Space of modular forms of level 832, weight 2, and Character 832.b

• Label: 832.2.b
• Level: $832$
• Weight: $2$
• Character orbit: 832.b
• Rep. character: $\chi_{832}(417,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $4$
• Sturm bound: $224$
• Trace bound: $15$

Defining parameters

Level:	\( N \)	\(=\)	\( 832 = 2^{6} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
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:			\(224\)
Trace bound:			\(15\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(832, [\chi])\).

	Total	New	Old
Modular forms	124	24	100
Cusp forms	100	24	76
Eisenstein series	24	0	24

Trace form

\( 24 q - 24 q^{9} - 24 q^{25} - 48 q^{33} + 48 q^{41} + 24 q^{49} + 48 q^{57} + 72 q^{81} - 96 q^{89} - 96 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(832, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
832.2.b.a	$832$	$2$	832.b	8.b	$2$	$4$	$4$	$6.644$	\(\Q(\zeta_{8})\)	None		✓			832.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_{2}+\beta_1)q^{3}+(2\beta_{2}-\beta_1)q^{5}+\cdots\)
832.2.b.b	$832$	$2$	832.b	8.b	$2$	$4$	$4$	$6.644$	\(\Q(\zeta_{8})\)	None		✓			832.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(12\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_{2}+\beta_1)q^{3}+(-2\beta_{2}+\beta_1)q^{5}+\cdots\)
832.2.b.c	$832$	$2$	832.b	8.b	$2$	$8$	$8$	$6.644$	8.0.195105024.2	None		✓			832.2.b.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{3}-\beta _{4}q^{5}+(-\beta _{1}-\beta _{7})q^{7}+\cdots\)
832.2.b.d	$832$	$2$	832.b	8.b	$2$	$8$	$8$	$6.644$	8.0.195105024.2	None		✓			832.2.b.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{3}+\beta _{4}q^{5}+(\beta _{1}+\beta _{7})q^{7}+(-1+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(832, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(832, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 2}\)