Space of modular forms of level 266, weight 4, and trivial character

• Label: 266.4.a
• Level: $266$
• Weight: $4$
• Character orbit: 266.a
• Rep. character: $\chi_{266}(1,\cdot)$
• Character field: $\Q$
• Dimension: $26$
• Newform subspaces: $8$
• Sturm bound: $160$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 266 = 2 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	266.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(160\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(266))\).

	Total	New	Old
Modular forms	124	26	98
Cusp forms	116	26	90
Eisenstein series	8	0	8

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	Dim
\(+\)	\(+\)	\(+\)	$+$	\(4\)
\(+\)	\(+\)	\(-\)	$-$	\(2\)
\(+\)	\(-\)	\(+\)	$-$	\(2\)
\(+\)	\(-\)	\(-\)	$+$	\(4\)
\(-\)	\(+\)	\(+\)	$-$	\(2\)
\(-\)	\(+\)	\(-\)	$+$	\(5\)
\(-\)	\(-\)	\(+\)	$+$	\(5\)
\(-\)	\(-\)	\(-\)	$-$	\(2\)
Plus space			\(+\)	\(18\)
Minus space			\(-\)	\(8\)

Trace form

\( 26 q + 4 q^{2} - 16 q^{3} + 104 q^{4} + 52 q^{5} + 16 q^{8} + 262 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(266))\) 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	7	19
266.4.a.a	$266$	$4$	266.a	1.a	$1$	$2$	$2$	$15.695$	\(\Q(\sqrt{85}) \)	None	✓	$1$	$1$	\(-4\)	\(-9\)	\(12\)	\(-14\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+(-4-\beta )q^{3}+4q^{4}+(7-2\beta )q^{5}+\cdots\)
266.4.a.b	$266$	$4$	266.a	1.a	$1$	$2$	$2$	$15.695$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-4\)	\(-1\)	\(2\)	\(14\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+(1-3\beta )q^{3}+4q^{4}+(3-4\beta )q^{5}+\cdots\)
266.4.a.c	$266$	$4$	266.a	1.a	$1$	$2$	$2$	$15.695$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$1$	\(4\)	\(-7\)	\(-14\)	\(14\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+(-2-3\beta )q^{3}+4q^{4}+(-9+\cdots)q^{5}+\cdots\)
266.4.a.d	$266$	$4$	266.a	1.a	$1$	$2$	$2$	$15.695$	\(\Q(\sqrt{37}) \)	None	✓	$1$	$1$	\(4\)	\(-3\)	\(-4\)	\(-14\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+(-1-\beta )q^{3}+4q^{4}+(-3+\cdots)q^{5}+\cdots\)
266.4.a.e	$266$	$4$	266.a	1.a	$1$	$4$	$4$	$15.695$	4.4.6939601.2	None	✓	$1$	$0$	\(-8\)	\(-6\)	\(7\)	\(-28\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+(-1-\beta _{1}-\beta _{2})q^{3}+4q^{4}+\cdots\)
266.4.a.f	$266$	$4$	266.a	1.a	$1$	$4$	$4$	$15.695$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$0$	\(-8\)	\(8\)	\(7\)	\(28\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+(2-\beta _{1})q^{3}+4q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots\)
266.4.a.g	$266$	$4$	266.a	1.a	$1$	$5$	$5$	$15.695$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$0$	\(10\)	\(-6\)	\(21\)	\(-35\)		$-$	$+$	$-$	$+$	$3$	$\mathrm{SU}(2)$	\(q+2q^{2}+(-1-\beta _{1})q^{3}+4q^{4}+(4-\beta _{1}+\cdots)q^{5}+\cdots\)
266.4.a.h	$266$	$4$	266.a	1.a	$1$	$5$	$5$	$15.695$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$0$	\(10\)	\(8\)	\(21\)	\(35\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+(2-\beta _{1})q^{3}+4q^{4}+(4-\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(266))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(266)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 2}\)