Properties

Label 11.4.c
Level 11
Weight 4
Character orbit c
Rep. character \(\chi_{11}(3,\cdot)\)
Character field \(\Q(\zeta_{5})\)
Dimension 8
Newforms 1
Sturm bound 4
Trace bound 0

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Defining parameters

Level: \( N \) = \( 11 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 11.c (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newforms: \( 1 \)
Sturm bound: \(4\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(11, [\chi])\).

Total New Old
Modular forms 16 16 0
Cusp forms 8 8 0
Eisenstein series 8 8 0

Trace form

\(8q \) \(\mathstrut -\mathstrut 7q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 3q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 29q^{6} \) \(\mathstrut -\mathstrut 35q^{7} \) \(\mathstrut +\mathstrut 47q^{8} \) \(\mathstrut +\mathstrut 31q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut -\mathstrut 7q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 3q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 29q^{6} \) \(\mathstrut -\mathstrut 35q^{7} \) \(\mathstrut +\mathstrut 47q^{8} \) \(\mathstrut +\mathstrut 31q^{9} \) \(\mathstrut +\mathstrut 40q^{10} \) \(\mathstrut +\mathstrut 67q^{11} \) \(\mathstrut +\mathstrut 190q^{12} \) \(\mathstrut -\mathstrut 65q^{13} \) \(\mathstrut -\mathstrut 196q^{14} \) \(\mathstrut -\mathstrut 121q^{15} \) \(\mathstrut -\mathstrut 377q^{16} \) \(\mathstrut -\mathstrut 31q^{17} \) \(\mathstrut -\mathstrut 102q^{18} \) \(\mathstrut +\mathstrut 148q^{19} \) \(\mathstrut +\mathstrut 342q^{20} \) \(\mathstrut +\mathstrut 334q^{21} \) \(\mathstrut +\mathstrut 647q^{22} \) \(\mathstrut -\mathstrut 12q^{23} \) \(\mathstrut -\mathstrut 447q^{24} \) \(\mathstrut -\mathstrut 201q^{25} \) \(\mathstrut -\mathstrut 140q^{26} \) \(\mathstrut +\mathstrut 72q^{27} \) \(\mathstrut -\mathstrut 42q^{28} \) \(\mathstrut -\mathstrut 199q^{29} \) \(\mathstrut -\mathstrut 114q^{30} \) \(\mathstrut -\mathstrut 361q^{31} \) \(\mathstrut +\mathstrut 324q^{32} \) \(\mathstrut -\mathstrut 232q^{33} \) \(\mathstrut -\mathstrut 298q^{34} \) \(\mathstrut +\mathstrut 237q^{35} \) \(\mathstrut +\mathstrut 120q^{36} \) \(\mathstrut +\mathstrut 81q^{37} \) \(\mathstrut -\mathstrut 52q^{38} \) \(\mathstrut +\mathstrut 365q^{39} \) \(\mathstrut +\mathstrut 532q^{40} \) \(\mathstrut -\mathstrut 31q^{41} \) \(\mathstrut +\mathstrut 170q^{42} \) \(\mathstrut -\mathstrut 650q^{43} \) \(\mathstrut -\mathstrut 1208q^{44} \) \(\mathstrut +\mathstrut 452q^{45} \) \(\mathstrut +\mathstrut 1204q^{46} \) \(\mathstrut +\mathstrut 857q^{47} \) \(\mathstrut +\mathstrut 644q^{48} \) \(\mathstrut +\mathstrut 1375q^{49} \) \(\mathstrut -\mathstrut 147q^{50} \) \(\mathstrut -\mathstrut 246q^{51} \) \(\mathstrut -\mathstrut 590q^{52} \) \(\mathstrut -\mathstrut 1493q^{53} \) \(\mathstrut -\mathstrut 3100q^{54} \) \(\mathstrut -\mathstrut 1583q^{55} \) \(\mathstrut -\mathstrut 1560q^{56} \) \(\mathstrut +\mathstrut 102q^{57} \) \(\mathstrut +\mathstrut 1392q^{58} \) \(\mathstrut +\mathstrut 676q^{59} \) \(\mathstrut +\mathstrut 1068q^{60} \) \(\mathstrut -\mathstrut 525q^{61} \) \(\mathstrut +\mathstrut 2456q^{62} \) \(\mathstrut -\mathstrut 68q^{63} \) \(\mathstrut +\mathstrut 471q^{64} \) \(\mathstrut +\mathstrut 1790q^{65} \) \(\mathstrut +\mathstrut 1014q^{66} \) \(\mathstrut +\mathstrut 86q^{67} \) \(\mathstrut +\mathstrut 710q^{68} \) \(\mathstrut -\mathstrut 42q^{69} \) \(\mathstrut -\mathstrut 144q^{70} \) \(\mathstrut +\mathstrut 1143q^{71} \) \(\mathstrut +\mathstrut 919q^{72} \) \(\mathstrut -\mathstrut 2155q^{73} \) \(\mathstrut -\mathstrut 1476q^{74} \) \(\mathstrut -\mathstrut 160q^{75} \) \(\mathstrut -\mathstrut 242q^{76} \) \(\mathstrut -\mathstrut 2015q^{77} \) \(\mathstrut -\mathstrut 1340q^{78} \) \(\mathstrut -\mathstrut 861q^{79} \) \(\mathstrut -\mathstrut 1916q^{80} \) \(\mathstrut -\mathstrut 26q^{81} \) \(\mathstrut -\mathstrut 3497q^{82} \) \(\mathstrut +\mathstrut 52q^{83} \) \(\mathstrut -\mathstrut 84q^{84} \) \(\mathstrut +\mathstrut 2383q^{85} \) \(\mathstrut +\mathstrut 1061q^{86} \) \(\mathstrut +\mathstrut 2310q^{87} \) \(\mathstrut +\mathstrut 4543q^{88} \) \(\mathstrut +\mathstrut 3782q^{89} \) \(\mathstrut -\mathstrut 1682q^{90} \) \(\mathstrut +\mathstrut 135q^{91} \) \(\mathstrut -\mathstrut 2450q^{92} \) \(\mathstrut -\mathstrut 2077q^{93} \) \(\mathstrut +\mathstrut 702q^{94} \) \(\mathstrut -\mathstrut 1317q^{95} \) \(\mathstrut +\mathstrut 1252q^{96} \) \(\mathstrut -\mathstrut 1344q^{97} \) \(\mathstrut +\mathstrut 2740q^{98} \) \(\mathstrut +\mathstrut 2099q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(11, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
11.4.c.a \(8\) \(0.649\) 8.0.\(\cdots\).1 None \(-7\) \(-3\) \(-7\) \(-35\) \(q+(-1+\beta _{1}+\beta _{2}-\beta _{4})q^{2}+(-2-2\beta _{2}+\cdots)q^{3}+\cdots\)