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

• Label: 78.2.b
• Level: $78$
• Weight: $2$
• Character orbit: 78.b
• Rep. character: $\chi_{78}(25,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• 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.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
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	18	2	16
Cusp forms	10	2	8
Eisenstein series	8	0	8

Trace form

\( 2 q + 2 q^{3} - 2 q^{4} + 2 q^{9} + O(q^{10}) \)

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.b.a	$78$	$2$	78.b	13.b	$2$	$2$	$2$	$0.623$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{3}-q^{4}+2iq^{5}+iq^{6}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(78, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 2}\)