Properties

Label 11.6.a
Level 11
Weight 6
Character orbit a
Rep. character \(\chi_{11}(1,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 2
Sturm bound 6
Trace bound 1

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Defining parameters

Level: \( N \) = \( 11 \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 11.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(6\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(11))\).

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

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators.

\(11\)Dim.
\(+\)\(1\)
\(-\)\(3\)

Trace form

\(4q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 19q^{3} \) \(\mathstrut +\mathstrut 68q^{4} \) \(\mathstrut +\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 146q^{6} \) \(\mathstrut +\mathstrut 94q^{7} \) \(\mathstrut -\mathstrut 372q^{8} \) \(\mathstrut -\mathstrut 25q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 19q^{3} \) \(\mathstrut +\mathstrut 68q^{4} \) \(\mathstrut +\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 146q^{6} \) \(\mathstrut +\mathstrut 94q^{7} \) \(\mathstrut -\mathstrut 372q^{8} \) \(\mathstrut -\mathstrut 25q^{9} \) \(\mathstrut -\mathstrut 338q^{10} \) \(\mathstrut +\mathstrut 242q^{11} \) \(\mathstrut +\mathstrut 1232q^{12} \) \(\mathstrut -\mathstrut 662q^{13} \) \(\mathstrut -\mathstrut 1060q^{14} \) \(\mathstrut +\mathstrut 1939q^{15} \) \(\mathstrut +\mathstrut 1736q^{16} \) \(\mathstrut +\mathstrut 1772q^{17} \) \(\mathstrut -\mathstrut 3634q^{18} \) \(\mathstrut +\mathstrut 996q^{19} \) \(\mathstrut -\mathstrut 3176q^{20} \) \(\mathstrut -\mathstrut 1058q^{21} \) \(\mathstrut +\mathstrut 484q^{22} \) \(\mathstrut +\mathstrut 643q^{23} \) \(\mathstrut -\mathstrut 14628q^{24} \) \(\mathstrut -\mathstrut 2821q^{25} \) \(\mathstrut +\mathstrut 16724q^{26} \) \(\mathstrut +\mathstrut 925q^{27} \) \(\mathstrut +\mathstrut 23552q^{28} \) \(\mathstrut -\mathstrut 8850q^{29} \) \(\mathstrut +\mathstrut 1510q^{30} \) \(\mathstrut -\mathstrut 10541q^{31} \) \(\mathstrut -\mathstrut 17528q^{32} \) \(\mathstrut +\mathstrut 5929q^{33} \) \(\mathstrut +\mathstrut 22576q^{34} \) \(\mathstrut -\mathstrut 24418q^{35} \) \(\mathstrut +\mathstrut 5044q^{36} \) \(\mathstrut +\mathstrut 29787q^{37} \) \(\mathstrut -\mathstrut 7704q^{38} \) \(\mathstrut +\mathstrut 10660q^{39} \) \(\mathstrut -\mathstrut 18924q^{40} \) \(\mathstrut +\mathstrut 4466q^{41} \) \(\mathstrut -\mathstrut 47228q^{42} \) \(\mathstrut -\mathstrut 30234q^{43} \) \(\mathstrut +\mathstrut 12100q^{44} \) \(\mathstrut +\mathstrut 18800q^{45} \) \(\mathstrut -\mathstrut 31642q^{46} \) \(\mathstrut -\mathstrut 10064q^{47} \) \(\mathstrut +\mathstrut 64904q^{48} \) \(\mathstrut +\mathstrut 31824q^{49} \) \(\mathstrut +\mathstrut 52126q^{50} \) \(\mathstrut -\mathstrut 33014q^{51} \) \(\mathstrut -\mathstrut 16936q^{52} \) \(\mathstrut +\mathstrut 20724q^{53} \) \(\mathstrut +\mathstrut 3154q^{54} \) \(\mathstrut +\mathstrut 5203q^{55} \) \(\mathstrut -\mathstrut 40392q^{56} \) \(\mathstrut +\mathstrut 25920q^{57} \) \(\mathstrut -\mathstrut 7476q^{58} \) \(\mathstrut -\mathstrut 10199q^{59} \) \(\mathstrut -\mathstrut 18016q^{60} \) \(\mathstrut +\mathstrut 1506q^{61} \) \(\mathstrut +\mathstrut 5798q^{62} \) \(\mathstrut -\mathstrut 12676q^{63} \) \(\mathstrut +\mathstrut 8320q^{64} \) \(\mathstrut +\mathstrut 14144q^{65} \) \(\mathstrut -\mathstrut 32186q^{66} \) \(\mathstrut -\mathstrut 17755q^{67} \) \(\mathstrut -\mathstrut 23576q^{68} \) \(\mathstrut -\mathstrut 20593q^{69} \) \(\mathstrut -\mathstrut 122612q^{70} \) \(\mathstrut +\mathstrut 70305q^{71} \) \(\mathstrut -\mathstrut 98496q^{72} \) \(\mathstrut +\mathstrut 17350q^{73} \) \(\mathstrut +\mathstrut 105042q^{74} \) \(\mathstrut +\mathstrut 19544q^{75} \) \(\mathstrut +\mathstrut 110064q^{76} \) \(\mathstrut +\mathstrut 8954q^{77} \) \(\mathstrut +\mathstrut 56104q^{78} \) \(\mathstrut +\mathstrut 190286q^{79} \) \(\mathstrut +\mathstrut 123544q^{80} \) \(\mathstrut -\mathstrut 141268q^{81} \) \(\mathstrut -\mathstrut 249260q^{82} \) \(\mathstrut -\mathstrut 246642q^{83} \) \(\mathstrut +\mathstrut 346016q^{84} \) \(\mathstrut -\mathstrut 117074q^{85} \) \(\mathstrut +\mathstrut 259164q^{86} \) \(\mathstrut +\mathstrut 61992q^{87} \) \(\mathstrut -\mathstrut 91476q^{88} \) \(\mathstrut -\mathstrut 89409q^{89} \) \(\mathstrut +\mathstrut 102056q^{90} \) \(\mathstrut -\mathstrut 121112q^{91} \) \(\mathstrut -\mathstrut 395872q^{92} \) \(\mathstrut +\mathstrut 80023q^{93} \) \(\mathstrut -\mathstrut 103600q^{94} \) \(\mathstrut -\mathstrut 14904q^{95} \) \(\mathstrut +\mathstrut 344q^{96} \) \(\mathstrut +\mathstrut 76589q^{97} \) \(\mathstrut +\mathstrut 70308q^{98} \) \(\mathstrut +\mathstrut 1331q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(11))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 11
11.6.a.a \(1\) \(1.764\) \(\Q\) None \(-4\) \(-15\) \(-19\) \(10\) \(+\) \(q-4q^{2}-15q^{3}-2^{4}q^{4}-19q^{5}+60q^{6}+\cdots\)
11.6.a.b \(3\) \(1.764\) 3.3.54492.1 None \(0\) \(34\) \(24\) \(84\) \(-\) \(q+\beta _{2}q^{2}+(11+\beta _{1}-\beta _{2})q^{3}+(30-6\beta _{1}+\cdots)q^{4}+\cdots\)