Space of modular forms of level 26, weight 6, and trivial character

• Label: 26.6.a
• Level: $26$
• Weight: $6$
• Character orbit: 26.a
• Rep. character: $\chi_{26}(1,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $3$
• Sturm bound: $21$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	26.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(21\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(26))\).

	Total	New	Old
Modular forms	19	5	14
Cusp forms	15	5	10
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
\(+\)	\(+\)	\(+\)		\(4\)	\(1\)	\(3\)		\(3\)	\(1\)	\(2\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)		\(6\)	\(2\)	\(4\)		\(5\)	\(2\)	\(3\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(5\)	\(2\)	\(3\)		\(4\)	\(2\)	\(2\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(4\)	\(0\)	\(4\)		\(3\)	\(0\)	\(3\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(8\)	\(1\)	\(7\)		\(6\)	\(1\)	\(5\)		\(2\)	\(0\)	\(2\)
Minus space		\(-\)		\(11\)	\(4\)	\(7\)		\(9\)	\(4\)	\(5\)		\(2\)	\(0\)	\(2\)

Trace form

5 * q - 4 * q^2 + 18 * q^3 + 80 * q^4 + 22 * q^5 + 312 * q^7 - 64 * q^8 + 683 * q^9 + 496 * q^10 - 384 * q^11 + 288 * q^12 - 169 * q^13 - 8 * q^14 - 2504 * q^15 + 1280 * q^16 + 392 * q^17 - 2900 * q^18 - 1332 * q^19 + 352 * q^20 - 3044 * q^21 - 224 * q^22 - 4156 * q^23 - 6867 * q^25 - 2028 * q^26 + 16146 * q^27 + 4992 * q^28 + 6122 * q^29 + 2456 * q^30 - 6368 * q^31 - 1024 * q^32 - 4340 * q^33 - 3080 * q^34 + 14842 * q^35 + 10928 * q^36 + 42102 * q^37 - 14640 * q^38 + 7936 * q^40 + 734 * q^41 - 12808 * q^42 + 5526 * q^43 - 6144 * q^44 - 38878 * q^45 - 7728 * q^46 - 64560 * q^47 + 4608 * q^48 + 46119 * q^49 + 29348 * q^50 - 42458 * q^51 - 2704 * q^52 + 13646 * q^53 - 52272 * q^54 - 22760 * q^55 - 128 * q^56 - 77648 * q^57 - 9288 * q^58 - 32292 * q^59 - 40064 * q^60 + 63642 * q^61 + 47856 * q^62 + 147600 * q^63 + 20480 * q^64 - 16224 * q^65 + 90944 * q^66 + 41680 * q^67 + 6272 * q^68 - 46788 * q^69 + 77584 * q^70 - 14176 * q^71 - 46400 * q^72 + 50422 * q^73 - 25968 * q^74 - 59164 * q^75 - 21312 * q^76 - 38256 * q^77 - 12168 * q^78 + 112708 * q^79 + 5632 * q^80 + 193637 * q^81 + 90136 * q^82 - 202896 * q^83 - 48704 * q^84 + 136096 * q^85 - 54656 * q^86 - 206184 * q^87 - 3584 * q^88 + 28670 * q^89 + 57688 * q^90 + 57798 * q^91 - 66496 * q^92 - 263712 * q^93 + 54328 * q^94 - 91924 * q^95 + 136986 * q^97 - 82212 * q^98 + 70148 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(26))\) 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
26.6.a.a	$26$	$6$	26.a	1.a	$1$	$1$	$1$	$4.170$	\(\Q\)	None	✓	✓	✓	✓	26.6.a.a	$1$	$1$	\(-4\)	\(0\)	\(-14\)	\(-170\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+2^{4}q^{4}-14q^{5}-170q^{7}+\cdots\)
26.6.a.b	$26$	$6$	26.a	1.a	$1$	$2$	$2$	$4.170$	\(\Q(\sqrt{2785}) \)	None	✓	✓	✓	✓	26.6.a.b	$1$	$0$	\(-8\)	\(9\)	\(-37\)	\(327\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+(5-\beta )q^{3}+2^{4}q^{4}+(-19+\cdots)q^{5}+\cdots\)
26.6.a.c	$26$	$6$	26.a	1.a	$1$	$2$	$2$	$4.170$	\(\Q(\sqrt{849}) \)	None	✓	✓	✓	✓	26.6.a.c	$1$	$0$	\(8\)	\(9\)	\(73\)	\(155\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+(5-\beta )q^{3}+2^{4}q^{4}+(35+3\beta )q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(26))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(26)) \simeq \) \(S_{6}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 2}\)