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

• Label: 324.6.l
• Level: $324$
• Weight: $6$
• Character orbit: 324.l
• Rep. character: $\chi_{324}(35,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $528$
• Sturm bound: $324$

Defining parameters

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	324.l (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 108 \)
Character field:			\(\Q(\zeta_{18})\)
Sturm bound:			\(324\)

Dimensions

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

	Total	New	Old
Modular forms	1656	552	1104
Cusp forms	1584	528	1056
Eisenstein series	72	24	48

Trace form

528 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 - 1509 * q^14 - 6 * q^16 + 18 * q^17 - 1233 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 - 11928 * q^29 - 7224 * q^32 - 102 * q^34 - 6 * q^37 - 14868 * q^38 - 9381 * q^40 - 43518 * q^41 + 158049 * q^44 - 3 * q^46 - 12 * q^49 - 105387 * q^50 - 68829 * q^52 - 193635 * q^56 + 9741 * q^58 - 12 * q^61 + 461448 * q^62 - 3 * q^64 + 35988 * q^65 - 389283 * q^68 - 50331 * q^70 - 6 * q^73 - 20397 * q^74 - 3078 * q^76 + 26196 * q^77 - 12 * q^82 - 18762 * q^85 + 279246 * q^86 + 98298 * q^88 - 474984 * q^89 + 164823 * q^92 - 277053 * q^94 + 174426 * q^97 - 1307970 * q^98

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

\( S_{6}^{\mathrm{old}}(324, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 2}\)