Space of modular forms of level 1856, weight 1, and Character 1856.h

• Label: 1856.1.h
• Level: $1856$
• Weight: $1$
• Character orbit: 1856.h
• Rep. character: $\chi_{1856}(1855,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $4$
• Sturm bound: $240$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1856 = 2^{6} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1856.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 116 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(240\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1856, [\chi])\).

	Total	New	Old
Modular forms	36	7	29
Cusp forms	24	5	19
Eisenstein series	12	2	10

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	5	0	0	0

Trace form

\( 5 q + 2 q^{5} + 3 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1856, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1856.1.h.a	$1856$	$1$	1856.h	116.d	$2$	$1$	$1$	$0.926$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-29}) \)	None	✓	$2$	$0$	\(0\)	\(-1\)	\(1\)	\(0\)	$1$		\(q-q^{3}+q^{5}-q^{11}+q^{13}-q^{15}+2q^{19}+\cdots\)
1856.1.h.b	$1856$	$1$	1856.h	116.d	$2$	$1$	$1$	$0.926$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-29}) \)	\(\Q(\sqrt{29}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q-2q^{5}-q^{9}+2q^{13}+3q^{25}+q^{29}+\cdots\)
1856.1.h.c	$1856$	$1$	1856.h	116.d	$2$	$1$	$1$	$0.926$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-29}) \)	None	✓	$2$	$0$	\(0\)	\(1\)	\(1\)	\(0\)	$1$		\(q+q^{3}+q^{5}+q^{11}+q^{13}+q^{15}-2q^{19}+\cdots\)
1856.1.h.d	$1856$	$1$	1856.h	116.d	$2$	$2$	$2$	$0.926$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-29}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q-\beta q^{3}+q^{5}+2q^{9}+\beta q^{11}-q^{13}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1856, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1856, [\chi]) \cong \)