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Properties

Label 5.22.a
Level $5$
Weight $22$
Character orbit 5.a
Rep. character $\chi_{5}(1,\cdot)$
Character field $\Q$
Dimension $7$
Newform subspaces $2$
Sturm bound $11$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 5 \)
Weight: \( k \) \(=\) \( 22 \)
Character orbit: \([\chi]\) \(=\) 5.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(11\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_0(5))\).

Total New Old
Modular forms 11 7 4
Cusp forms 9 7 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.
\(+\)\(3\)
\(-\)\(4\)

Trace form

\( 7 q + 1598 q^{2} + 135434 q^{3} + 10156404 q^{4} + 9765625 q^{5} - 134284136 q^{6} + 1197030358 q^{7} + 6286638600 q^{8} + 23738514151 q^{9} + O(q^{10}) \) \( 7 q + 1598 q^{2} + 135434 q^{3} + 10156404 q^{4} + 9765625 q^{5} - 134284136 q^{6} + 1197030358 q^{7} + 6286638600 q^{8} + 23738514151 q^{9} + 41230468750 q^{10} + 36915589184 q^{11} - 503308196432 q^{12} + 57357098574 q^{13} + 442007689008 q^{14} + 303183593750 q^{15} - 1311300484848 q^{16} + 733529966678 q^{17} + 81647171463494 q^{18} + 20282453842260 q^{19} + 79825507812500 q^{20} - 393096502255116 q^{21} - 203004688093624 q^{22} + 388545505306914 q^{23} - 60402224293920 q^{24} + 667572021484375 q^{25} - 393923079662716 q^{26} - 1611730473858100 q^{27} - 247898758582784 q^{28} + 2205150977956090 q^{29} - 1784817265625000 q^{30} + 1314904316573524 q^{31} + 6022308475794208 q^{32} - 47425047428324192 q^{33} + 22647614408032988 q^{34} - 1677761308593750 q^{35} + 108438862405790372 q^{36} + 26872991516371118 q^{37} + 38176781255684600 q^{38} - 101643150674642668 q^{39} + 39532105078125000 q^{40} - 200890308543164006 q^{41} - 334487502048658944 q^{42} + 395111109322505394 q^{43} - 374190571247623952 q^{44} + 192649051884765625 q^{45} - 66245447433411696 q^{46} + 47044210186534238 q^{47} + 192063027362083264 q^{48} + 46967908925791099 q^{49} + 152397155761718750 q^{50} + 1799568223710501124 q^{51} + 1711589438388353048 q^{52} - 2532372504975675466 q^{53} - 4745878732696436240 q^{54} + 298228161250000000 q^{55} + 3579690160855388160 q^{56} + 6067235229019091000 q^{57} - 14098088367269025500 q^{58} + 9343397897212744580 q^{59} + 2133178135468750000 q^{60} - 10173783479756547666 q^{61} + 28533087758085932736 q^{62} + 8967507041593209174 q^{63} - 38086581234543958976 q^{64} + 16305734683457031250 q^{65} - 55052939083404862432 q^{66} + 10473435607038416278 q^{67} + 9049459099955001256 q^{68} - 99535341024990147108 q^{69} + 48914097521718750000 q^{70} + 9719710503077767804 q^{71} + 273453111111150138600 q^{72} - 34103167714234877586 q^{73} - 151516771487276236652 q^{74} + 12915992736816406250 q^{75} + 20327109513274986320 q^{76} + 392698243802630342496 q^{77} - 452912683312301552432 q^{78} - 326331098506183861160 q^{79} + 191870807912656250000 q^{80} + 112233362070071869027 q^{81} + 787498996898908950316 q^{82} - 324246264182686907646 q^{83} - 1444856778433938010752 q^{84} + 338436056994941406250 q^{85} - 308758989954091563256 q^{86} + 1011767514843797750300 q^{87} - 624045884838102832800 q^{88} - 519584921854713878730 q^{89} + 1316318276168808593750 q^{90} - 283308006346291986196 q^{91} + 3458344050732703820928 q^{92} - 430585694785886094312 q^{93} - 3480710271939349970272 q^{94} + 1075710350170117187500 q^{95} - 1756686888340402147456 q^{96} + 1183125700288881568238 q^{97} - 1026968381183437208114 q^{98} - 2826043630301167165888 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_0(5))\) 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
5.22.a.a 5.a 1.a $3$ $13.974$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-1312\) \(52194\) \(-29296875\) \(684416558\) $+$ $\mathrm{SU}(2)$ \(q+(-437+\beta _{1})q^{2}+(17400+8\beta _{1}+\cdots)q^{3}+\cdots\)
5.22.a.b 5.a 1.a $4$ $13.974$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(2910\) \(83240\) \(39062500\) \(512613800\) $-$ $\mathrm{SU}(2)$ \(q+(728-\beta _{1})q^{2}+(20803+14\beta _{1}+\beta _{3})q^{3}+\cdots\)

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_0(5))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_0(5)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)