Space of modular forms of level 712, weight 6, and Character 712.x

• Label: 712.6.x
• Level: $712$
• Weight: $6$
• Character orbit: 712.x
• Rep. character: $\chi_{712}(45,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $4480$
• Sturm bound: $540$

Defining parameters

Level:	\( N \)	\(=\)	\( 712 = 2^{3} \cdot 89 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	712.x (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 712 \)
Character field:			\(\Q(\zeta_{22})\)
Sturm bound:			\(540\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(712, [\chi])\).

	Total	New	Old
Modular forms	4520	4520	0
Cusp forms	4480	4480	0
Eisenstein series	40	40	0

Trace form

\( 4480 q - 9 q^{2} - 9 q^{4} - 73 q^{6} - 18 q^{7} - 9 q^{8} + 35946 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(712, [\chi])\) into newform subspaces

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