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

• Label: 432.8.u
• Level: $432$
• Weight: $8$
• Character orbit: 432.u
• Rep. character: $\chi_{432}(49,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $750$
• Sturm bound: $576$

Defining parameters

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	432.u (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 27 \)
Character field:			\(\Q(\zeta_{9})\)
Sturm bound:			\(576\)

Dimensions

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

	Total	New	Old
Modular forms	3060	762	2298
Cusp forms	2988	750	2238
Eisenstein series	72	12	60

Trace form

750 * q + 6 * q^3 - 6 * q^5 + 6 * q^7 - 6 * q^9 + 6 * q^11 - 6 * q^13 + 6 * q^15 - 3 * q^17 + 3 * q^19 - 6 * q^21 + 6 * q^23 - 6 * q^25 - 550128 * q^27 - 192042 * q^29 + 6 * q^31 - 74268 * q^33 - 1543497 * q^35 - 3 * q^37 + 1471434 * q^39 + 450900 * q^41 + 6 * q^43 + 1513494 * q^45 - 1480008 * q^47 - 6 * q^49 - 6555 * q^51 - 12 * q^53 + 12 * q^55 - 1293087 * q^57 + 5920764 * q^59 - 6 * q^61 - 7378584 * q^63 - 6322350 * q^65 + 6 * q^67 + 5272818 * q^69 + 15032265 * q^71 - 3 * q^73 - 1101276 * q^75 - 8923854 * q^77 + 6 * q^79 - 8523822 * q^81 + 7174416 * q^83 + 234369 * q^85 + 13742340 * q^87 + 11948151 * q^89 + 3 * q^91 - 6 * q^93 - 8508141 * q^95 - 15889092 * q^97 - 111014166 * 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.

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

\( S_{8}^{\mathrm{old}}(432, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)