Space of modular forms of level 1296, weight 1, and Character 1296.g

• Label: 1296.1.g
• Level: $1296$
• Weight: $1$
• Character orbit: 1296.g
• Rep. character: $\chi_{1296}(1135,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $216$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1296 = 2^{4} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1296.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(216\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1296, [\chi])\).

	Total	New	Old
Modular forms	51	2	49
Cusp forms	15	2	13
Eisenstein series	36	0	36

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

\( 2 q + 2 q^{13} + 4 q^{25} - 2 q^{37} + 2 q^{49} - 2 q^{61} + 2 q^{73} - 6 q^{85} - 4 q^{97}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1296, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1296.1.g.a	$1296$	$1$	1296.g	4.b	$2$	$2$	$2$	$0.647$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-1}) \)	None	✓	✓	✓	✓	1296.1.g.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta q^{5}+q^{13}+\beta q^{17}+2q^{25}+\beta q^{29}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1296, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1296, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)