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

• Label: 507.4.e
• Level: $507$
• Weight: $4$
• Character orbit: 507.e
• Rep. character: $\chi_{507}(22,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $156$
• Sturm bound: $242$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	392	156	236
Cusp forms	336	156	180
Eisenstein series	56	0	56

Trace form

156 * q + 4 * q^2 - 6 * q^3 - 320 * q^4 + 16 * q^5 - 22 * q^7 - 96 * q^8 - 702 * q^9 - 132 * q^10 + 48 * q^11 + 192 * q^12 - 32 * q^14 + 12 * q^15 - 1216 * q^16 + 20 * q^17 - 72 * q^18 + 108 * q^19 - 524 * q^20 - 36 * q^21 + 496 * q^22 - 152 * q^23 - 180 * q^24 + 4684 * q^25 + 108 * q^27 - 72 * q^28 + 100 * q^29 + 288 * q^30 - 244 * q^31 + 448 * q^32 - 96 * q^33 - 1384 * q^34 + 56 * q^35 - 2880 * q^36 + 132 * q^37 - 824 * q^38 + 1336 * q^40 - 1000 * q^41 - 72 * q^42 - 374 * q^43 - 280 * q^44 - 72 * q^45 - 28 * q^46 + 1440 * q^47 - 552 * q^48 - 3440 * q^49 + 940 * q^50 + 1368 * q^51 - 96 * q^53 - 268 * q^55 + 1492 * q^56 + 840 * q^57 + 520 * q^58 + 1484 * q^59 - 2448 * q^60 - 1678 * q^61 + 2088 * q^62 - 198 * q^63 + 8912 * q^64 - 624 * q^66 - 6 * q^67 + 852 * q^68 - 768 * q^69 + 4616 * q^70 - 952 * q^71 + 432 * q^72 + 212 * q^73 + 896 * q^74 + 366 * q^75 - 1964 * q^76 - 7560 * q^77 + 1468 * q^79 - 1996 * q^80 - 6318 * q^81 + 1308 * q^82 - 1848 * q^83 + 648 * q^84 - 136 * q^85 - 3744 * q^86 - 1440 * q^87 + 3288 * q^88 + 2312 * q^89 + 2376 * q^90 - 800 * q^92 + 210 * q^93 - 272 * q^94 + 2340 * q^95 + 5160 * q^96 + 2322 * q^97 - 2680 * 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

\( S_{4}^{\mathrm{old}}(507, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)