Space of modular forms of level 324, weight 9, and Character 324.n

• Label: 324.9.n
• Level: $324$
• Weight: $9$
• Character orbit: 324.n
• Rep. character: $\chi_{324}(7,\cdot)$
• Character field: $\Q(\zeta_{54})$
• Dimension: $7740$
• Sturm bound: $486$

Defining parameters

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	324.n (of order \(54\) and degree \(18\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 324 \)
Character field:			\(\Q(\zeta_{54})\)
Sturm bound:			\(486\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(324, [\chi])\).

	Total	New	Old
Modular forms	7812	7812	0
Cusp forms	7740	7740	0
Eisenstein series	72	72	0

Trace form

7740 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 9 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 39542103 * q^42 + 17341110 * q^44 - 36 * q^45 - 18 * q^46 - 15217803 * q^48 - 36 * q^49 - 104798439 * q^50 - 18 * q^52 - 18 * q^53 + 75728376 * q^54 + 168856740 * q^56 - 36 * q^57 - 18 * q^58 - 125543709 * q^60 - 36 * q^61 - 223709625 * q^62 - 18 * q^64 - 36 * q^65 + 254302758 * q^66 + 79719507 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 - 59067 * q^78 - 36 * q^80 - 36 * q^81 - 36 * q^82 - 59067 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 + 258942060 * q^89 + 504195723 * q^90 + 843921432 * q^92 - 260033796 * q^93 - 18 * q^94 - 1223629425 * q^96 - 36 * q^97 - 1058901273 * q^98

Decomposition of \(S_{9}^{\mathrm{new}}(324, [\chi])\) into newform subspaces

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