Space of modular forms of level 1368, weight 2, and Character 1368.db

• Label: 1368.2.db
• Level: $1368$
• Weight: $2$
• Character orbit: 1368.db
• Rep. character: $\chi_{1368}(11,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $472$
• Sturm bound: $480$

Defining parameters

Level:	\( N \)	\(=\)	\( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1368.db (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1368 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1368, [\chi])\).

	Total	New	Old
Modular forms	488	488	0
Cusp forms	472	472	0
Eisenstein series	16	16	0

Trace form

472 * q - 3 * q^2 - 2 * q^3 + q^4 - 5 * q^6 - 2 * q^9 - 6 * q^10 - 12 * q^11 - 7 * q^12 + q^16 + 12 * q^18 - 8 * q^19 - 27 * q^20 - 10 * q^22 + 24 * q^24 + 436 * q^25 - 8 * q^27 - 6 * q^28 + 25 * q^30 - 3 * q^32 - 22 * q^33 - 22 * q^34 - 30 * q^35 + q^36 - 3 * q^38 + 12 * q^40 + 33 * q^42 + 2 * q^43 + 45 * q^44 - 24 * q^46 + 20 * q^48 + 208 * q^49 - 21 * q^50 - 14 * q^51 - 15 * q^52 + q^54 - 48 * q^56 + 10 * q^57 - 6 * q^58 - 6 * q^60 + 6 * q^62 - 32 * q^64 - 12 * q^65 - 39 * q^66 + 2 * q^67 - 18 * q^68 - 36 * q^70 - 29 * q^72 - 4 * q^73 - 60 * q^74 + 88 * q^75 + 19 * q^76 + 70 * q^78 - 6 * q^80 - 6 * q^81 + 2 * q^82 - 12 * q^83 + 18 * q^84 - 57 * q^86 + 14 * q^88 - 16 * q^90 - 18 * q^91 - 63 * q^92 - 6 * q^94 - 11 * q^96 + 2 * q^97 - 96 * q^98 - 48 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1368, [\chi])\) into newform subspaces

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