Properties

Label 2.20.a
Level $2$
Weight $20$
Character orbit 2.a
Rep. character $\chi_{2}(1,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $2$
Sturm bound $5$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 2 \)
Weight: \( k \) \(=\) \( 20 \)
Character orbit: \([\chi]\) \(=\) 2.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(5\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{20}(\Gamma_0(2))\).

Total New Old
Modular forms 6 2 4
Cusp forms 4 2 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.

\(2\)Dim.
\(+\)\(1\)
\(-\)\(1\)

Trace form

\( 2q - 66120q^{3} + 524288q^{4} + 989820q^{5} - 20447232q^{6} + 52177840q^{7} + 658846314q^{9} + O(q^{10}) \) \( 2q - 66120q^{3} + 524288q^{4} + 989820q^{5} - 20447232q^{6} + 52177840q^{7} + 658846314q^{9} - 6197084160q^{10} + 18120369384q^{11} - 17332961280q^{12} + 1276754860q^{13} - 72279392256q^{14} + 208962833040q^{15} + 137438953472q^{16} - 1123052861340q^{17} + 1351970979840q^{18} - 497744747240q^{19} + 259475374080q^{20} + 1093896907584q^{21} - 2805257994240q^{22} - 1558014516720q^{23} - 5360119185408q^{24} + 35592433931150q^{25} - 34573670940672q^{26} + 2340400843440q^{27} + 13678107688960q^{28} - 126085309807860q^{29} + 194756062740480q^{30} + 73528521137344q^{31} - 489654350059680q^{33} - 164688713220096q^{34} + 880165751260320q^{35} + 172712608137216q^{36} - 220384762054340q^{37} - 1089278257397760q^{38} + 1306163651014608q^{39} - 1624528430039040q^{40} - 159817982504076q^{41} + 1856110508113920q^{42} + 1375186650672040q^{43} + 4750146111799296q^{44} - 15654227352447060q^{45} + 4258570240524288q^{46} + 11861897154251040q^{47} - 4543731801784320q^{48} - 11471945302016814q^{49} - 6133997843251200q^{50} + 43550987411484144q^{51} + 334693626019840q^{52} - 46640312146730340q^{53} - 27666922450452480q^{54} + 42126101503752240q^{55} - 18947609003556864q^{56} + 58937293382267040q^{57} + 34472506561658880q^{58} - 83330198435011320q^{59} + 54778352904437760q^{60} - 132955759859505716q^{61} + 97497308693790720q^{62} - 169196834444461200q^{63} + 36028797018963968q^{64} + 409292669266505640q^{65} - 92513869070598144q^{66} - 5143890515758280q^{67} - 294401569283112960q^{68} - 114576279457684032q^{69} - 197447026904924160q^{70} + 180975996855926064q^{71} + 354411080539176960q^{72} + 703681071936580660q^{73} - 364822243968024576q^{74} - 937459949877022200q^{75} - 130480799020482560q^{76} + 859479344831540160q^{77} + 1129952509883842560q^{78} - 2579721560929264160q^{79} + 68019912462827520q^{80} + 235884640246337682q^{81} + 2016621232631316480q^{82} - 353130710209828200q^{83} + 286758510941700096q^{84} + 1390810498655755320q^{85} - 5131367195035041792q^{86} + 2823952586343155280q^{87} - 735381551642050560q^{88} - 913988698539478380q^{89} - 1372359070549278720q^{90} + 4799704578625074464q^{91} - 408424157471047680q^{92} - 6233247947858430720q^{93} + 6320574270101520384q^{94} + 12628930149584974800q^{95} - 1405123083739594752q^{96} - 24626536111267629500q^{97} - 3771382564430807040q^{98} - 1264593396103377912q^{99} + O(q^{100}) \)

Decomposition of \(S_{20}^{\mathrm{new}}(\Gamma_0(2))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
2.20.a.a \(1\) \(4.576\) \(\Q\) None \(-512\) \(-13092\) \(6546750\) \(96674264\) \(+\) \(q-2^{9}q^{2}-13092q^{3}+2^{18}q^{4}+6546750q^{5}+\cdots\)
2.20.a.b \(1\) \(4.576\) \(\Q\) None \(512\) \(-53028\) \(-5556930\) \(-44496424\) \(-\) \(q+2^{9}q^{2}-53028q^{3}+2^{18}q^{4}-5556930q^{5}+\cdots\)

Decomposition of \(S_{20}^{\mathrm{old}}(\Gamma_0(2))\) into lower level spaces

\( S_{20}^{\mathrm{old}}(\Gamma_0(2)) \cong \) \(S_{20}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)