Space of modular forms of level 266, weight 2, and trivial character

• Label: 266.2.a
• Level: $266$
• Weight: $2$
• Character orbit: 266.a
• Rep. character: $\chi_{266}(1,\cdot)$
• Character field: $\Q$
• Dimension: $9$
• Newform subspaces: $4$
• Sturm bound: $80$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 266 = 2 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	266.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(80\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(266))\).

	Total	New	Old
Modular forms	44	9	35
Cusp forms	37	9	28
Eisenstein series	7	0	7

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

\(2\)	\(7\)	\(19\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(2\)	\(0\)	\(2\)		\(2\)	\(0\)	\(2\)		\(0\)	\(0\)	\(0\)
\(+\)	\(+\)	\(-\)	\(-\)		\(8\)	\(2\)	\(6\)		\(7\)	\(2\)	\(5\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(+\)	\(-\)		\(6\)	\(2\)	\(4\)		\(5\)	\(2\)	\(3\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)	\(+\)		\(6\)	\(0\)	\(6\)		\(5\)	\(0\)	\(5\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(+\)	\(-\)		\(7\)	\(3\)	\(4\)		\(6\)	\(3\)	\(3\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)	\(+\)		\(5\)	\(0\)	\(5\)		\(4\)	\(0\)	\(4\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)	\(+\)		\(4\)	\(0\)	\(4\)		\(3\)	\(0\)	\(3\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)		\(6\)	\(2\)	\(4\)		\(5\)	\(2\)	\(3\)		\(1\)	\(0\)	\(1\)
Plus space			\(+\)		\(17\)	\(0\)	\(17\)		\(14\)	\(0\)	\(14\)		\(3\)	\(0\)	\(3\)
Minus space			\(-\)		\(27\)	\(9\)	\(18\)		\(23\)	\(9\)	\(14\)		\(4\)	\(0\)	\(4\)

Trace form

9 * q + q^2 + 4 * q^3 + 9 * q^4 + 6 * q^5 - 4 * q^6 - q^7 + q^8 + 17 * q^9 + 6 * q^10 + 8 * q^11 + 4 * q^12 + 6 * q^13 - q^14 + 9 * q^16 - 6 * q^17 - 3 * q^18 - q^19 + 6 * q^20 + 4 * q^21 - 12 * q^22 - 8 * q^23 - 4 * q^24 + 19 * q^25 - 2 * q^26 - 8 * q^27 - q^28 - 10 * q^29 - 16 * q^30 + 32 * q^31 + q^32 - 24 * q^33 + 18 * q^34 - 2 * q^35 + 17 * q^36 + 14 * q^37 - q^38 - 24 * q^39 + 6 * q^40 - 14 * q^41 - 8 * q^43 + 8 * q^44 - 18 * q^45 - 24 * q^47 + 4 * q^48 + 9 * q^49 - 17 * q^50 - 32 * q^51 + 6 * q^52 - 26 * q^53 - 40 * q^54 - 32 * q^55 - q^56 + 2 * q^58 - 20 * q^59 + 6 * q^61 - 24 * q^62 - 13 * q^63 + 9 * q^64 - 52 * q^65 - 24 * q^66 - 4 * q^67 - 6 * q^68 - 32 * q^69 - 6 * q^70 - 3 * q^72 + 10 * q^73 + 2 * q^74 + 4 * q^75 - q^76 - 4 * q^77 + 8 * q^78 + 32 * q^79 + 6 * q^80 + 33 * q^81 + 2 * q^82 - 4 * q^83 + 4 * q^84 + 4 * q^85 - 12 * q^86 - 32 * q^87 - 12 * q^88 + 34 * q^89 + 6 * q^90 + 18 * q^91 - 8 * q^92 + 8 * q^93 + 8 * q^94 - 6 * q^95 - 4 * q^96 + 42 * q^97 + q^98 + 56 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(266))\) 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	7	19
266.2.a.a	$266$	$2$	266.a	1.a	$1$	$2$	$2$	$2.124$	\(\Q(\sqrt{29}) \)	None	✓	✓	✓	✓	266.2.a.a	$1$	$0$	\(-2\)	\(1\)	\(-1\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1-\beta )q^{3}+q^{4}-\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)
266.2.a.b	$266$	$2$	266.a	1.a	$1$	$2$	$2$	$2.124$	\(\Q(\sqrt{5}) \)	None	✓	✓	✓	✓	266.2.a.b	$1$	$0$	\(-2\)	\(3\)	\(1\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1+\beta )q^{3}+q^{4}+(2-3\beta )q^{5}+\cdots\)
266.2.a.c	$266$	$2$	266.a	1.a	$1$	$2$	$2$	$2.124$	\(\Q(\sqrt{13}) \)	None	✓	✓	✓	✓	266.2.a.c	$1$	$0$	\(2\)	\(1\)	\(1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta q^{3}+q^{4}+(1-\beta )q^{5}+\beta q^{6}+\cdots\)
266.2.a.d	$266$	$2$	266.a	1.a	$1$	$3$	$3$	$2.124$	3.3.469.1	None	✓	✓	✓	✓	266.2.a.d	$1$	$0$	\(3\)	\(-1\)	\(5\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{2}q^{3}+q^{4}+(2-\beta _{1})q^{5}+\beta _{2}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(266))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(266)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 2}\)