Space of modular forms of level 147, weight 6, and Character 147.o

• Label: 147.6.o
• Level: $147$
• Weight: $6$
• Character orbit: 147.o
• Rep. character: $\chi_{147}(5,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $1092$
• Sturm bound: $112$

Defining parameters

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	147.o (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 147 \)
Character field:			\(\Q(\zeta_{42})\)
Sturm bound:			\(112\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(147, [\chi])\).

	Total	New	Old
Modular forms	1140	1140	0
Cusp forms	1092	1092	0
Eisenstein series	48	48	0

Trace form

1092 * q - 11 * q^3 - 1434 * q^4 + 266 * q^6 - 113 * q^7 + 1507 * q^9 + 722 * q^10 + 2265 * q^12 - 28 * q^13 + 590 * q^15 + 20902 * q^16 + 2559 * q^18 - 1137 * q^19 + 4486 * q^21 - 8480 * q^22 - 9572 * q^24 + 48553 * q^25 - 14105 * q^27 - 988 * q^28 + 9077 * q^30 + 21867 * q^31 - 28688 * q^33 - 43092 * q^34 - 24038 * q^36 + 55738 * q^37 + 10053 * q^39 - 210318 * q^40 - 4312 * q^42 - 57946 * q^43 - 56927 * q^45 + 239492 * q^46 + 114071 * q^49 - 24596 * q^51 + 13412 * q^52 - 114548 * q^54 - 64498 * q^55 + 130814 * q^57 - 91938 * q^58 + 52620 * q^60 - 89267 * q^61 + 74395 * q^63 + 478240 * q^64 + 279528 * q^66 + 20105 * q^67 + 331702 * q^69 - 848652 * q^70 - 185082 * q^72 - 376783 * q^73 + 30475 * q^75 - 132132 * q^76 + 22488 * q^78 + 234973 * q^79 + 1133087 * q^81 + 100030 * q^82 - 197548 * q^84 - 13156 * q^85 - 338590 * q^87 - 88430 * q^88 - 937475 * q^90 + 307711 * q^91 - 40325 * q^93 - 293516 * q^94 + 560728 * q^96 - 553432 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(147, [\chi])\) into newform subspaces

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