Space of modular forms of level 507, weight 3, and Character 507.g

• Label: 507.3.g
• Level: $507$
• Weight: $3$
• Character orbit: 507.g
• Rep. character: $\chi_{507}(70,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $104$
• Sturm bound: $182$

Defining parameters

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	507.g (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(182\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(507, [\chi])\).

	Total	New	Old
Modular forms	272	104	168
Cusp forms	216	104	112
Eisenstein series	56	0	56

Trace form

104 * q - 4 * q^2 + 20 * q^5 - 8 * q^7 + 24 * q^8 + 312 * q^9 + 20 * q^11 - 12 * q^15 - 544 * q^16 - 12 * q^18 + 40 * q^19 - 44 * q^20 + 48 * q^21 + 136 * q^22 - 36 * q^24 - 32 * q^28 - 32 * q^29 - 32 * q^31 - 148 * q^32 + 36 * q^33 - 96 * q^34 - 48 * q^35 + 16 * q^37 + 8 * q^40 + 116 * q^41 + 216 * q^42 + 92 * q^44 + 60 * q^45 + 264 * q^46 - 100 * q^47 - 96 * q^48 - 20 * q^50 + 272 * q^53 + 264 * q^55 - 120 * q^57 + 104 * q^58 - 316 * q^59 - 12 * q^60 - 248 * q^61 - 24 * q^63 - 432 * q^66 - 176 * q^67 - 96 * q^68 - 184 * q^70 - 4 * q^71 + 72 * q^72 + 64 * q^73 + 232 * q^74 - 112 * q^76 - 256 * q^79 + 332 * q^80 + 936 * q^81 + 212 * q^83 + 240 * q^84 + 168 * q^85 - 24 * q^87 + 452 * q^89 + 920 * q^92 + 24 * q^93 - 136 * q^94 - 24 * q^96 - 128 * q^97 - 724 * q^98 + 60 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(507, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(507, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(507, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)