Space of modular forms of level 268, weight 2, and trivial character

• Label: 268.2.a
• Level: $268$
• Weight: $2$
• Character orbit: 268.a
• Rep. character: $\chi_{268}(1,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $3$
• Sturm bound: $68$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 268 = 2^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	268.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(68\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(268))\).

	Total	New	Old
Modular forms	37	5	32
Cusp forms	32	5	27
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.

\(2\)	\(67\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(8\)	\(0\)	\(8\)		\(7\)	\(0\)	\(7\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)		\(11\)	\(0\)	\(11\)		\(9\)	\(0\)	\(9\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)		\(9\)	\(3\)	\(6\)		\(8\)	\(3\)	\(5\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(9\)	\(2\)	\(7\)		\(8\)	\(2\)	\(6\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(17\)	\(2\)	\(15\)		\(15\)	\(2\)	\(13\)		\(2\)	\(0\)	\(2\)
Minus space		\(-\)		\(20\)	\(3\)	\(17\)		\(17\)	\(3\)	\(14\)		\(3\)	\(0\)	\(3\)

Trace form

5 * q - 2 * q^7 + 7 * q^9 + 2 * q^11 - 6 * q^13 - 2 * q^15 + 3 * q^17 - 5 * q^19 + 4 * q^21 - 5 * q^23 - 9 * q^25 + 6 * q^27 + 3 * q^29 - 4 * q^31 - 2 * q^33 - 2 * q^35 - 19 * q^37 + 12 * q^39 + 2 * q^41 + 20 * q^43 + 12 * q^45 + 7 * q^47 - 5 * q^49 + 2 * q^51 - 8 * q^55 + 6 * q^57 + 15 * q^59 - 2 * q^61 - 16 * q^63 - 30 * q^65 - q^67 - 8 * q^69 - 16 * q^71 + 17 * q^73 - 6 * q^75 + 2 * q^77 + 14 * q^79 - 19 * q^81 + 14 * q^83 - 10 * q^85 - 12 * q^87 - 17 * q^89 - 6 * q^91 - 34 * q^93 - 12 * q^95 - 22 * q^97 + 34 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(268))\) 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	67
268.2.a.a	$268$	$2$	268.a	1.a	$1$	$1$	$1$	$2.140$	\(\Q\)	None	✓	✓			268.2.a.a	$1$	$0$	\(0\)	\(2\)	\(2\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+2q^{5}+2q^{7}+q^{9}-4q^{11}+\cdots\)
268.2.a.b	$268$	$2$	268.a	1.a	$1$	$2$	$2$	$2.140$	\(\Q(\sqrt{5}) \)	None	✓	✓	✓	✓	268.2.a.b	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(-5\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+(-1+2\beta )q^{5}+(-2+\cdots)q^{7}+\cdots\)
268.2.a.c	$268$	$2$	268.a	1.a	$1$	$2$	$2$	$2.140$	\(\Q(\sqrt{21}) \)	None	✓	✓	✓		268.2.a.c	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}+(1-\beta )q^{7}+(2+\beta )q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(268))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(268)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(67))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(134))\)\(^{\oplus 2}\)