Space of modular forms of level 1664, weight 1, and Character 1664.h

• Label: 1664.1.h
• Level: $1664$
• Weight: $1$
• Character orbit: 1664.h
• Rep. character: $\chi_{1664}(831,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $5$
• Sturm bound: $224$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1664 = 2^{7} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1664.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 104 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(224\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1664, [\chi])\).

	Total	New	Old
Modular forms	42	10	32
Cusp forms	26	10	16
Eisenstein series	16	0	16

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	10	0	0	0

Trace form

\( 10 q + 2 q^{9} + 2 q^{25} + 10 q^{49} + 10 q^{81}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1664, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1664.1.h.a	$1664$	$1$	1664.h	104.h	$2$	$1$	$1$	$0.830$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-26}) \)	\(\Q(\sqrt{26}) \)	✓	✓			1664.1.h.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q-2q^{5}-q^{9}+q^{13}+2q^{17}+3q^{25}+\cdots\)
1664.1.h.b	$1664$	$1$	1664.h	104.h	$2$	$1$	$1$	$0.830$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-26}) \)	\(\Q(\sqrt{26}) \)	✓	✓			1664.1.h.a	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q+2q^{5}-q^{9}-q^{13}+2q^{17}+3q^{25}+\cdots\)
1664.1.h.c	$1664$	$1$	1664.h	104.h	$2$	$2$	$2$	$0.830$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-26}) \)	None	✓	✓			1664.1.h.c	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q-\beta q^{3}-q^{5}-\beta q^{7}+2q^{9}-q^{13}+\cdots\)
1664.1.h.d	$1664$	$1$	1664.h	104.h	$2$	$2$	$2$	$0.830$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-26}) \)	None	✓	✓			1664.1.h.c	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q-\beta q^{3}+q^{5}+\beta q^{7}+2q^{9}+q^{13}+\cdots\)
1664.1.h.e	$1664$	$1$	1664.h	104.h	$2$	$4$	$4$	$0.830$	\(\Q(\zeta_{8})\)	$D_{4}$	\(\Q(\sqrt{-13}) \)	None		✓	✓		1664.1.h.e	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$		\(q+(-\zeta_{8}+\zeta_{8}^{3})q^{7}-q^{9}+(-\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1664, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1664, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 3}\)