Space of modular forms of level 725, weight 1, and Character 725.h

• Label: 725.1.h
• Level: $725$
• Weight: $1$
• Character orbit: 725.h
• Rep. character: $\chi_{725}(57,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $75$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	725.h (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 145 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(75\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(725, [\chi])\).

	Total	New	Old
Modular forms	18	6	12
Cusp forms	6	2	4
Eisenstein series	12	4	8

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

\( 2 q + 2 q^{7} - 2 q^{13} - 2 q^{16} + 2 q^{23} - 2 q^{28} + 2 q^{36} - 2 q^{52} + 2 q^{53} + 2 q^{63} - 2 q^{67} - 2 q^{81} - 2 q^{83} - 4 q^{91} + 2 q^{92}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(725, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
725.1.h.a	$725$	$1$	725.h	145.h	$4$	$2$	$1$	$0.362$	\(\Q(\sqrt{-1}) \)	$D_{4}$	None	\(\Q(\sqrt{29}) \)			✓	✓	145.1.h.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$		\(q-i q^{4}+(-i+1)q^{7}+i q^{9}+(-i-1)q^{13}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(725, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(725, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 2}\)