Space of modular forms of level 832, weight 4, and Character 832.b

• Label: 832.4.b
• Level: $832$
• Weight: $4$
• Character orbit: 832.b
• Rep. character: $\chi_{832}(417,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $4$
• Sturm bound: $448$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 832 = 2^{6} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	832.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(448\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(832, [\chi])\).

	Total	New	Old
Modular forms	348	72	276
Cusp forms	324	72	252
Eisenstein series	24	0	24

Trace form

\( 72 q - 648 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(832, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
832.4.b.a	$832$	$4$	832.b	8.b	$2$	$12$	$12$	$49.090$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			832.4.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-20\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{7})q^{3}+(3\beta _{7}-\beta _{8})q^{5}+(-2+\cdots)q^{7}+\cdots\)
832.4.b.b	$832$	$4$	832.b	8.b	$2$	$12$	$12$	$49.090$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			832.4.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(20\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{7})q^{3}+(-3\beta _{7}+\beta _{8})q^{5}+(2+\cdots)q^{7}+\cdots\)
832.4.b.c	$832$	$4$	832.b	8.b	$2$	$24$	$24$	$49.090$		None		✓			832.4.b.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-104\)		$\mathrm{SU}(2)[C_{2}]$
832.4.b.d	$832$	$4$	832.b	8.b	$2$	$24$	$24$	$49.090$		None		✓			832.4.b.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(104\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(832, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(832, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 2}\)