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

• Label: 1805.1.h
• Level: $1805$
• Weight: $1$
• Character orbit: 1805.h
• Rep. character: $\chi_{1805}(69,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $6$
• 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.h (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q(\zeta_{6})\)
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	46	38	8
Cusp forms	6	6	0
Eisenstein series	40	32	8

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	6	0	0	0

Trace form

\( 6 q - q^{4} + q^{5} + 4 q^{6} - q^{9} + O(q^{10}) \)

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.h.a	$1805$	$1$	1805.h	95.h	$6$	$2$	$1$	$0.901$	\(\Q(\sqrt{-3}) \)	$D_{2}$	\(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-95}) \)	\(\Q(\sqrt{5}) \)		$8$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$1$		\(q+\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{9}-q^{11}+\cdots\)
1805.1.h.b	$1805$	$1$	1805.h	95.h	$6$	$4$	$2$	$0.901$	\(\Q(\sqrt{2}, \sqrt{-3})\)	$D_{4}$	\(\Q(\sqrt{-95}) \)	None		$8$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q-\beta _{1}q^{2}+\beta _{1}q^{3}+\beta _{2}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)