Space of modular forms of level 432, weight 8, and Character 432.bj

• Label: 432.8.bj
• Level: $432$
• Weight: $8$
• Character orbit: 432.bj
• Rep. character: $\chi_{432}(11,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $6024$
• Sturm bound: $576$

Defining parameters

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	432.bj (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 432 \)
Character field:			\(\Q(\zeta_{36})\)
Sturm bound:			\(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(432, [\chi])\).

	Total	New	Old
Modular forms	6072	6072	0
Cusp forms	6024	6024	0
Eisenstein series	48	48	0

Trace form

6024 * q - 12 * q^2 - 12 * q^3 - 12 * q^4 - 12 * q^5 - 12 * q^6 - 24 * q^7 - 18 * q^8 - 6 * q^10 - 12 * q^11 - 36066 * q^12 - 12 * q^13 - 12 * q^14 - 12 * q^16 - 36 * q^17 - 12 * q^18 - 6 * q^19 + 261606 * q^20 - 12 * q^21 - 12 * q^22 - 24 * q^23 + 448518 * q^24 - 12 * q^27 - 24 * q^28 - 12 * q^29 - 12 * q^30 - 12 * q^32 - 24 * q^33 - 780 * q^34 - 18 * q^35 - 12 * q^36 - 6 * q^37 - 12 * q^38 - 24 * q^39 - 12 * q^40 - 5788392 * q^42 - 12 * q^43 - 18 * q^44 - 12 * q^45 - 6 * q^46 - 12 * q^48 - 24 * q^49 - 1485288 * q^50 - 13134 * q^51 - 12 * q^52 + 23559804 * q^54 - 48 * q^55 - 4941270 * q^56 - 7768614 * q^58 - 11841528 * q^59 + 13388328 * q^60 - 12 * q^61 - 25222644 * q^62 - 6 * q^64 - 24 * q^65 - 60783090 * q^66 - 12 * q^67 + 7042350 * q^68 - 12 * q^69 + 4941246 * q^70 - 36 * q^71 + 41353152 * q^72 + 11655912 * q^74 + 2202552 * q^75 - 12 * q^76 - 12 * q^77 - 38641446 * q^78 - 24 * q^81 - 24 * q^82 + 14348808 * q^83 + 15098640 * q^84 - 468762 * q^85 + 61774848 * q^86 - 24 * q^87 - 12 * q^88 - 28697826 * q^90 - 6 * q^91 + 40830570 * q^92 - 12 * q^93 - 12 * q^94 + 85313184 * q^96 - 24 * q^97 - 18 * q^98 - 12 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(432, [\chi])\) into newform subspaces

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