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

• Label: 3969.2.db
• Level: $3969$
• Weight: $2$
• Character orbit: 3969.db
• Rep. character: $\chi_{3969}(5,\cdot)$
• Character field: $\Q(\zeta_{378})$
• Dimension: $54216$
• Sturm bound: $1008$

Defining parameters

Level:	\( N \)	\(=\)	\( 3969 = 3^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3969.db (of order \(378\) and degree \(108\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3969 \)
Character field:			\(\Q(\zeta_{378})\)
Sturm bound:			\(1008\)

Dimensions

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

	Total	New	Old
Modular forms	54648	54648	0
Cusp forms	54216	54216	0
Eisenstein series	432	432	0

Trace form

54216 * q - 117 * q^2 - 99 * q^3 - 117 * q^4 - 99 * q^5 - 126 * q^6 - 108 * q^7 - 90 * q^8 - 117 * q^9 - 99 * q^10 - 117 * q^11 - 99 * q^12 - 126 * q^13 - 108 * q^14 - 90 * q^15 - 117 * q^16 - 99 * q^17 - 54 * q^18 - 162 * q^19 - 126 * q^20 - 54 * q^21 - 90 * q^22 - 252 * q^23 - 99 * q^24 - 117 * q^25 - 135 * q^26 - 126 * q^27 - 54 * q^28 - 90 * q^29 - 108 * q^30 - 162 * q^31 - 117 * q^32 - 99 * q^33 - 126 * q^34 - 135 * q^35 - 90 * q^36 - 117 * q^37 - 99 * q^38 - 117 * q^39 - 99 * q^40 - 180 * q^41 - 198 * q^42 - 90 * q^43 - 117 * q^44 - 99 * q^45 - 117 * q^46 - 693 * q^47 + 297 * q^48 - 108 * q^49 - 216 * q^50 - 117 * q^51 - 99 * q^52 - 189 * q^53 - 99 * q^54 - 63 * q^55 - 90 * q^57 - 117 * q^58 - 99 * q^59 - 117 * q^60 - 99 * q^61 - 423 * q^62 - 216 * q^63 - 90 * q^64 - 117 * q^65 - 99 * q^66 - 54 * q^67 - 27 * q^68 - 72 * q^69 - 162 * q^70 - 90 * q^71 - 117 * q^72 - 99 * q^73 - 117 * q^74 - 99 * q^75 - 126 * q^76 - 180 * q^77 - 63 * q^78 - 54 * q^79 - 117 * q^81 - 198 * q^82 - 126 * q^83 - 288 * q^84 - 90 * q^85 - 117 * q^86 - 99 * q^87 - 117 * q^88 - 99 * q^89 - 126 * q^90 - 108 * q^91 - 1260 * q^92 - 117 * q^93 - 99 * q^94 - 225 * q^95 - 99 * q^96 + 279 * q^98 - 108 * 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.