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

• Label: 507.4.f
• Level: $507$
• Weight: $4$
• Character orbit: 507.f
• Rep. character: $\chi_{507}(239,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $288$
• Sturm bound: $242$

Defining parameters

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	507.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 39 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(242\)

Dimensions

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

	Total	New	Old
Modular forms	392	328	64
Cusp forms	336	288	48
Eisenstein series	56	40	16

Trace form

288 * q + 4 * q^3 - 44 * q^6 - 4 * q^7 + 4 * q^9 + 76 * q^15 - 3496 * q^16 - 296 * q^18 - 148 * q^19 + 208 * q^21 + 440 * q^22 - 36 * q^24 + 844 * q^27 - 264 * q^28 + 84 * q^31 - 872 * q^33 - 816 * q^34 + 1440 * q^37 - 4560 * q^40 + 480 * q^42 - 260 * q^45 + 1560 * q^46 + 416 * q^48 + 232 * q^54 + 488 * q^55 - 1028 * q^57 + 1352 * q^58 + 1064 * q^60 - 2056 * q^61 + 652 * q^63 + 9732 * q^66 - 844 * q^67 - 1192 * q^70 - 6984 * q^72 + 416 * q^73 - 2712 * q^76 - 7528 * q^79 - 2492 * q^81 - 5204 * q^84 + 8304 * q^85 - 1880 * q^87 + 4156 * q^93 + 2432 * q^94 + 5956 * q^96 + 5232 * q^97 - 1700 * 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

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