Space of modular forms of level 3064, weight 1, and Character 3064.e

• Label: 3064.1.e
• Level: $3064$
• Weight: $1$
• Character orbit: 3064.e
• Rep. character: $\chi_{3064}(765,\cdot)$
• Character field: $\Q$
• Dimension: $27$
• Newform subspaces: $7$
• Sturm bound: $384$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 3064 = 2^{3} \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3064.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3064 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(384\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3064, [\chi])\).

	Total	New	Old
Modular forms	29	29	0
Cusp forms	27	27	0
Eisenstein series	2	2	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	27	0	0	0

Trace form

\( 27 q - 2 q^{2} + 10 q^{4} - 2 q^{8} - 7 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3064, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3064.1.e.a	$3064$	$1$	3064.e	3064.e	$2$	$1$	$1$	$1.529$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-766}) \)	None	✓	$2$	$0$	\(1\)	\(0\)	\(-2\)	\(-1\)	$1$		\(q+q^{2}+q^{4}-2q^{5}-q^{7}+q^{8}+q^{9}+\cdots\)
3064.1.e.b	$3064$	$1$	3064.e	3064.e	$2$	$1$	$1$	$1.529$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-383}) \), \(\Q(\sqrt{-766}) \)	\(\Q(\sqrt{2}) \)	✓	$4$	$0$	\(1\)	\(0\)	\(0\)	\(-2\)	$1$		\(q+q^{2}+q^{4}-2q^{7}+q^{8}+q^{9}-2q^{14}+\cdots\)
3064.1.e.c	$3064$	$1$	3064.e	3064.e	$2$	$1$	$1$	$1.529$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-766}) \)	None	✓	$2$	$0$	\(1\)	\(0\)	\(2\)	\(-1\)	$1$		\(q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}+q^{9}+\cdots\)
3064.1.e.d	$3064$	$1$	3064.e	3064.e	$2$	$2$	$2$	$1.529$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-766}) \)	None	✓	$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$		\(q-q^{2}+q^{4}-\beta q^{5}-q^{8}+q^{9}+\beta q^{10}+\cdots\)
3064.1.e.e	$3064$	$1$	3064.e	3064.e	$2$	$2$	$2$	$1.529$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-766}) \)	None	✓	$4$	$0$	\(2\)	\(0\)	\(0\)	\(2\)	$1$		\(q+q^{2}+q^{4}+q^{7}+q^{8}+q^{9}-\beta q^{11}+\cdots\)
3064.1.e.f	$3064$	$1$	3064.e	3064.e	$2$	$4$	$4$	$1.529$	\(\Q(\zeta_{24})^+\)	$D_{12}$	\(\Q(\sqrt{-766}) \)	None	✓	$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$1$		\(q-q^{2}+q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\beta _{2}q^{7}+\cdots\)
3064.1.e.g	$3064$	$1$	3064.e	3064.e	$2$	$16$	$16$	$1.529$	\(\Q(\zeta_{34})\)	$D_{34}$	\(\Q(\sqrt{-383}) \)	None		$4$	$0$	\(-1\)	\(0\)	\(0\)	\(2\)	$1$		\(q-\zeta_{34}^{9}q^{2}+(\zeta_{34}^{6}+\zeta_{34}^{11})q^{3}-\zeta_{34}q^{4}+\cdots\)