Space of modular forms of level 1823, weight 1, and Character 1823.b

• Label: 1823.1.b
• Level: $1823$
• Weight: $1$
• Character orbit: 1823.b
• Rep. character: $\chi_{1823}(1822,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $6$
• Sturm bound: $152$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 1823 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1823.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1823 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(152\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1823, [\chi])\).

	Total	New	Old
Modular forms	25	25	0
Cusp forms	24	24	0
Eisenstein series	1	1	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	22	0	2	0

Trace form

\( 24 q + q^{2} - 3 q^{3} + 21 q^{4} - 4 q^{6} - q^{7} - 4 q^{8} + 21 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1823, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1823.1.b.a	$1823$	$1$	1823.b	1823.b	$2$	$1$	$1$	$0.910$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-1823}) \)	None	✓	$2$	$0$	\(-1\)	\(-1\)	\(0\)	\(2\)	$1$		\(q-q^{2}-q^{3}+q^{6}+2q^{7}+q^{8}+2q^{11}+\cdots\)
1823.1.b.b	$1823$	$1$	1823.b	1823.b	$2$	$2$	$2$	$0.910$	\(\Q(\sqrt{-2}) \)	$S_{4}$	None	None		$2$	$0$	\(2\)	\(-2\)	\(0\)	\(0\)	$1$		\(q+q^{2}-q^{3}-\beta q^{5}-q^{6}-q^{8}-\beta q^{10}+\cdots\)
1823.1.b.c	$1823$	$1$	1823.b	1823.b	$2$	$2$	$2$	$0.910$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-1823}) \)	None	✓	$2$	$0$	\(4\)	\(-1\)	\(0\)	\(-1\)	$1$		\(q+2q^{2}+(-1+\beta )q^{3}+3q^{4}+(-2+\cdots)q^{6}+\cdots\)
1823.1.b.d	$1823$	$1$	1823.b	1823.b	$2$	$3$	$3$	$0.910$	\(\Q(\zeta_{18})^+\)	$D_{9}$	\(\Q(\sqrt{-1823}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$1$		\(q+(\beta _{1}-\beta _{2})q^{2}-\beta _{1}q^{3}+(1-\beta _{1})q^{4}+\cdots\)
1823.1.b.e	$1823$	$1$	1823.b	1823.b	$2$	$4$	$4$	$0.910$	\(\Q(\zeta_{15})^+\)	$D_{15}$	\(\Q(\sqrt{-1823}) \)	None	✓	$2$	$0$	\(-4\)	\(1\)	\(0\)	\(-2\)	$1$		\(q-q^{2}+\beta _{1}q^{3}-\beta _{1}q^{6}+\beta _{3}q^{7}+q^{8}+\cdots\)
1823.1.b.f	$1823$	$1$	1823.b	1823.b	$2$	$12$	$12$	$0.910$	\(\Q(\zeta_{45})^+\)	$D_{45}$	\(\Q(\sqrt{-1823}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$1$		\(q+\beta _{9}q^{2}+\beta _{7}q^{3}+(1-\beta _{5}-\beta _{9})q^{4}+\cdots\)