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

• Label: 432.4.y
• Level: $432$
• Weight: $4$
• Character orbit: 432.y
• Rep. character: $\chi_{432}(37,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $280$
• Sturm bound: $288$

Defining parameters

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	432.y (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 144 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(288\)

Dimensions

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

	Total	New	Old
Modular forms	888	296	592
Cusp forms	840	280	560
Eisenstein series	48	16	32

Trace form

280 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 + 8 * q^8 - 8 * q^10 + 2 * q^11 - 2 * q^13 + 34 * q^14 - 2 * q^16 + 16 * q^17 - 8 * q^19 + 156 * q^20 - 2 * q^22 - 536 * q^26 - 264 * q^28 + 2 * q^29 - 4 * q^31 + 982 * q^32 - 18 * q^34 + 508 * q^35 - 8 * q^37 - 1202 * q^38 - 2 * q^40 - 2 * q^43 + 1548 * q^44 + 32 * q^46 - 1876 * q^47 + 5680 * q^49 - 1032 * q^50 - 2 * q^52 + 8 * q^53 - 1684 * q^56 + 592 * q^58 - 1018 * q^59 - 2 * q^61 - 3652 * q^62 + 532 * q^64 + 4 * q^65 - 2 * q^67 + 1664 * q^68 + 684 * q^70 + 1822 * q^74 + 1114 * q^76 + 1374 * q^77 - 4 * q^79 - 4752 * q^80 - 1444 * q^82 + 1222 * q^83 - 252 * q^85 - 2518 * q^86 + 2086 * q^88 - 1380 * q^91 - 2896 * q^92 + 30 * q^94 + 6084 * q^95 - 4 * q^97 + 7400 * q^98

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

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

Decomposition of \(S_{4}^{\mathrm{old}}(432, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(432, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)