Space of modular forms of level 26, weight 10, and trivial character

• Label: 26.10.a
• Level: $26$
• Weight: $10$
• Character orbit: 26.a
• Rep. character: $\chi_{26}(1,\cdot)$
• Character field: $\Q$
• Dimension: $9$
• Newform subspaces: $5$
• Sturm bound: $35$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	26.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(35\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(26))\).

	Total	New	Old
Modular forms	33	9	24
Cusp forms	29	9	20
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
\(+\)	\(+\)	\(+\)		\(7\)	\(2\)	\(5\)		\(6\)	\(2\)	\(4\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)		\(9\)	\(3\)	\(6\)		\(8\)	\(3\)	\(5\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(9\)	\(3\)	\(6\)		\(8\)	\(3\)	\(5\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(8\)	\(1\)	\(7\)		\(7\)	\(1\)	\(6\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(15\)	\(3\)	\(12\)		\(13\)	\(3\)	\(10\)		\(2\)	\(0\)	\(2\)
Minus space		\(-\)		\(18\)	\(6\)	\(12\)		\(16\)	\(6\)	\(10\)		\(2\)	\(0\)	\(2\)

Trace form

9 * q - 16 * q^2 + 150 * q^3 + 2304 * q^4 - 3298 * q^5 + 4992 * q^6 + 2132 * q^7 - 4096 * q^8 + 79379 * q^9 - 51264 * q^10 + 6004 * q^11 + 38400 * q^12 - 28561 * q^13 + 188064 * q^14 + 108856 * q^15 + 589824 * q^16 + 1410060 * q^17 - 367184 * q^18 + 688368 * q^19 - 844288 * q^20 - 1467308 * q^21 + 2874304 * q^22 + 3479948 * q^23 + 1277952 * q^24 + 8214973 * q^25 - 1370928 * q^26 - 5353146 * q^27 + 545792 * q^28 - 8970022 * q^29 + 6108896 * q^30 + 13863172 * q^31 - 1048576 * q^32 - 18703340 * q^33 - 15118624 * q^34 - 3619018 * q^35 + 20321024 * q^36 - 18451986 * q^37 + 5038592 * q^38 - 13123584 * q^40 - 63822306 * q^41 - 9909280 * q^42 - 62315734 * q^43 + 1537024 * q^44 + 12026402 * q^45 - 40011200 * q^46 + 21777004 * q^47 + 9830400 * q^48 + 118416303 * q^49 + 38179728 * q^50 - 270160814 * q^51 - 7311616 * q^52 + 107905926 * q^53 + 139666752 * q^54 + 1394160 * q^55 + 48144384 * q^56 + 232423840 * q^57 - 38120480 * q^58 - 166476856 * q^59 + 27867136 * q^60 + 98399450 * q^61 + 4508544 * q^62 + 847163868 * q^63 + 150994944 * q^64 - 4684004 * q^65 - 470113024 * q^66 + 434036572 * q^67 + 360975360 * q^68 - 309458940 * q^69 - 319215936 * q^70 + 90936916 * q^71 - 93999104 * q^72 - 812313354 * q^73 + 309678656 * q^74 - 558944404 * q^75 + 176222208 * q^76 - 1052812784 * q^77 - 74030112 * q^78 + 491552580 * q^79 - 216137728 * q^80 + 934255625 * q^81 + 366921056 * q^82 - 736088244 * q^83 - 375630848 * q^84 - 109876504 * q^85 - 2275819776 * q^86 + 1293433272 * q^87 + 735821824 * q^88 + 1467376398 * q^89 - 1897745312 * q^90 - 807533714 * q^91 + 890866688 * q^92 - 1956561648 * q^93 - 505543520 * q^94 - 523767444 * q^95 + 327155712 * q^96 + 360112114 * q^97 + 1557524592 * q^98 - 5923423792 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(26))\) 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
26.10.a.a	$26$	$10$	26.a	1.a	$1$	$1$	$1$	$13.391$	\(\Q\)	None	✓	✓			26.10.a.a	$1$	$1$	\(-16\)	\(-273\)	\(1015\)	\(3955\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2^{4}q^{2}-273q^{3}+2^{8}q^{4}+1015q^{5}+\cdots\)
26.10.a.b	$26$	$10$	26.a	1.a	$1$	$1$	$1$	$13.391$	\(\Q\)	None	✓	✓			26.10.a.b	$1$	$1$	\(-16\)	\(192\)	\(-1310\)	\(-5810\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2^{4}q^{2}+192q^{3}+2^{8}q^{4}-1310q^{5}+\cdots\)
26.10.a.c	$26$	$10$	26.a	1.a	$1$	$1$	$1$	$13.391$	\(\Q\)	None	✓	✓	✓	✓	26.10.a.c	$1$	$1$	\(16\)	\(75\)	\(-1979\)	\(-10115\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2^{4}q^{2}+75q^{3}+2^{8}q^{4}-1979q^{5}+\cdots\)
26.10.a.d	$26$	$10$	26.a	1.a	$1$	$3$	$3$	$13.391$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	✓	✓	✓	26.10.a.d	$1$	$0$	\(-48\)	\(0\)	\(248\)	\(-2956\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-2^{4}q^{2}-\beta _{2}q^{3}+2^{8}q^{4}+(79-11\beta _{1}+\cdots)q^{5}+\cdots\)
26.10.a.e	$26$	$10$	26.a	1.a	$1$	$3$	$3$	$13.391$	3.3.2119705.1	None	✓	✓	✓	✓	26.10.a.e	$1$	$0$	\(48\)	\(156\)	\(-1272\)	\(17058\)		$-$	$+$	$-$	$2\cdot 3^{3}$	$\mathrm{SU}(2)$	\(q+2^{4}q^{2}+(52-\beta _{1}-\beta _{2})q^{3}+2^{8}q^{4}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(26))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(26)) \simeq \) \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 2}\)