Space of modular forms of level 464, weight 4, and Character 464.e

• Label: 464.4.e
• Level: $464$
• Weight: $4$
• Character orbit: 464.e
• Rep. character: $\chi_{464}(289,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $4$
• Sturm bound: $240$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 464 = 2^{4} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	464.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(240\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(464, [\chi])\).

	Total	New	Old
Modular forms	186	46	140
Cusp forms	174	44	130
Eisenstein series	12	2	10

Trace form

\( 44 q - 4 q^{5} + 16 q^{7} - 380 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(464, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
464.4.e.a	$464$	$4$	464.e	29.b	$2$	$6$	$6$	$27.377$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(22\)	\(28\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(4+\beta _{4})q^{5}+(5+\beta _{4})q^{7}+\cdots\)
464.4.e.b	$464$	$4$	464.e	29.b	$2$	$8$	$8$	$27.377$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-22\)	\(-12\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-3-\beta _{4})q^{5}+(-1+\beta _{2}+\cdots)q^{7}+\cdots\)
464.4.e.c	$464$	$4$	464.e	29.b	$2$	$8$	$8$	$27.377$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-22\)	\(-12\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-3-\beta _{2})q^{5}+(-1-\beta _{4}+\cdots)q^{7}+\cdots\)
464.4.e.d	$464$	$4$	464.e	29.b	$2$	$22$	$22$	$27.377$		None		$2$	$0$	\(0\)	\(0\)	\(18\)	\(12\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(464, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(464, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(58, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(116, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(232, [\chi])\)\(^{\oplus 2}\)