Space of modular forms of level 1980, weight 2, and Character 1980.bt

• Label: 1980.2.bt
• Level: $1980$
• Weight: $2$
• Character orbit: 1980.bt
• Rep. character: $\chi_{1980}(179,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $576$
• Sturm bound: $864$

Defining parameters

Level:	\( N \)	\(=\)	\( 1980 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1980.bt (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 660 \)
Character field:			\(\Q(\zeta_{10})\)
Sturm bound:			\(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1980, [\chi])\).

	Total	New	Old
Modular forms	1792	576	1216
Cusp forms	1664	576	1088
Eisenstein series	128	0	128

Trace form

\( 576 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1980, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1980, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1980, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(660, [\chi])\)\(^{\oplus 2}\)