Space of modular forms of level 26, weight 4, and trivial character

• Label: 26.4.a
• Level: $26$
• Weight: $4$
• Character orbit: 26.a
• Rep. character: $\chi_{26}(1,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $3$
• Sturm bound: $14$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	26.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(14\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(26))\).

	Total	New	Old
Modular forms	13	3	10
Cusp forms	9	3	6
Eisenstein series	4	0	4

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		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(4\)	\(1\)	\(3\)		\(3\)	\(1\)	\(2\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)		\(2\)	\(0\)	\(2\)		\(1\)	\(0\)	\(1\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(3\)	\(0\)	\(3\)		\(2\)	\(0\)	\(2\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(4\)	\(2\)	\(2\)		\(3\)	\(2\)	\(1\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(8\)	\(3\)	\(5\)		\(6\)	\(3\)	\(3\)		\(2\)	\(0\)	\(2\)
Minus space		\(-\)		\(5\)	\(0\)	\(5\)		\(3\)	\(0\)	\(3\)		\(2\)	\(0\)	\(2\)

Trace form

3 * q + 2 * q^2 + 6 * q^3 + 12 * q^4 + 10 * q^5 + 4 * q^7 + 8 * q^8 - 55 * q^9 - 24 * q^10 - 84 * q^11 + 24 * q^12 + 13 * q^13 - 68 * q^14 - 56 * q^15 + 48 * q^16 - 4 * q^17 - 38 * q^18 + 168 * q^19 + 40 * q^20 + 172 * q^21 - 16 * q^22 + 44 * q^23 + 359 * q^25 + 78 * q^26 - 234 * q^27 + 16 * q^28 + 62 * q^29 - 244 * q^30 + 212 * q^31 + 32 * q^32 - 308 * q^33 + 196 * q^34 - 746 * q^35 - 220 * q^36 - 198 * q^37 - 24 * q^38 - 96 * q^40 - 358 * q^41 + 116 * q^42 + 490 * q^43 - 336 * q^44 - 442 * q^45 + 296 * q^46 - 372 * q^47 + 96 * q^48 + 957 * q^49 + 734 * q^50 + 130 * q^51 + 52 * q^52 + 794 * q^53 + 72 * q^54 + 480 * q^55 - 272 * q^56 + 112 * q^57 + 884 * q^58 + 48 * q^59 - 224 * q^60 - 170 * q^61 - 744 * q^62 + 348 * q^63 + 192 * q^64 - 156 * q^65 - 160 * q^66 - 1036 * q^67 - 16 * q^68 + 588 * q^69 - 2328 * q^70 - 1228 * q^71 - 152 * q^72 - 798 * q^73 + 1368 * q^74 + 620 * q^75 + 672 * q^76 - 1752 * q^77 + 156 * q^78 + 1332 * q^79 + 160 * q^80 + 419 * q^81 - 1964 * q^82 + 948 * q^83 + 688 * q^84 - 2072 * q^85 - 512 * q^86 - 792 * q^87 - 64 * q^88 + 1562 * q^89 - 92 * q^90 - 442 * q^91 + 176 * q^92 + 1056 * q^93 - 580 * q^94 + 2876 * q^95 - 2794 * q^97 + 1842 * q^98 + 1160 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(26))\) 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
26.4.a.a	$26$	$4$	26.a	1.a	$1$	$1$	$1$	$1.534$	\(\Q\)	None	✓	✓	✓	✓	26.4.a.a	$1$	$0$	\(-2\)	\(3\)	\(11\)	\(19\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+3q^{3}+4q^{4}+11q^{5}-6q^{6}+\cdots\)
26.4.a.b	$26$	$4$	26.a	1.a	$1$	$1$	$1$	$1.534$	\(\Q\)	None	✓	✓			26.4.a.b	$1$	$0$	\(2\)	\(-1\)	\(17\)	\(-35\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-q^{3}+4q^{4}+17q^{5}-2q^{6}+\cdots\)
26.4.a.c	$26$	$4$	26.a	1.a	$1$	$1$	$1$	$1.534$	\(\Q\)	None	✓	✓			26.4.a.c	$1$	$0$	\(2\)	\(4\)	\(-18\)	\(20\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+4q^{3}+4q^{4}-18q^{5}+8q^{6}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(26))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(26)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 2}\)