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Properties

Label 11.4.a
Level $11$
Weight $4$
Character orbit 11.a
Rep. character $\chi_{11}(1,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $4$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 11.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(4\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(11))\).

Total New Old
Modular forms 4 2 2
Cusp forms 2 2 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
\(+\)\(2\)

Trace form

\( 2 q + 2 q^{2} - 2 q^{3} - 8 q^{4} + 2 q^{5} - 26 q^{6} + 20 q^{7} - 12 q^{8} + 44 q^{9} + O(q^{10}) \) \( 2 q + 2 q^{2} - 2 q^{3} - 8 q^{4} + 2 q^{5} - 26 q^{6} + 20 q^{7} - 12 q^{8} + 44 q^{9} + 50 q^{10} - 22 q^{11} - 40 q^{12} + 80 q^{13} - 4 q^{14} - 194 q^{15} - 8 q^{16} - 124 q^{17} + 92 q^{18} + 72 q^{19} + 88 q^{20} + 76 q^{21} - 22 q^{22} - 98 q^{23} + 252 q^{24} + 136 q^{25} - 40 q^{26} - 182 q^{27} - 128 q^{28} + 144 q^{29} - 266 q^{30} - 34 q^{31} - 104 q^{32} + 22 q^{33} - 52 q^{34} - 172 q^{35} - 80 q^{36} + 54 q^{37} + 432 q^{38} + 400 q^{39} - 492 q^{40} + 536 q^{41} - 140 q^{42} - 60 q^{43} + 88 q^{44} + 428 q^{45} - 314 q^{46} - 272 q^{47} + 776 q^{48} - 390 q^{49} + 232 q^{50} - 164 q^{51} - 560 q^{52} - 492 q^{53} - 110 q^{54} - 22 q^{55} + 120 q^{56} - 1512 q^{57} - 192 q^{58} + 634 q^{59} + 632 q^{60} + 840 q^{61} + 134 q^{62} + 248 q^{63} + 224 q^{64} - 880 q^{65} + 286 q^{66} + 754 q^{67} + 640 q^{68} + 962 q^{69} + 284 q^{70} - 678 q^{71} - 744 q^{72} - 400 q^{73} + 6 q^{74} - 520 q^{75} + 432 q^{76} - 220 q^{77} - 440 q^{78} + 316 q^{79} - 1544 q^{80} - 1294 q^{81} + 512 q^{82} + 468 q^{83} - 736 q^{84} + 452 q^{85} - 156 q^{86} + 1200 q^{87} + 132 q^{88} - 1842 q^{89} + 1532 q^{90} + 1280 q^{91} - 40 q^{92} - 638 q^{93} - 992 q^{94} + 2952 q^{95} - 952 q^{96} + 2194 q^{97} - 870 q^{98} - 484 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(11))\) 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
11.4.a.a 11.a 1.a $2$ $0.649$ \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(2\) \(20\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(-1-4\beta )q^{3}+(-4+2\beta )q^{4}+\cdots\)