Space of modular forms of level 324, weight 6, and Character 324.m

• Label: 324.6.m
• Level: $324$
• Weight: $6$
• Character orbit: 324.m
• Rep. character: $\chi_{324}(13,\cdot)$
• Character field: $\Q(\zeta_{27})$
• Dimension: $810$
• Sturm bound: $324$

Defining parameters

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	324.m (of order \(27\) and degree \(18\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 81 \)
Character field:			\(\Q(\zeta_{27})\)
Sturm bound:			\(324\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(324, [\chi])\).

	Total	New	Old
Modular forms	4914	810	4104
Cusp forms	4806	810	3996
Eisenstein series	108	0	108

Trace form

810 * q - 13743 * q^21 - 297 * q^23 + 17523 * q^27 + 3753 * q^29 - 36747 * q^33 - 19413 * q^35 - 84690 * q^41 + 136026 * q^45 + 84834 * q^47 - 126315 * q^51 - 151686 * q^53 - 41526 * q^57 + 100485 * q^59 + 266274 * q^63 - 226674 * q^65 - 24813 * q^67 + 94950 * q^69 + 406872 * q^71 - 56250 * q^75 - 566064 * q^77 + 324270 * q^79 - 454968 * q^81 - 340488 * q^83 + 79650 * q^85 + 405936 * q^87 + 405549 * q^89 + 852894 * q^93 + 931266 * q^95 + 238437 * q^97 - 908586 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(324, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(324, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(324, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 2}\)