Space of modular forms of level 145, weight 1, and Character 145.h

• Label: 145.1.h
• Level: $145$
• Weight: $1$
• Character orbit: 145.h
• Rep. character: $\chi_{145}(28,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $15$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 145 = 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	145.h (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 145 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(15\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(145, [\chi])\).

	Total	New	Old
Modular forms	6	6	0
Cusp forms	2	2	0
Eisenstein series	4	4	0

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

\( 2 q - 2 q^{7} + 2 q^{13} - 2 q^{16} - 2 q^{20} - 2 q^{23} - 2 q^{25} + 2 q^{28} + 2 q^{35} + 2 q^{36} + 2 q^{45} + 2 q^{52} - 2 q^{53} - 2 q^{63} + 2 q^{65} + 2 q^{67} - 2 q^{81} + 2 q^{83} - 4 q^{91} - 2 q^{92}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(145, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
145.1.h.a	$145$	$1$	145.h	145.h	$4$	$2$	$1$	$0.072$	\(\Q(\sqrt{-1}) \)	$D_{4}$	None	\(\Q(\sqrt{29}) \)		✓	✓	✓	145.1.h.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q-i q^{4}-i q^{5}+(i-1)q^{7}+i q^{9}+\cdots\)