Space of modular forms of level 145, weight 2, and trivial character

• Label: 145.2.a
• Level: $145$
• Weight: $2$
• Character orbit: 145.a
• Rep. character: $\chi_{145}(1,\cdot)$
• Character field: $\Q$
• Dimension: $9$
• Newform subspaces: $4$
• Sturm bound: $30$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 145 = 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	145.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(30\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(145))\).

	Total	New	Old
Modular forms	16	9	7
Cusp forms	13	9	4
Eisenstein series	3	0	3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(5\)	\(29\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(1\)
\(+\)	\(-\)	$-$	\(3\)
\(-\)	\(+\)	$-$	\(3\)
\(-\)	\(-\)	$+$	\(2\)
Plus space		\(+\)	\(3\)
Minus space		\(-\)	\(6\)

Trace form

\( 9 q + q^{2} - 4 q^{3} + 7 q^{4} + q^{5} + 4 q^{6} - 4 q^{7} + 9 q^{8} + 5 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(145))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5	29
145.2.a.a	$145$	$2$	145.a	1.a	$1$	$1$	$1$	$1.158$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-q^{5}-2q^{7}+3q^{8}-3q^{9}+\cdots\)
145.2.a.b	$145$	$2$	145.a	1.a	$1$	$2$	$2$	$1.158$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(-2\)	\(-4\)	\(2\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}-2q^{3}+(1-2\beta )q^{4}+\cdots\)
145.2.a.c	$145$	$2$	145.a	1.a	$1$	$3$	$3$	$1.158$	3.3.148.1	None	✓	$1$	$0$	\(1\)	\(2\)	\(3\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
145.2.a.d	$145$	$2$	145.a	1.a	$1$	$3$	$3$	$1.158$	3.3.148.1	None	✓	$1$	$0$	\(3\)	\(-2\)	\(-3\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(145))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(145)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 2}\)