Space of modular forms of level 1596, weight 1, and Character 1596.bo

• Label: 1596.1.bo
• Level: $1596$
• Weight: $1$
• Character orbit: 1596.bo
• Rep. character: $\chi_{1596}(1361,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $320$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1596 = 2^{2} \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1596.bo (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 399 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(320\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1596, [\chi])\).

	Total	New	Old
Modular forms	28	4	24
Cusp forms	4	4	0
Eisenstein series	24	0	24

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

\( 4 q + q^{7} + 4 q^{9} - 3 q^{13} + 3 q^{19} - 3 q^{21} + 2 q^{25} + 3 q^{31} - 3 q^{37} + q^{39} + q^{43} + q^{49} + q^{57} + q^{63} + 3 q^{67} - 3 q^{79} + 4 q^{81} - 3 q^{91} + q^{93}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1596, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1596.1.bo.a	$1596$	$1$	1596.bo	399.r	$6$	$2$	$1$	$0.797$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		✓			1596.1.bo.a	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(2\)	$1$		\(q-q^{3}+q^{7}+q^{9}-\zeta_{6}q^{13}+\zeta_{6}q^{19}+\cdots\)
1596.1.bo.b	$1596$	$1$	1596.bo	399.r	$6$	$2$	$1$	$0.797$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		✓			1596.1.bo.b	$4$	$0$	\(0\)	\(2\)	\(0\)	\(-1\)	$1$		\(q+q^{3}-\zeta_{6}q^{7}+q^{9}-\zeta_{6}q^{13}+q^{19}+\cdots\)