Space of modular forms of level 464, weight 1, and Character 464.h

• Label: 464.1.h
• Level: $464$
• Weight: $1$
• Character orbit: 464.h
• Rep. character: $\chi_{464}(463,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $60$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 464 = 2^{4} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	464.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 116 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(60\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(464, [\chi])\).

	Total	New	Old
Modular forms	15	3	12
Cusp forms	9	3	6
Eisenstein series	6	0	6

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	3	0	0	0

Trace form

\( 3 q + 3 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(464, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
464.1.h.a	$464$	$1$	464.h	116.d	$2$	$1$	$1$	$0.232$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-29}) \)	\(\Q(\sqrt{29}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q+2q^{5}-q^{9}-2q^{13}+3q^{25}-q^{29}+\cdots\)
464.1.h.b	$464$	$1$	464.h	116.d	$2$	$2$	$2$	$0.232$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-29}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q-\beta q^{3}-q^{5}+2q^{9}+\beta q^{11}+q^{13}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(464, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(464, [\chi]) \cong \)