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

• Label: 1680.2.et
• Level: $1680$
• Weight: $2$
• Character orbit: 1680.et
• Rep. character: $\chi_{1680}(653,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $1504$
• Sturm bound: $768$

Defining parameters

Level:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.et (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1680 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(768\)

Dimensions

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

	Total	New	Old
Modular forms	1568	1568	0
Cusp forms	1504	1504	0
Eisenstein series	64	64	0

Trace form

1504 * q - 16 * q^6 + 12 * q^10 - 14 * q^12 - 16 * q^15 - 8 * q^16 - 10 * q^18 - 8 * q^21 - 12 * q^24 - 24 * q^28 + 6 * q^30 - 16 * q^31 - 4 * q^33 + 16 * q^36 + 24 * q^39 - 4 * q^40 + 30 * q^42 - 32 * q^43 - 22 * q^45 - 8 * q^46 - 20 * q^48 - 4 * q^51 - 28 * q^52 - 8 * q^54 - 24 * q^57 - 4 * q^58 + 40 * q^60 - 8 * q^61 + 20 * q^63 - 4 * q^66 - 8 * q^67 + 24 * q^69 - 80 * q^70 - 6 * q^72 - 14 * q^75 - 32 * q^76 - 32 * q^78 - 8 * q^81 + 104 * q^82 + 60 * q^84 + 24 * q^85 - 12 * q^87 + 52 * q^88 + 152 * q^90 - 16 * q^91 - 24 * q^94 - 76 * q^96 - 32 * q^97

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

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