Space of modular forms of level 2808, weight 2, and Character 2808.he

• Label: 2808.2.he
• Level: $2808$
• Weight: $2$
• Character orbit: 2808.he
• Rep. character: $\chi_{2808}(67,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $6000$
• Sturm bound: $1008$

Defining parameters

Level:	\( N \)	\(=\)	\( 2808 = 2^{3} \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2808.he (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2808 \)
Character field:			\(\Q(\zeta_{36})\)
Sturm bound:			\(1008\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2808, [\chi])\).

	Total	New	Old
Modular forms	6096	6096	0
Cusp forms	6000	6000	0
Eisenstein series	96	96	0

Trace form

6000 * q - 12 * q^2 - 12 * q^3 - 18 * q^4 - 12 * q^6 - 6 * q^8 - 12 * q^9 - 24 * q^11 - 24 * q^14 - 6 * q^16 - 36 * q^17 - 12 * q^18 - 12 * q^19 - 12 * q^20 - 6 * q^22 + 6 * q^24 - 42 * q^26 - 48 * q^27 - 24 * q^28 + 126 * q^30 - 12 * q^32 - 24 * q^33 - 24 * q^34 - 24 * q^35 - 18 * q^36 - 24 * q^40 - 24 * q^41 - 6 * q^42 - 36 * q^43 + 42 * q^44 - 6 * q^46 - 6 * q^48 - 36 * q^49 + 6 * q^50 - 108 * q^51 - 66 * q^52 - 12 * q^54 - 18 * q^56 + 12 * q^57 - 66 * q^58 - 96 * q^59 + 66 * q^60 - 18 * q^62 - 24 * q^65 - 24 * q^66 - 24 * q^67 - 54 * q^68 - 120 * q^70 - 276 * q^72 - 12 * q^73 + 78 * q^74 - 36 * q^75 + 36 * q^76 + 6 * q^78 - 24 * q^80 - 12 * q^81 - 36 * q^82 - 24 * q^83 + 120 * q^84 - 228 * q^86 - 18 * q^88 - 12 * q^89 + 162 * q^90 - 12 * q^91 - 144 * q^92 - 6 * q^94 + 174 * q^96 - 24 * q^97 - 234 * q^98 - 24 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(2808, [\chi])\) into newform subspaces

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