Space of modular forms of level 3255, weight 1, and Character 3255.o

• Label: 3255.1.o
• Level: $3255$
• Weight: $1$
• Character orbit: 3255.o
• Rep. character: $\chi_{3255}(3254,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $10$
• Sturm bound: $512$
• Trace bound: $21$

Defining parameters

Level:	\( N \)	\(=\)	\( 3255 = 3 \cdot 5 \cdot 7 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3255.o (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3255 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(512\)
Trace bound:			\(21\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3255, [\chi])\).

	Total	New	Old
Modular forms	32	32	0
Cusp forms	24	24	0
Eisenstein series	8	8	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	24	0	0	0

Trace form

\( 24 q + 8 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3255, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3255.1.o.a	$3255$	$1$	3255.o	3255.o	$2$	$2$	$2$	$1.624$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-3255}) \)	None	✓	$2$	$0$	\(-1\)	\(-2\)	\(-2\)	\(-2\)	$1$		\(q+(-1+\beta )q^{2}-q^{3}+(1-\beta )q^{4}-q^{5}+\cdots\)
3255.1.o.b	$3255$	$1$	3255.o	3255.o	$2$	$2$	$2$	$1.624$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-3255}) \)	None	✓	$2$	$0$	\(-1\)	\(-2\)	\(2\)	\(2\)	$1$		\(q+(-1+\beta )q^{2}-q^{3}+(1-\beta )q^{4}+q^{5}+\cdots\)
3255.1.o.c	$3255$	$1$	3255.o	3255.o	$2$	$2$	$2$	$1.624$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-3255}) \)	None	✓	$2$	$0$	\(-1\)	\(2\)	\(-2\)	\(-2\)	$1$		\(q+(-1+\beta )q^{2}+q^{3}+(1-\beta )q^{4}-q^{5}+\cdots\)
3255.1.o.d	$3255$	$1$	3255.o	3255.o	$2$	$2$	$2$	$1.624$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-3255}) \)	None	✓	$2$	$0$	\(-1\)	\(2\)	\(2\)	\(2\)	$1$		\(q-\beta q^{2}+q^{3}+\beta q^{4}+q^{5}-\beta q^{6}+q^{7}+\cdots\)
3255.1.o.e	$3255$	$1$	3255.o	3255.o	$2$	$2$	$2$	$1.624$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-3255}) \)	None	✓	$2$	$0$	\(1\)	\(-2\)	\(-2\)	\(2\)	$1$		\(q+\beta q^{2}-q^{3}+\beta q^{4}-q^{5}-\beta q^{6}+q^{7}+\cdots\)
3255.1.o.f	$3255$	$1$	3255.o	3255.o	$2$	$2$	$2$	$1.624$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-3255}) \)	None	✓	$2$	$0$	\(1\)	\(-2\)	\(2\)	\(-2\)	$1$		\(q+(1-\beta )q^{2}-q^{3}+(1-\beta )q^{4}+q^{5}+\cdots\)
3255.1.o.g	$3255$	$1$	3255.o	3255.o	$2$	$2$	$2$	$1.624$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-3255}) \)	None	✓	$2$	$0$	\(1\)	\(2\)	\(-2\)	\(2\)	$1$		\(q+(1-\beta )q^{2}+q^{3}+(1-\beta )q^{4}-q^{5}+\cdots\)
3255.1.o.h	$3255$	$1$	3255.o	3255.o	$2$	$2$	$2$	$1.624$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-3255}) \)	None	✓	$2$	$0$	\(1\)	\(2\)	\(2\)	\(-2\)	$1$		\(q+\beta q^{2}+q^{3}+\beta q^{4}+q^{5}+\beta q^{6}-q^{7}+\cdots\)
3255.1.o.i	$3255$	$1$	3255.o	3255.o	$2$	$4$	$4$	$1.624$	\(\Q(\zeta_{8})\)	$D_{4}$	\(\Q(\sqrt{-651}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{8}^{2}q^{3}-q^{4}-\zeta_{8}q^{5}+\zeta_{8}^{2}q^{7}+\cdots\)
3255.1.o.j	$3255$	$1$	3255.o	3255.o	$2$	$4$	$4$	$1.624$	\(\Q(\zeta_{8})\)	$D_{4}$	\(\Q(\sqrt{-651}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{8}^{2}q^{3}-q^{4}+\zeta_{8}^{3}q^{5}-\zeta_{8}^{2}q^{7}+\cdots\)