Space of modular forms of level 78, weight 2, and Character 78.g

• Label: 78.2.g
• Level: $78$
• Weight: $2$
• Character orbit: 78.g
• Rep. character: $\chi_{78}(5,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $28$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 78 = 2 \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	78.g (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 39 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(28\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(78, [\chi])\).

	Total	New	Old
Modular forms	36	12	24
Cusp forms	20	12	8
Eisenstein series	16	0	16

Trace form

\( 12 q - 12 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(78, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
78.2.g.a	$78$	$2$	78.g	39.f	$4$	$12$	$6$	$0.623$	12.0.\(\cdots\).52	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{2}q^{2}-\beta _{4}q^{3}+\beta _{8}q^{4}+(-\beta _{1}-\beta _{11})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(78, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(78, [\chi]) \cong \)