Properties

Label 1.20.a
Level $1$
Weight $20$
Character orbit 1.a
Rep. character $\chi_{1}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $1$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 20 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(1\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{20}(\Gamma_0(1))\).

Total New Old
Modular forms 2 2 0
Cusp forms 1 1 0
Eisenstein series 1 1 0

Trace form

\( q + 456q^{2} + 50652q^{3} - 316352q^{4} - 2377410q^{5} + 23097312q^{6} - 16917544q^{7} - 383331840q^{8} + 1403363637q^{9} + O(q^{10}) \) \( q + 456q^{2} + 50652q^{3} - 316352q^{4} - 2377410q^{5} + 23097312q^{6} - 16917544q^{7} - 383331840q^{8} + 1403363637q^{9} - 1084098960q^{10} - 16212108q^{11} - 16023861504q^{12} + 50421615062q^{13} - 7714400064q^{14} - 120420571320q^{15} - 8939761664q^{16} + 225070099506q^{17} + 639933818472q^{18} - 1710278572660q^{19} + 752098408320q^{20} - 856907438688q^{21} - 7392721248q^{22} + 14036534788872q^{23} - 19416524359680q^{24} - 13421408020025q^{25} + 22992256468272q^{26} + 12212307114840q^{27} + 5351898879488q^{28} + 1137835269510q^{29} - 54911780521920q^{30} - 104626880141728q^{31} + 196899752411136q^{32} - 821175694416q^{33} + 102631965374736q^{34} + 40219938281040q^{35} - 443956893292224q^{36} - 169392327370594q^{37} - 779887029132960q^{38} + 2553955646120424q^{39} + 911336949734400q^{40} - 3309984750560838q^{41} - 390749792041728q^{42} + 1127913532193492q^{43} + 5128732790016q^{44} - 3336370744240170q^{45} + 6400659863725632q^{46} + 3498693987674256q^{47} - 452816807804928q^{48} - 11112691890381207q^{49} - 6120162057131400q^{50} + 11400250680177912q^{51} - 15950978768093824q^{52} + 29956294112980302q^{53} + 5568812044367040q^{54} + 38542827680280q^{55} + 6485033269800960q^{56} - 86629030262374320q^{57} + 518852882896560q^{58} + 58391397642732420q^{59} + 38095288578224640q^{60} + 23373685132672742q^{61} - 47709857344627968q^{62} - 23741466076947528q^{63} + 94473296862773248q^{64} - 119872851864549420q^{65} - 374456116653696q^{66} - 205102524257382244q^{67} - 71201376118922112q^{68} + 710978560125944544q^{69} + 18340291856154240q^{70} - 177902341950417768q^{71} - 537953965160302080q^{72} + 299853775038660122q^{73} - 77242901280990864q^{74} - 679821159030306300q^{75} + 541050047018136320q^{76} + 274269050422752q^{77} + 1164603774630913344q^{78} - 92227090144007440q^{79} + 21253478777610240q^{80} - 1012497699493199799q^{81} - 1509353046255742128q^{82} + 1208542823470585932q^{83} + 271084382043826176q^{84} - 535083905266559460q^{85} + 514328570680232352q^{86} + 57633632071220520q^{87} + 6214617189918720q^{88} + 4371201192290304330q^{89} - 1521385059373517520q^{90} - 853009891362447728q^{91} - 4440485853529234944q^{92} - 5299560732938806656q^{93} + 1595404458379460736q^{94} + 4066033381427610600q^{95} + 9973366259128860672q^{96} - 635013222218448094q^{97} - 5067387502013830392q^{98} - 22751482846316796q^{99} + O(q^{100}) \)

Decomposition of \(S_{20}^{\mathrm{new}}(\Gamma_0(1))\) into newform subspaces

Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1.20.a.a \(1\) \(2.288\) \(\Q\) None \(456\) \(50652\) \(-2377410\) \(-16917544\) \(+\) \(q+456q^{2}+50652q^{3}-316352q^{4}+\cdots\)