4.b.f	4
		507.4.b.g	6
		507.4.b.h	8
		507.4.b.i	10
		507.4.b.j	18
		507.4.b.k	18
507.4.e	\(\chi_{507}(22, \cdot)\)	n/a	156	2
507.4.f	\(\chi_{507}(239, \cdot)\)	n/a	288	2
507.4.j	\(\chi_{507}(316, \cdot)\)	n/a	152	2
507.4.k	\(\chi_{507}(80, \cdot)\)	n/a	576	4
507.4.m	\(\chi_{507}(40, \cdot)\)	n/a	1080	12
507.4.p	\(\chi_{507}(25, \cdot)\)	n/a	1104	12
507.4.q	\(\chi_{507}(16, \cdot)\)	n/a	2160	24
507.4.s	\(\chi_{507}(5, \cdot)\)	n/a	4320	24
507.4.t	\(\chi_{507}(4, \cdot)\)	n/a	2208	24
507.4.x	\(\chi_{507}(2, \cdot)\)	n/a	8640	48

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(507))\) into lower level spaces

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