Properties

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 $1$

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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

\( 9 q - 4002 q^{2} - 172396 q^{3} + 183464148 q^{4} + 244140625 q^{5} + 1731399928 q^{6} + 6543128808 q^{7} - 101081972280 q^{8} + 2365562653957 q^{9} + O(q^{10}) \) \( 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} + O(q^{100}) \)

Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_0(5))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5
5.26.a.a 5.a 1.a $4$ $19.800$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(600\) \(-798600\) \(-976562500\) \(-48938107000\) $+$ $\mathrm{SU}(2)$ \(q+(150-\beta _{1})q^{2}+(-199650+17\beta _{1}+\cdots)q^{3}+\cdots\)
5.26.a.b 5.a 1.a $5$ $19.800$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-4602\) \(626204\) \(1220703125\) \(55481235808\) $-$ $\mathrm{SU}(2)$ \(q+(-920-\beta _{1})q^{2}+(125251-5^{2}\beta _{1}+\cdots)q^{3}+\cdots\)

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

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