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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 11
11.6.a.a 11.a 1.a $1$ $1.764$ \(\Q\) None \(-4\) \(-15\) \(-19\) \(10\) $+$ $\mathrm{SU}(2)$ \(q-4q^{2}-15q^{3}-2^{4}q^{4}-19q^{5}+60q^{6}+\cdots\)
11.6.a.b 11.a 1.a $3$ $1.764$ 3.3.54492.1 None \(0\) \(34\) \(24\) \(84\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+(11+\beta _{1}-\beta _{2})q^{3}+(30-6\beta _{1}+\cdots)q^{4}+\cdots\)