Space of modular forms of level 26, weight 2, and trivial character

• Label: 26.2.a
• Level: $26$
• Weight: $2$
• Character orbit: 26.a
• Rep. character: $\chi_{26}(1,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $2$
• Sturm bound: $7$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	26.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(7\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(26))\).

	Total	New	Old
Modular forms	5	2	3
Cusp forms	2	2	0
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.

\(2\)	\(13\)	Fricke	Dim
\(+\)	\(-\)	\(-\)	\(1\)
\(-\)	\(+\)	\(-\)	\(1\)
Plus space		\(+\)	\(0\)
Minus space		\(-\)	\(2\)

Trace form

2 * q - 2 * q^3 + 2 * q^4 - 4 * q^5 - 4 * q^6 + 4 * q^9 + 2 * q^10 + 4 * q^11 - 2 * q^12 + 2 * q^14 + 2 * q^16 - 6 * q^17 + 8 * q^18 + 8 * q^19 - 4 * q^20 - 4 * q^21 - 8 * q^22 - 4 * q^23 - 4 * q^24 - 2 * q^26 - 14 * q^27 + 8 * q^29 + 6 * q^30 + 12 * q^33 + 2 * q^35 + 4 * q^36 - 4 * q^37 + 4 * q^38 + 4 * q^39 + 2 * q^40 - 2 * q^42 - 6 * q^43 + 4 * q^44 - 4 * q^46 + 16 * q^47 - 2 * q^48 - 12 * q^49 - 8 * q^50 + 6 * q^51 + 12 * q^53 - 4 * q^54 - 16 * q^55 + 2 * q^56 - 16 * q^57 - 4 * q^58 - 16 * q^59 + 8 * q^62 + 8 * q^63 + 2 * q^64 - 2 * q^65 + 12 * q^67 - 6 * q^68 + 12 * q^69 - 4 * q^70 - 8 * q^71 + 8 * q^72 - 8 * q^73 + 10 * q^74 + 16 * q^75 + 8 * q^76 - 8 * q^77 + 2 * q^78 + 4 * q^79 - 4 * q^80 + 10 * q^81 + 12 * q^83 - 4 * q^84 + 12 * q^85 - 4 * q^86 - 8 * q^88 - 12 * q^90 - 2 * q^91 - 4 * q^92 - 16 * q^93 + 10 * q^94 - 12 * q^95 - 4 * q^96 + 4 * q^97 - 24 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(26))\) 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	13
26.2.a.a	$26$	$2$	26.a	1.a	$1$	$1$	$1$	$0.208$	\(\Q\)	None	✓	✓	✓	✓	26.2.a.a	$1$	$0$	\(-1\)	\(1\)	\(-3\)	\(-1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{7}+\cdots\)
26.2.a.b	$26$	$2$	26.a	1.a	$1$	$1$	$1$	$0.208$	\(\Q\)	None	✓	✓	✓	✓	26.2.a.b	$1$	$0$	\(1\)	\(-3\)	\(-1\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-3q^{3}+q^{4}-q^{5}-3q^{6}+q^{7}+\cdots\)