Space of modular forms of level 106, weight 2, and trivial character

• Label: 106.2.a
• Level: $106$
• Weight: $2$
• Character orbit: 106.a
• Rep. character: $\chi_{106}(1,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $4$
• Sturm bound: $27$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 106 = 2 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	106.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(27\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(106))\).

	Total	New	Old
Modular forms	15	4	11
Cusp forms	12	4	8
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.

\(2\)	\(53\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(1\)
\(+\)	\(-\)	$-$	\(1\)
\(-\)	\(+\)	$-$	\(2\)
Plus space		\(+\)	\(1\)
Minus space		\(-\)	\(3\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(106))\) 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	53
106.2.a.a	$106$	$2$	106.a	1.a	$1$	$1$	$1$	$0.846$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(-4\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}-q^{8}+\cdots\)
106.2.a.b	$106$	$2$	106.a	1.a	$1$	$1$	$1$	$0.846$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(2\)	\(1\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2q^{3}+q^{4}+q^{5}-2q^{6}-2q^{7}+\cdots\)
106.2.a.c	$106$	$2$	106.a	1.a	$1$	$1$	$1$	$0.846$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(-2\)	\(3\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-2q^{3}+q^{4}+3q^{5}-2q^{6}+2q^{7}+\cdots\)
106.2.a.d	$106$	$2$	106.a	1.a	$1$	$1$	$1$	$0.846$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(1\)	\(0\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}-4q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(106))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(106)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(53))\)\(^{\oplus 2}\)