Properties

Label 11.6.a
Level $11$
Weight $6$
Character orbit 11.a
Rep. character $\chi_{11}(1,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
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: \(\Q\)
Newform subspaces: \( 2 \)
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 and the Fricke involution.

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

Trace form

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

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(11))\) into newform subspaces

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 \(0\) \(34\) \(24\) \(84\) \(-\) \(q+\beta _{2}q^{2}+(11+\beta _{1}-\beta _{2})q^{3}+(30-6\beta _{1}+\cdots)q^{4}+\cdots\)