Space of modular forms of level 507, weight 4, and Character 507.m

• Label: 507.4.m
• Level: $507$
• Weight: $4$
• Character orbit: 507.m
• Rep. character: $\chi_{507}(40,\cdot)$
• Character field: $\Q(\zeta_{13})$
• Dimension: $1080$
• Sturm bound: $242$

Defining parameters

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	507.m (of order \(13\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 169 \)
Character field:			\(\Q(\zeta_{13})\)
Sturm bound:			\(242\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(507, [\chi])\).

	Total	New	Old
Modular forms	2208	1080	1128
Cusp forms	2160	1080	1080
Eisenstein series	48	0	48

Trace form

1080 * q - 4 * q^2 - 352 * q^4 - 16 * q^5 - 32 * q^7 - 48 * q^8 - 810 * q^9 + 96 * q^11 - 24 * q^12 - 208 * q^13 + 192 * q^14 + 24 * q^15 - 1232 * q^16 + 56 * q^17 - 36 * q^18 - 216 * q^19 + 92 * q^20 - 84 * q^21 - 544 * q^22 + 48 * q^23 + 180 * q^24 - 2478 * q^25 + 48 * q^28 - 296 * q^29 + 120 * q^30 - 1532 * q^31 - 938 * q^32 - 192 * q^33 - 3690 * q^34 - 112 * q^35 - 3168 * q^36 + 12 * q^37 + 1262 * q^38 - 156 * q^39 + 3080 * q^40 - 296 * q^41 - 3930 * q^42 + 288 * q^43 - 20 * q^44 - 144 * q^45 - 248 * q^46 + 48 * q^47 + 336 * q^48 - 5490 * q^49 + 380 * q^50 + 528 * q^51 + 3926 * q^52 + 1216 * q^53 - 164 * q^55 - 520 * q^56 + 84 * q^57 + 1208 * q^58 - 7872 * q^59 - 1308 * q^60 - 1280 * q^61 + 6210 * q^62 - 288 * q^63 - 4292 * q^64 + 416 * q^65 + 1224 * q^66 - 4476 * q^67 + 11030 * q^68 - 72 * q^69 - 11888 * q^70 - 4484 * q^71 - 432 * q^72 + 1804 * q^73 + 8264 * q^74 + 624 * q^75 + 13040 * q^76 + 280 * q^77 - 9126 * q^78 + 204 * q^79 + 700 * q^80 - 7290 * q^81 - 10254 * q^82 + 3072 * q^83 - 624 * q^84 + 8800 * q^85 - 456 * q^86 + 6996 * q^87 - 12416 * q^88 - 1376 * q^89 - 6136 * q^91 - 3276 * q^92 + 7854 * q^93 + 25506 * q^94 + 6672 * q^95 - 840 * q^96 + 4512 * q^97 + 5644 * q^98 + 864 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(507, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(507, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(507, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)