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

• Label: 432.8.v
• Level: $432$
• Weight: $8$
• Character orbit: 432.v
• Rep. character: $\chi_{432}(35,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $664$
• Sturm bound: $576$

Defining parameters

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	432.v (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 144 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(576\)

Dimensions

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

	Total	New	Old
Modular forms	2040	680	1360
Cusp forms	1992	664	1328
Eisenstein series	48	16	32

Trace form

664 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 + 261624 * q^20 - 2 * q^22 + 12 * q^23 + 65528 * q^28 + 6 * q^29 + 6 * q^32 + 254 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 2165008 * q^46 - 36235896 * q^49 + 742644 * q^50 - 2 * q^52 - 16 * q^55 - 4941252 * q^56 + 2589532 * q^58 - 11841510 * q^59 - 2 * q^61 - 10490732 * q^64 + 12 * q^65 - 2 * q^67 + 7042368 * q^68 - 1647088 * q^70 + 11655930 * q^74 + 7301794 * q^76 + 6 * q^77 - 3563748 * q^82 + 14348826 * q^83 + 156248 * q^85 + 61774866 * q^86 - 15250730 * q^88 + 3294164 * q^91 + 40830588 * q^92 + 510 * q^94 - 4 * q^97

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

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

Decomposition of \(S_{8}^{\mathrm{old}}(432, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(432, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)