Space of modular forms of level 3192, weight 2, and Character 3192.do

• Label: 3192.2.do
• Level: $3192$
• Weight: $2$
• Character orbit: 3192.do
• Rep. character: $\chi_{3192}(1147,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $640$
• Sturm bound: $1280$

Defining parameters

Level:	\( N \)	\(=\)	\( 3192 = 2^{3} \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3192.do (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1064 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(1280\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3192, [\chi])\).

	Total	New	Old
Modular forms	1296	640	656
Cusp forms	1264	640	624
Eisenstein series	32	0	32

Trace form

\( 640 q + 24 q^{8} + 320 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3192, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3192, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3192, [\chi]) \cong \)