↑

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 $0$

Related objects

Downloads

Learn more

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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1.20.a.a 1.a 1.a $1$ $2.288$ \(\Q\) None \(456\) \(50652\) \(-2377410\) \(-16917544\) $+$ $\mathrm{SU}(2)$ \(q+456q^{2}+50652q^{3}-316352q^{4}+\cdots\)