Space of modular forms of level 832, weight 1, and Character 832.t

• Label: 832.1.t
• Level: $832$
• Weight: $1$
• Character orbit: 832.t
• Rep. character: $\chi_{832}(385,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $112$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 832 = 2^{6} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	832.t (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(112\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(832, [\chi])\).

	Total	New	Old
Modular forms	30	6	24
Cusp forms	6	2	4
Eisenstein series	24	4	20

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

\( 2 q - 2 q^{5} - 2 q^{9} - 2 q^{37} - 2 q^{41} + 2 q^{45} + 4 q^{53} + 4 q^{61} - 2 q^{65} + 2 q^{73} + 2 q^{81} - 4 q^{85} - 2 q^{89} + 2 q^{97}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(832, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
832.1.t.a	$832$	$1$	832.t	13.d	$4$	$2$	$1$	$0.415$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-1}) \)	None			✓	✓	416.1.t.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q+(i-1)q^{5}-q^{9}+i q^{13}+2 i q^{17}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(832, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(832, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 2}\)