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Properties

Label 2.20
Level 2
Weight 20
Dimension 2
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 5
Trace bound 0

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Defining parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 20 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{20}(\Gamma_1(2))\).

Total New Old
Modular forms 6 2 4
Cusp forms 4 2 2
Eisenstein series 2 0 2

Trace form

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{20}^{\mathrm{new}}(\Gamma_1(2))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
2.20.a \(\chi_{2}(1, \cdot)\) 2.20.a.a 1 1
2.20.a.b 1

Decomposition of \(S_{20}^{\mathrm{old}}(\Gamma_1(2))\) into lower level spaces

\( S_{20}^{\mathrm{old}}(\Gamma_1(2)) \cong \) \(S_{20}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)