Space of modular forms of level 343, weight 4, and Character 343.c

• Label: 343.4.c
• Level: $343$
• Weight: $4$
• Character orbit: 343.c
• Rep. character: $\chi_{343}(18,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $144$
• Sturm bound: $130$

Defining parameters

Level:	\( N \)	\(=\)	\( 343 = 7^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	343.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Sturm bound:			\(130\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(343, [\chi])\).

	Total	New	Old
Modular forms	210	144	66
Cusp forms	182	144	38
Eisenstein series	28	0	28

Trace form

144 * q - q^2 - 283 * q^4 - 18 * q^8 - 664 * q^9 + 6 * q^11 + 48 * q^15 - 1187 * q^16 - 53 * q^18 - 4 * q^22 + 90 * q^23 - 1868 * q^25 + 8 * q^29 - 130 * q^30 - 69 * q^32 + 5466 * q^36 + 104 * q^37 + 224 * q^39 - 244 * q^43 - 160 * q^44 + 212 * q^46 - 5438 * q^50 + 80 * q^51 + 1924 * q^53 + 832 * q^57 + 1118 * q^58 - 210 * q^60 + 10474 * q^64 - 28 * q^65 - 610 * q^67 - 1084 * q^71 + 285 * q^72 - 1846 * q^74 + 644 * q^78 - 498 * q^79 - 5980 * q^81 + 6992 * q^85 + 5563 * q^86 + 4921 * q^88 - 7814 * q^92 - 1348 * q^93 + 108 * q^95 - 21300 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(343, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(343, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(343, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)