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

• Label: 147.6.k
• Level: $147$
• Weight: $6$
• Character orbit: 147.k
• Rep. character: $\chi_{147}(20,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $552$
• Sturm bound: $112$

Defining parameters

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	147.k (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 147 \)
Character field:			\(\Q(\zeta_{14})\)
Sturm bound:			\(112\)

Dimensions

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

	Total	New	Old
Modular forms	576	576	0
Cusp forms	552	552	0
Eisenstein series	24	24	0

Trace form

552 * q - 7 * q^3 + 1462 * q^4 - 287 * q^6 - 126 * q^7 - 955 * q^9 - 14 * q^10 - 3822 * q^12 - 14 * q^13 - 605 * q^15 - 23690 * q^16 + 4926 * q^18 - 4123 * q^21 + 8450 * q^22 - 7 * q^24 - 59102 * q^25 + 14084 * q^27 - 20832 * q^28 + 16696 * q^30 - 7 * q^33 + 43050 * q^34 + 24023 * q^36 + 48042 * q^37 + 20127 * q^39 + 21882 * q^40 + 74725 * q^42 + 68430 * q^43 + 83384 * q^45 + 80482 * q^46 + 56154 * q^49 - 47713 * q^51 - 66990 * q^52 - 7 * q^54 - 382256 * q^55 - 130829 * q^57 - 90594 * q^58 + 43641 * q^60 + 374836 * q^61 + 120617 * q^63 + 472002 * q^64 + 58653 * q^66 - 32464 * q^67 - 331723 * q^69 + 275520 * q^70 - 385503 * q^72 - 14 * q^73 - 395521 * q^75 + 132090 * q^76 - 69159 * q^78 + 396432 * q^79 - 212351 * q^81 + 440216 * q^82 - 612794 * q^84 + 13126 * q^85 - 477743 * q^87 - 177202 * q^88 - 151417 * q^90 - 766906 * q^91 + 342827 * q^93 - 729778 * q^94 + 1376690 * q^96 + 553396 * 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.