Space of modular forms of level 1680, weight 2, and Character 1680.ck

• Label: 1680.2.ck
• Level: $1680$
• Weight: $2$
• Character orbit: 1680.ck
• Rep. character: $\chi_{1680}(461,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $512$
• Sturm bound: $768$

Defining parameters

Level:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.ck (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 336 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1680, [\chi])\).

	Total	New	Old
Modular forms	784	512	272
Cusp forms	752	512	240
Eisenstein series	32	0	32

Trace form

\( 512 q - 32 q^{16} + 40 q^{18} - 48 q^{22} + 24 q^{28} + 20 q^{42} + 80 q^{51} - 32 q^{58} + 56 q^{60} + 48 q^{64} - 64 q^{67} - 56 q^{72} + 16 q^{84} + 32 q^{88} - 48 q^{91}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1680, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1680, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1680, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)