Space of modular forms of level 5, weight 26, and trivial character

• Label: 5.26.a
• Level: $5$
• Weight: $26$
• Character orbit: 5.a
• Rep. character: $\chi_{5}(1,\cdot)$
• Character field: $\Q$
• Dimension: $9$
• Newform subspaces: $2$
• Sturm bound: $13$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	5.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(13\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_0(5))\).

	Total	New	Old
Modular forms	13	9	4
Cusp forms	11	9	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.

\(5\)	Dim
\(+\)	\(4\)
\(-\)	\(5\)

Trace form

9 * q - 4002 * q^2 - 172396 * q^3 + 183464148 * q^4 + 244140625 * q^5 + 1731399928 * q^6 + 6543128808 * q^7 - 101081972280 * q^8 + 2365562653957 * q^9 - 1270019531250 * q^10 - 27786412242132 * q^11 - 68422875582512 * q^12 + 220275163302414 * q^13 - 335586152474544 * q^14 + 347852539062500 * q^15 + 233630870981904 * q^16 + 2841751737326178 * q^17 + 114435516345254 * q^18 + 7707230814435540 * q^19 - 332916992187500 * q^20 - 9653074697712 * q^21 - 24264570707350104 * q^22 + 324730477826668824 * q^23 - 11930030532605280 * q^24 + 536441802978515625 * q^25 - 1840936241106797052 * q^26 - 616576469248728280 * q^27 + 7460551168186390176 * q^28 - 20253459016714290 * q^29 + 2358825583984375000 * q^30 - 11206126532829054432 * q^31 - 17481045614240873952 * q^32 + 21495795663454819408 * q^33 - 18606428016132802404 * q^34 + 25493003615234375000 * q^35 - 98062101856393879996 * q^36 + 9156020287154409318 * q^37 + 60516990815238896280 * q^38 - 1533135878503973896 * q^39 - 134264878388671875000 * q^40 + 562947806422155247818 * q^41 + 197044147055009475936 * q^42 - 1321060245929686734756 * q^43 + 287557672085459120496 * q^44 - 441789297125732421875 * q^45 + 1136774999854291432368 * q^46 + 2140441407206432771088 * q^47 + 4388391998086191424 * q^48 + 430841304629954339313 * q^49 - 238537788391113281250 * q^50 - 2411999560815594757592 * q^51 - 5358740220726552489192 * q^52 + 5582189630338765603254 * q^53 - 349528153920799942160 * q^54 + 4759886557385742187500 * q^55 - 25386088690665040925760 * q^56 + 6463841607189211455440 * q^57 + 19528677380655136236420 * q^58 - 18764367737052863672580 * q^59 + 3828342639425781250000 * q^60 - 39330429406392586888482 * q^61 - 3387185265634263698304 * q^62 + 34818662529560120817384 * q^63 + 63524301486907126175808 * q^64 + 524251672562011718750 * q^65 + 91579433032783869849056 * q^66 + 109602276017722838891028 * q^67 - 269493353307885380540184 * q^68 - 6731324978687779171536 * q^69 - 135631629528128906250000 * q^70 + 329933179404118091229768 * q^71 + 651674850937592404267560 * q^72 - 578107228546908018325926 * q^73 - 601739877589346422756524 * q^74 - 10275602340698242187500 * q^75 - 398308030502190717127920 * q^76 - 501697267892420228433984 * q^77 + 822483197934526611655888 * q^78 + 208304674973308436769360 * q^79 + 1429771768622816406250000 * q^80 - 1475434223732099110565231 * q^81 + 1043883358198078825109196 * q^82 + 1876801646020830546135684 * q^83 - 5452584697477773642785664 * q^84 + 858552747817035644531250 * q^85 - 2174652566034039762960792 * q^86 + 5808903586894731691339160 * q^87 - 4216063541689362176038560 * q^88 - 2768843004233767564336470 * q^89 + 4415886138960560058593750 * q^90 + 6874743950935309657069008 * q^91 + 13190242110052756103759328 * q^92 - 5779813589219968851924192 * q^93 - 15706516515126242542310784 * q^94 + 4697056954578872070312500 * q^95 + 2629518045091574574451328 * q^96 + 37152087992100438181379538 * q^97 - 46079972861881665096048114 * q^98 - 42088187551082075224420036 * q^99

Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_0(5))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5
5.26.a.a	$5$	$26$	5.a	1.a	$1$	$4$	$4$	$19.800$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	✓	✓	✓	5.26.a.a	$1$	$1$	\(600\)	\(-798600\)	\(-976562500\)	\(-48938107000\)		$+$	$+$	$2^{14}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q+(150-\beta _{1})q^{2}+(-199650+17\beta _{1}+\cdots)q^{3}+\cdots\)
5.26.a.b	$5$	$26$	5.a	1.a	$1$	$5$	$5$	$19.800$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	✓	✓	✓	5.26.a.b	$1$	$0$	\(-4602\)	\(626204\)	\(1220703125\)	\(55481235808\)		$-$	$-$	$2^{12}\cdot 3^{3}\cdot 5^{4}$	$\mathrm{SU}(2)$	\(q+(-920-\beta _{1})q^{2}+(125251-5^{2}\beta _{1}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{26}^{\mathrm{old}}(\Gamma_0(5))\) into lower level spaces

\( S_{26}^{\mathrm{old}}(\Gamma_0(5)) \simeq \) \(S_{26}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)