Space of modular forms of level 1805, weight 1, and Character 1805.o

• Label: 1805.1.o
• Level: $1805$
• Weight: $1$
• Character orbit: 1805.o
• Rep. character: $\chi_{1805}(299,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $18$
• Newform subspaces: $2$
• Sturm bound: $190$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1805.o (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(190\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1805, [\chi])\).

	Total	New	Old
Modular forms	138	114	24
Cusp forms	18	18	0
Eisenstein series	120	96	24

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	18	0	0	0

Trace form

\( 18 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1805, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1805.1.o.a	$1805$	$1$	1805.o	95.o	$18$	$6$	$1$	$0.901$	\(\Q(\zeta_{18})\)	$D_{2}$	\(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-95}) \)	\(\Q(\sqrt{5}) \)		$24$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{18}^{2}q^{4}-\zeta_{18}^{7}q^{5}-\zeta_{18}^{8}q^{9}+\cdots\)
1805.1.o.b	$1805$	$1$	1805.o	95.o	$18$	$12$	$2$	$0.901$	12.0.\(\cdots\).2	$D_{4}$	\(\Q(\sqrt{-95}) \)	None		$24$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(\beta _{5}+\beta _{11})q^{2}+\beta _{5}q^{3}+(-\beta _{4}-\beta _{10}+\cdots)q^{4}+\cdots\)