Space of modular forms of level 1380, weight 2, and Character 1380.g

• Label: 1380.2.g
• Level: $1380$
• Weight: $2$
• Character orbit: 1380.g
• Rep. character: $\chi_{1380}(919,\cdot)$
• Character field: $\Q$
• Dimension: $144$
• Sturm bound: $576$

Defining parameters

Level:	\( N \)	\(=\)	\( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1380.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 460 \)
Character field:			\(\Q\)
Sturm bound:			\(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1380, [\chi])\).

	Total	New	Old
Modular forms	296	144	152
Cusp forms	280	144	136
Eisenstein series	16	0	16

Trace form

\( 144 q + 4 q^{4} + 4 q^{6} + 144 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1380, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1380, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1380, [\chi]) \cong \)