Space of modular forms of level 464, weight 6, and Character 464.e

• Label: 464.6.e
• Level: $464$
• Weight: $6$
• Character orbit: 464.e
• Rep. character: $\chi_{464}(289,\cdot)$
• Character field: $\Q$
• Dimension: $74$
• Newform subspaces: $4$
• Sturm bound: $360$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 464 = 2^{4} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 6 \)
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:			\(360\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(464, [\chi])\).

	Total	New	Old
Modular forms	306	76	230
Cusp forms	294	74	220
Eisenstein series	12	2	10

Trace form

\( 74 q - 40 q^{5} - 96 q^{7} - 5834 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(464, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
464.6.e.a	$464$	$6$	464.e	29.b	$2$	$12$	$12$	$74.418$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-10\)	\(-76\)	$2^{20}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-1-\beta _{4})q^{5}+(-6-\beta _{3}+\cdots)q^{7}+\cdots\)
464.6.e.b	$464$	$6$	464.e	29.b	$2$	$12$	$12$	$74.418$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-10\)	\(-76\)	$2^{20}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{3}+(-1-\beta _{1})q^{5}+(-6-\beta _{1}+\cdots)q^{7}+\cdots\)
464.6.e.c	$464$	$6$	464.e	29.b	$2$	$12$	$12$	$74.418$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(46\)	\(-20\)	$2^{24}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+(4-\beta _{6})q^{5}+(-2-\beta _{2})q^{7}+\cdots\)
464.6.e.d	$464$	$6$	464.e	29.b	$2$	$38$	$38$	$74.418$		None		$2$	$0$	\(0\)	\(0\)	\(-66\)	\(76\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{6}^{\mathrm{old}}(464, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(464, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(58, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(116, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(232, [\chi])\)\(^{\oplus 2}\)