Space of modular forms of level 232, weight 4, and Character 232.m

• Label: 232.4.m
• Level: $232$
• Weight: $4$
• Character orbit: 232.m
• Rep. character: $\chi_{232}(25,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $138$
• Newform subspaces: $2$
• Sturm bound: $120$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 232 = 2^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	232.m (of order \(7\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q(\zeta_{7})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(120\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(232, [\chi])\).

	Total	New	Old
Modular forms	564	138	426
Cusp forms	516	138	378
Eisenstein series	48	0	48

Trace form

\( 138 q + 4 q^{5} - 12 q^{7} - 197 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(232, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
232.4.m.a	$232$	$4$	232.m	29.d	$7$	$66$	$11$	$13.688$		None		$2$	$0$	\(0\)	\(1\)	\(16\)	\(-71\)		$\mathrm{SU}(2)[C_{7}]$
232.4.m.b	$232$	$4$	232.m	29.d	$7$	$72$	$12$	$13.688$		None		$2$	$0$	\(0\)	\(-1\)	\(-12\)	\(59\)		$\mathrm{SU}(2)[C_{7}]$

Decomposition of \(S_{4}^{\mathrm{old}}(232, [\chi])\) into lower level spaces

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