Space of modular forms of level 145, weight 2, and Character 145.d

• Label: 145.2.d
• Level: $145$
• Weight: $2$
• Character orbit: 145.d
• Rep. character: $\chi_{145}(144,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $3$
• Sturm bound: $30$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 145 = 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	145.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 145 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(30\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(145, [\chi])\).

	Total	New	Old
Modular forms	16	16	0
Cusp forms	12	12	0
Eisenstein series	4	4	0

Trace form

\( 12 q + 4 q^{4} + 2 q^{5} - 4 q^{6} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(145, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
145.2.d.a	$145$	$2$	145.d	145.d	$2$	$4$	$4$	$1.158$	\(\Q(\sqrt{-3}, \sqrt{17})\)	None		✓			145.2.d.a	$2$	$0$	\(-4\)	\(2\)	\(3\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-\beta _{2}q^{3}-q^{4}+(1+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
145.2.d.b	$145$	$2$	145.d	145.d	$2$	$4$	$4$	$1.158$	\(\Q(i, \sqrt{5})\)	None		✓			145.2.d.b	$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+3q^{4}+(-1-\beta _{1})q^{5}+\beta _{1}q^{7}+\cdots\)
145.2.d.c	$145$	$2$	145.d	145.d	$2$	$4$	$4$	$1.158$	\(\Q(\sqrt{-3}, \sqrt{17})\)	None		✓			145.2.d.a	$2$	$0$	\(4\)	\(-2\)	\(3\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+(-1+\beta _{2})q^{3}-q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)