Space of modular forms of level 1911, weight 1, and Character 1911.h

• Label: 1911.1.h
• Level: $1911$
• Weight: $1$
• Character orbit: 1911.h
• Rep. character: $\chi_{1911}(1520,\cdot)$
• Character field: $\Q$
• Dimension: $13$
• Newform subspaces: $5$
• Sturm bound: $261$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1911.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 39 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(261\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1911, [\chi])\).

	Total	New	Old
Modular forms	32	23	9
Cusp forms	16	13	3
Eisenstein series	16	10	6

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	13	0	0	0

Trace form

\( 13 q + q^{3} + 11 q^{4} + 13 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1911, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1911.1.h.a	$1911$	$1$	1911.h	39.d	$2$	$1$	$1$	$0.954$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-39}) \)	\(\Q(\sqrt{13}) \)	✓	$4$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$1$		\(q+q^{3}-q^{4}+q^{9}-q^{12}+q^{13}+q^{16}+\cdots\)
1911.1.h.b	$1911$	$1$	1911.h	39.d	$2$	$2$	$2$	$0.954$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-39}) \)	None	✓	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$		\(q-\beta q^{2}-q^{3}+q^{4}-\beta q^{5}+\beta q^{6}+q^{9}+\cdots\)
1911.1.h.c	$1911$	$1$	1911.h	39.d	$2$	$2$	$2$	$0.954$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-39}) \)	None	✓	$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$		\(q-\beta q^{2}+q^{3}+q^{4}+\beta q^{5}-\beta q^{6}+q^{9}+\cdots\)
1911.1.h.d	$1911$	$1$	1911.h	39.d	$2$	$4$	$4$	$0.954$	\(\Q(\zeta_{16})^+\)	$D_{8}$	\(\Q(\sqrt{-39}) \)	None	✓	$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$		\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\)
1911.1.h.e	$1911$	$1$	1911.h	39.d	$2$	$4$	$4$	$0.954$	\(\Q(\zeta_{16})^+\)	$D_{8}$	\(\Q(\sqrt{-39}) \)	None	✓	$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$		\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1911, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1911, [\chi]) \cong \)