Space of modular forms of level 648, weight 3, and Character 648.z

• Label: 648.3.z
• Level: $648$
• Weight: $3$
• Character orbit: 648.z
• Rep. character: $\chi_{648}(5,\cdot)$
• Character field: $\Q(\zeta_{54})$
• Dimension: $3852$
• Sturm bound: $324$

Defining parameters

Level:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	648.z (of order \(54\) and degree \(18\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 648 \)
Character field:			\(\Q(\zeta_{54})\)
Sturm bound:			\(324\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(648, [\chi])\).

	Total	New	Old
Modular forms	3924	3924	0
Cusp forms	3852	3852	0
Eisenstein series	72	72	0

Trace form

3852 * q - 18 * q^2 - 18 * q^4 - 18 * q^6 - 36 * q^7 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 18 * q^14 - 36 * q^15 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 18 * q^22 - 36 * q^23 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 18 * q^30 - 36 * q^31 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 18 * q^38 - 36 * q^39 - 18 * q^40 - 36 * q^41 - 513 * q^42 + 630 * q^44 - 18 * q^46 - 36 * q^47 + 477 * q^48 - 36 * q^49 - 369 * q^50 - 18 * q^52 + 108 * q^54 - 18 * q^55 - 396 * q^56 - 36 * q^57 - 18 * q^58 - 837 * q^60 + 873 * q^62 - 36 * q^63 - 18 * q^64 - 36 * q^65 + 918 * q^66 - 693 * q^68 - 18 * q^70 - 36 * q^71 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 + 63 * q^78 - 36 * q^79 - 36 * q^81 - 36 * q^82 - 99 * q^84 - 18 * q^86 - 36 * q^87 - 18 * q^88 - 36 * q^89 + 1053 * q^90 + 1332 * q^92 - 18 * q^94 - 36 * q^95 + 1269 * q^96 - 36 * q^97 + 1521 * q^98

Decomposition of \(S_{3}^{\mathrm{new}}(648, [\chi])\) into newform subspaces

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