Space of modular forms of level 148, weight 2, and trivial character

• Label: 148.2.a
• Level: $148$
• Weight: $2$
• Character orbit: 148.a
• Rep. character: $\chi_{148}(1,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $38$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 148 = 2^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	148.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(38\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(148))\).

	Total	New	Old
Modular forms	22	3	19
Cusp forms	17	3	14
Eisenstein series	5	0	5

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

\(2\)	\(37\)	Fricke	Dim
\(-\)	\(+\)	$-$	\(2\)
\(-\)	\(-\)	$+$	\(1\)
Plus space		\(+\)	\(1\)
Minus space		\(-\)	\(2\)

Trace form

\( 3 q - 2 q^{3} - 2 q^{7} + q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(148))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	37
148.2.a.a	$148$	$2$	148.a	1.a	$1$	$1$	$1$	$1.182$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-4\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{5}-3q^{7}-2q^{9}+5q^{11}+\cdots\)
148.2.a.b	$148$	$2$	148.a	1.a	$1$	$2$	$2$	$1.182$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(4\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+2q^{5}+\beta q^{7}+(1+\beta )q^{9}+\beta q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(148))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(148)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(74))\)\(^{\oplus 2}\)