Space of modular forms of level 3360, weight 2, and Character 3360.fj

• Label: 3360.2.fj
• Level: $3360$
• Weight: $2$
• Character orbit: 3360.fj
• Rep. character: $\chi_{3360}(629,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $3040$
• Sturm bound: $1536$

Defining parameters

Level:	\( N \)	\(=\)	\( 3360 = 2^{5} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3360.fj (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3360 \)
Character field:			\(\Q(\zeta_{8})\)
Sturm bound:			\(1536\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3360, [\chi])\).

	Total	New	Old
Modular forms	3104	3104	0
Cusp forms	3040	3040	0
Eisenstein series	64	64	0

Trace form

\( 3040 q - 32 q^{4} - 16 q^{9} - 32 q^{16} - 8 q^{21} - 16 q^{25} - 32 q^{30} + 64 q^{36} - 16 q^{39} - 32 q^{46} - 64 q^{51} + 24 q^{60} + 64 q^{64} - 8 q^{70} + 88 q^{84} - 96 q^{85} - 16 q^{91} - 16 q^{99}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3360, [\chi])\) into newform subspaces

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