Space of modular forms of level 3009, weight 2, and Character 3009.o

• Label: 3009.2.o
• Level: $3009$
• Weight: $2$
• Character orbit: 3009.o
• Rep. character: $\chi_{3009}(1946,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $1424$
• Sturm bound: $720$

Defining parameters

Level:	\( N \)	\(=\)	\( 3009 = 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3009.o (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3009 \)
Character field:			\(\Q(\zeta_{8})\)
Sturm bound:			\(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3009, [\chi])\).

	Total	New	Old
Modular forms	1456	1456	0
Cusp forms	1424	1424	0
Eisenstein series	32	32	0

Trace form

\( 1424 q - 8 q^{3} - 16 q^{7} + 16 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3009, [\chi])\) into newform subspaces

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