Space of modular forms of level 432, weight 4, and Character 432.bg

• Label: 432.4.bg
• Level: $432$
• Weight: $4$
• Character orbit: 432.bg
• Rep. character: $\chi_{432}(13,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $2568$
• Sturm bound: $288$

Defining parameters

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	432.bg (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 432 \)
Character field:			\(\Q(\zeta_{36})\)
Sturm bound:			\(288\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(432, [\chi])\).

	Total	New	Old
Modular forms	2616	2616	0
Cusp forms	2568	2568	0
Eisenstein series	48	48	0

Trace form

2568 * q - 12 * q^2 - 12 * q^3 - 12 * q^4 - 12 * q^5 - 12 * q^6 - 6 * q^8 - 6 * q^10 - 12 * q^11 - 246 * q^12 - 12 * q^13 - 12 * q^14 - 24 * q^15 - 12 * q^16 - 12 * q^17 - 12 * q^18 - 6 * q^19 + 450 * q^20 - 12 * q^21 - 12 * q^22 + 738 * q^24 - 24 * q^26 - 12 * q^27 - 24 * q^28 - 12 * q^29 - 12 * q^30 - 24 * q^31 - 12 * q^32 - 24 * q^33 + 36 * q^34 - 6 * q^35 - 12 * q^36 - 6 * q^37 - 12 * q^38 - 12 * q^40 - 4752 * q^42 - 12 * q^43 - 6 * q^44 - 12 * q^45 - 6 * q^46 - 24 * q^47 - 12 * q^48 - 24 * q^49 + 6384 * q^50 + 150 * q^51 - 12 * q^52 - 24 * q^53 - 8916 * q^54 - 2070 * q^56 - 1794 * q^58 - 3072 * q^59 - 3672 * q^60 - 12 * q^61 + 1248 * q^62 - 24 * q^63 - 6 * q^64 - 24 * q^65 - 6210 * q^66 - 12 * q^67 + 4974 * q^68 - 12 * q^69 - 2070 * q^70 + 2880 * q^72 + 5448 * q^74 + 4944 * q^75 - 12 * q^76 - 12 * q^77 + 2250 * q^78 - 24 * q^79 - 204 * q^80 - 24 * q^81 - 24 * q^82 + 3648 * q^83 - 12348 * q^84 + 738 * q^85 - 8352 * q^86 - 12 * q^88 - 4386 * q^90 - 6 * q^91 - 9474 * q^92 - 12 * q^93 - 12 * q^94 - 24 * q^95 + 5064 * q^96 - 24 * q^97 - 6 * q^98 - 12 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(432, [\chi])\) into newform subspaces

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