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

• Label: 1296.1.o
• Level: $1296$
• Weight: $1$
• Character orbit: 1296.o
• Rep. character: $\chi_{1296}(271,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $10$
• Newform subspaces: $4$
• Sturm bound: $216$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1296 = 2^{4} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1296.o (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 36 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(216\)
Trace bound:			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	94	10	84
Cusp forms	22	10	12
Eisenstein series	72	0	72

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	10	0	0	0

Trace form

\( 10 q + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1296.1.o.a	$1296$	$1$	1296.o	36.f	$6$	$2$	$1$	$0.647$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-3\)	$1$		\(q+(-1+\zeta_{6}^{2})q^{7}+\zeta_{6}^{2}q^{13}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{19}+\cdots\)
1296.1.o.b	$1296$	$1$	1296.o	36.f	$6$	$2$	$1$	$0.647$	\(\Q(\sqrt{-3}) \)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{3}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{6}^{2}q^{13}+\zeta_{6}q^{25}+q^{37}+\zeta_{6}^{2}q^{49}+\cdots\)
1296.1.o.c	$1296$	$1$	1296.o	36.f	$6$	$2$	$1$	$0.647$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(3\)	$1$		\(q+(1-\zeta_{6}^{2})q^{7}+\zeta_{6}^{2}q^{13}+(-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{19}+\cdots\)
1296.1.o.d	$1296$	$1$	1296.o	36.f	$6$	$4$	$2$	$0.647$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-1}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$		\(q+(\zeta_{12}+\zeta_{12}^{3})q^{5}-\zeta_{12}^{2}q^{13}+(\zeta_{12}+\cdots)q^{17}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(1296, [\chi]) \cong \)