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		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(2\)	\(1\)	\(1\)		\(2\)	\(1\)	\(1\)		\(0\)	\(0\)	\(0\)
\(+\)	\(-\)	\(-\)		\(5\)	\(1\)	\(4\)		\(4\)	\(1\)	\(3\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(4\)	\(2\)	\(2\)		\(3\)	\(2\)	\(1\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(4\)	\(0\)	\(4\)		\(3\)	\(0\)	\(3\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(6\)	\(1\)	\(5\)		\(5\)	\(1\)	\(4\)		\(1\)	\(0\)	\(1\)
Minus space		\(-\)		\(9\)	\(3\)	\(6\)		\(7\)	\(3\)	\(4\)		\(2\)	\(0\)	\(2\)

Trace form

4 * q + 4 * q^4 - 2 * q^6 - 4 * q^7 - 2 * q^9 + 6 * q^10 - 2 * q^11 - 2 * q^13 + 4 * q^16 + 8 * q^17 - 16 * q^19 - 12 * q^21 - 4 * q^22 - 8 * q^23 - 2 * q^24 + 6 * q^25 + 4 * q^26 - 4 * q^28 + 14 * q^29 - 12 * q^30 + 4 * q^31 + 20 * q^33 - 8 * q^34 + 4 * q^35 - 2 * q^36 - 10 * q^37 + 6 * q^38 + 4 * q^39 + 6 * q^40 + 4 * q^41 - 4 * q^42 - 14 * q^43 - 2 * q^44 + 12 * q^45 - 4 * q^46 + 4 * q^47 - 4 * q^49 - 8 * q^50 - 8 * q^51 - 2 * q^52 - 2 * q^53 - 2 * q^54 + 12 * q^55 + 6 * q^57 + 16 * q^58 + 22 * q^59 + 4 * q^61 - 2 * q^62 + 8 * q^63 + 4 * q^64 - 20 * q^65 - 8 * q^66 + 12 * q^67 + 8 * q^68 + 14 * q^69 + 8 * q^70 + 36 * q^71 - 16 * q^73 - 32 * q^75 - 16 * q^76 - 16 * q^77 + 22 * q^78 - 8 * q^79 - 20 * q^81 + 20 * q^82 - 20 * q^83 - 12 * q^84 - 8 * q^85 - 8 * q^86 - 20 * q^87 - 4 * q^88 + 46 * q^89 - 6 * q^90 - 20 * q^91 - 8 * q^92 + 4 * q^93 + 8 * q^94 + 12 * q^95 - 2 * q^96 + 16 * q^98 + 10 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	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	✓	✓	✓	✓	106.2.a.a	$1$	$1$	\(-1\)	\(-1\)	\(-4\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}-q^{8}+\cdots\)
106.2.a.b	$106$	$2$	106.a	1.a	$1$	$1$	$1$	$0.846$	\(\Q\)	None	✓	✓	✓	✓	106.2.a.b	$1$	$0$	\(-1\)	\(2\)	\(1\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2q^{3}+q^{4}+q^{5}-2q^{6}-2q^{7}+\cdots\)
106.2.a.c	$106$	$2$	106.a	1.a	$1$	$1$	$1$	$0.846$	\(\Q\)	None	✓	✓			106.2.a.c	$1$	$0$	\(1\)	\(-2\)	\(3\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-2q^{3}+q^{4}+3q^{5}-2q^{6}+2q^{7}+\cdots\)
106.2.a.d	$106$	$2$	106.a	1.a	$1$	$1$	$1$	$0.846$	\(\Q\)	None	✓	✓			106.2.a.d	$1$	$0$	\(1\)	\(1\)	\(0\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}-4q^{7}+q^{8}+\cdots\)

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

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