Space of modular forms of level 147, weight 8, and Character 147.o

• Label: 147.8.o
• Level: $147$
• Weight: $8$
• Character orbit: 147.o
• Rep. character: $\chi_{147}(5,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $1548$
• Sturm bound: $149$

Defining parameters

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	147.o (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 147 \)
Character field:			\(\Q(\zeta_{42})\)
Sturm bound:			\(149\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(147, [\chi])\).

	Total	New	Old
Modular forms	1596	1596	0
Cusp forms	1548	1548	0
Eisenstein series	48	48	0

Trace form

1548 * q - 11 * q^3 - 8218 * q^4 - 3262 * q^6 - 729 * q^7 + 6019 * q^9 + 602 * q^10 - 18087 * q^12 - 28 * q^13 - 16978 * q^15 + 515814 * q^16 - 8193 * q^18 - 52701 * q^19 - 70316 * q^21 + 226808 * q^22 + 211540 * q^24 + 1937215 * q^25 + 439243 * q^27 - 710396 * q^28 - 42211 * q^30 - 601749 * q^31 + 66010 * q^33 + 2434348 * q^34 - 1538438 * q^36 + 2949266 * q^37 - 470331 * q^39 - 89726 * q^40 - 397264 * q^42 + 905102 * q^43 + 4828033 * q^45 - 6906332 * q^46 - 616071 * q^49 - 1913960 * q^51 - 373052 * q^52 + 6743884 * q^54 + 10584182 * q^55 - 7242832 * q^57 + 4289166 * q^58 - 19068300 * q^60 - 8682301 * q^61 - 10449965 * q^63 + 64549248 * q^64 - 37185120 * q^66 + 5782517 * q^67 - 18454898 * q^69 + 843220 * q^70 - 2277570 * q^72 - 2038429 * q^73 + 6479551 * q^75 - 34761636 * q^76 - 57074856 * q^78 + 2091549 * q^79 - 55693369 * q^81 - 57790530 * q^82 - 153512332 * q^84 - 30316348 * q^85 + 44338154 * q^87 - 552782 * q^88 + 224944573 * q^90 - 54198069 * q^91 + 20991625 * q^93 - 22978956 * q^94 - 40615736 * q^96 + 75876560 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(147, [\chi])\) into newform subspaces

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