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

• Label: 1296.1.q
• Level: $1296$
• Weight: $1$
• Character orbit: 1296.q
• Rep. character: $\chi_{1296}(593,\cdot)$
• Character field: $\Q(\zeta_{6})$
• 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.q (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{6})\)
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	80	4	76
Cusp forms	8	2	6
Eisenstein series	72	2	70

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

\( 2 q - q^{7} + q^{13} + 2 q^{19} - q^{25} + 2 q^{31} - 2 q^{37} + 2 q^{43} + q^{61} - q^{67} - 2 q^{73} - q^{79} - 2 q^{91} + q^{97}+O(q^{100}) \)

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.q.a	$1296$	$1$	1296.q	9.d	$6$	$2$	$1$	$0.647$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None			✓	✓	108.1.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$1$		\(q-\zeta_{6}q^{7}-\zeta_{6}^{2}q^{13}+q^{19}-\zeta_{6}q^{25}+\cdots\)

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

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