Space of modular forms of level 3969, weight 2, and Character 3969.cf

• Label: 3969.2.cf
• Level: $3969$
• Weight: $2$
• Character orbit: 3969.cf
• Rep. character: $\chi_{3969}(362,\cdot)$
• Character field: $\Q(\zeta_{54})$
• Dimension: $6408$
• Sturm bound: $1008$

Defining parameters

Level:	\( N \)	\(=\)	\( 3969 = 3^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3969.cf (of order \(54\) and degree \(18\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 567 \)
Character field:			\(\Q(\zeta_{54})\)
Sturm bound:			\(1008\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3969, [\chi])\).

	Total	New	Old
Modular forms	9216	6552	2664
Cusp forms	8928	6408	2520
Eisenstein series	288	144	144

Trace form

6408 * q + 9 * q^2 + 27 * q^3 + 9 * q^4 + 27 * q^5 - 72 * q^8 + 9 * q^9 + 27 * q^10 + 9 * q^11 + 27 * q^12 - 72 * q^15 + 9 * q^16 + 27 * q^17 + 9 * q^18 + 27 * q^19 - 72 * q^22 - 18 * q^23 + 27 * q^24 + 9 * q^25 + 27 * q^26 - 72 * q^29 + 117 * q^30 + 27 * q^31 + 9 * q^32 + 27 * q^33 - 72 * q^36 + 9 * q^37 + 27 * q^38 + 9 * q^39 + 27 * q^40 + 54 * q^41 - 72 * q^43 + 9 * q^44 + 27 * q^45 + 9 * q^46 + 27 * q^47 - 297 * q^48 - 72 * q^50 + 9 * q^51 + 27 * q^52 + 27 * q^53 + 405 * q^54 - 72 * q^57 + 9 * q^58 + 27 * q^59 + 9 * q^60 + 27 * q^61 + 297 * q^62 - 72 * q^64 + 45 * q^65 + 27 * q^66 + 9 * q^67 + 27 * q^68 - 54 * q^69 - 216 * q^71 + 225 * q^72 + 27 * q^73 + 9 * q^74 + 27 * q^75 - 333 * q^78 - 207 * q^79 + 9 * q^81 + 54 * q^82 + 36 * q^85 + 153 * q^86 + 27 * q^87 + 9 * q^88 + 27 * q^89 - 414 * q^92 + 81 * q^93 + 27 * q^94 + 225 * q^95 + 27 * q^96 - 36 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(3969, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3969, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3969, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(567, [\chi])\)\(^{\oplus 2}\)