Space of modular forms of level 3, weight 26, and trivial character

• Label: 3.26.a
• Level: $3$
• Weight: $26$
• Character orbit: 3.a
• Rep. character: $\chi_{3}(1,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $2$
• Sturm bound: $8$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(8\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_0(3))\).

	Total	New	Old
Modular forms	9	5	4
Cusp forms	7	5	2
Eisenstein series	2	0	2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)	Dim
\(+\)	\(2\)
\(-\)	\(3\)

Trace form

5 * q - 4002 * q^2 + 531441 * q^3 + 116355284 * q^4 + 407709006 * q^5 - 1782453114 * q^6 - 39309958472 * q^7 - 291312800760 * q^8 + 1412147682405 * q^9 + 6147590052564 * q^10 - 24134783749332 * q^11 + 34618009344372 * q^12 + 142994137728454 * q^13 + 281682671800272 * q^14 - 390085403083146 * q^15 - 378809104605424 * q^16 + 6183897836895738 * q^17 - 1130283004996962 * q^18 + 9614719536266548 * q^19 - 77002472769731976 * q^20 + 10663264277029944 * q^21 + 26761044671198856 * q^22 + 84783342948789624 * q^23 - 130050447316112376 * q^24 - 99189140617918789 * q^25 + 147840851396154660 * q^26 + 150094635296999121 * q^27 + 2191353545749530016 * q^28 - 2502539841117381594 * q^29 + 5622001512394220676 * q^30 + 954876643541101456 * q^31 - 21954104161995916512 * q^32 + 6505256343289039452 * q^33 - 1854027316439415972 * q^34 - 10429196484047083440 * q^35 + 32862168927235115604 * q^36 + 69152558317233520798 * q^37 - 318832149907630898760 * q^38 + 187748226389447040366 * q^39 + 524570550230746268208 * q^40 - 597401254139237025294 * q^41 + 652099689206655819984 * q^42 + 272662541690214829324 * q^43 - 1971518245902562385040 * q^44 + 115149065583709247886 * q^45 + 1122026015545224939216 * q^46 - 1317381085286900621232 * q^47 + 2746532159144226606096 * q^48 + 1759829504488690145757 * q^49 - 8748160206152998259166 * q^50 + 3772100494132165133010 * q^51 + 456938492077599979288 * q^52 + 562007823967323032094 * q^53 - 503417406786135051834 * q^54 + 9480212039078845571016 * q^55 + 17341408417833155830080 * q^56 - 9661681057738447542780 * q^57 - 31236506660525159082780 * q^58 + 32201402276983996948092 * q^59 - 49422263670781084662984 * q^60 - 35650844679114201340778 * q^61 + 75489372062508933475296 * q^62 - 11102293350334319017032 * q^63 - 27045286271674562960320 * q^64 + 77231798191654195817028 * q^65 - 85732038362088400645080 * q^66 - 83472346788757030801532 * q^67 + 303643995600011618215656 * q^68 - 103047076779758115574248 * q^69 - 183924416222173820086560 * q^70 + 383358431003395605774120 * q^71 - 82275339289628704525560 * q^72 + 73225288673685458167474 * q^73 - 525224845214049550608588 * q^74 + 355922403636181174181199 * q^75 + 235955349730005758966032 * q^76 - 1585949533175292431417184 * q^77 + 893336260671388338546132 * q^78 + 760218847521043733000320 * q^79 - 2337439770619285359693216 * q^80 + 398832215384362549316805 * q^81 + 3692827177594097874372396 * q^82 - 936536331267412457078796 * q^83 + 1404155691579558819001248 * q^84 - 3147845920523300761594308 * q^85 - 2134843460602993978402872 * q^86 + 1329414084492021374701230 * q^87 + 2854164686565702215990880 * q^88 - 1229086967010673719324222 * q^89 + 1736261009020856945587284 * q^90 + 6852388264039769311678736 * q^91 - 727913052083093798383392 * q^92 - 635639340921259388051088 * q^93 - 16997751485168022275936544 * q^94 + 2339560291274106904595064 * q^95 - 13229430648783271528771296 * q^96 - 17623548522544072790935382 * q^97 + 38198701780426394919644526 * q^98 - 6816375787393008053380692 * q^99

Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_0(3))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3
3.26.a.a	$3$	$26$	3.a	1.a	$1$	$2$	$2$	$11.880$	\(\Q(\sqrt{1287001}) \)	None	✓	✓	✓	✓	3.26.a.a	$1$	$1$	\(-324\)	\(-1062882\)	\(570861756\)	\(-29687385728\)		$+$	$+$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	\(q+(-162-\beta )q^{2}-3^{12}q^{3}+(12803848+\cdots)q^{4}+\cdots\)
3.26.a.b	$3$	$26$	3.a	1.a	$1$	$3$	$3$	$11.880$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	✓	✓	✓	3.26.a.b	$1$	$0$	\(-3678\)	\(1594323\)	\(-163152750\)	\(-9622572744\)		$-$	$-$	$2^{6}\cdot 3^{5}\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q+(-1226+\beta _{1})q^{2}+3^{12}q^{3}+(30249196+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{26}^{\mathrm{old}}(\Gamma_0(3))\) into lower level spaces

\( S_{26}^{\mathrm{old}}(\Gamma_0(3)) \simeq \) \(S_{26}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)