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

• Label: 507.4.x
• Level: $507$
• Weight: $4$
• Character orbit: 507.x
• Rep. character: $\chi_{507}(2,\cdot)$
• Character field: $\Q(\zeta_{156})$
• Dimension: $8640$
• Sturm bound: $242$

Defining parameters

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	507.x (of order \(156\) and degree \(48\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 507 \)
Character field:			\(\Q(\zeta_{156})\)
Sturm bound:			\(242\)

Dimensions

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

	Total	New	Old
Modular forms	8832	8832	0
Cusp forms	8640	8640	0
Eisenstein series	192	192	0

Trace form

8640 * q - 50 * q^3 - 92 * q^4 - 2 * q^6 - 124 * q^7 - 50 * q^9 + 52 * q^10 - 52 * q^12 - 24 * q^13 - 122 * q^15 - 5668 * q^16 - 308 * q^18 - 364 * q^19 - 134 * q^21 - 48 * q^22 - 1978 * q^24 - 104 * q^25 - 356 * q^27 + 652 * q^28 - 2526 * q^30 + 76 * q^31 - 62 * q^33 + 292 * q^34 - 3112 * q^36 - 2036 * q^37 - 6934 * q^39 + 1984 * q^40 - 416 * q^42 - 1520 * q^43 - 5386 * q^45 + 456 * q^46 + 338 * q^48 + 2896 * q^49 - 52 * q^51 + 4232 * q^52 - 1982 * q^54 + 8636 * q^55 + 1222 * q^57 - 1012 * q^58 + 2808 * q^60 - 1036 * q^61 - 2442 * q^63 - 104 * q^64 - 4910 * q^66 - 13072 * q^67 + 2324 * q^69 - 13144 * q^70 + 3848 * q^72 - 3676 * q^73 - 18068 * q^75 - 8504 * q^76 - 12344 * q^78 + 5528 * q^79 - 1922 * q^81 + 12172 * q^82 - 1136 * q^84 - 5084 * q^85 - 1762 * q^87 + 11660 * q^88 - 52 * q^90 + 8804 * q^91 - 7678 * q^93 + 35156 * q^94 - 1534 * q^96 + 100 * q^97 + 13042 * 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.