Space of modular forms of level 3120, weight 2, and Character 3120.em

• Label: 3120.2.em
• Level: $3120$
• Weight: $2$
• Character orbit: 3120.em
• Rep. character: $\chi_{3120}(1793,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $328$
• Sturm bound: $1344$

Defining parameters

Level:	\( N \)	\(=\)	\( 3120 = 2^{4} \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3120.em (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 195 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3120, [\chi])\).

	Total	New	Old
Modular forms	1392	344	1048
Cusp forms	1296	328	968
Eisenstein series	96	16	80

Trace form

\( 328 q + 4 q^{3} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3120, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3120, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3120, [\chi]) \cong \)