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Properties

Label 11.8.a
Level $11$
Weight $8$
Character orbit 11.a
Rep. character $\chi_{11}(1,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $2$
Sturm bound $8$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 11.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(8\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(11))\).

Total New Old
Modular forms 8 6 2
Cusp forms 6 6 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
\(+\)\(4\)
\(-\)\(2\)

Trace form

\( 6 q - 8 q^{2} - 41 q^{3} + 500 q^{4} + 67 q^{5} + 862 q^{6} - 1058 q^{7} + 60 q^{8} + 1787 q^{9} + O(q^{10}) \) \( 6 q - 8 q^{2} - 41 q^{3} + 500 q^{4} + 67 q^{5} + 862 q^{6} - 1058 q^{7} + 60 q^{8} + 1787 q^{9} + 5750 q^{10} - 2662 q^{11} - 28288 q^{12} + 4594 q^{13} - 15236 q^{14} - 6149 q^{15} + 46376 q^{16} + 45832 q^{17} - 66886 q^{18} + 32564 q^{19} + 21128 q^{20} + 46906 q^{21} - 10648 q^{22} - 70501 q^{23} + 245964 q^{24} + 24731 q^{25} - 250916 q^{26} - 135695 q^{27} - 490704 q^{28} + 413118 q^{29} - 256826 q^{30} + 132691 q^{31} + 11192 q^{32} + 38599 q^{33} + 488 q^{34} + 639478 q^{35} + 815092 q^{36} - 749803 q^{37} - 801480 q^{38} - 1384652 q^{39} + 1781268 q^{40} + 6226 q^{41} + 1680964 q^{42} + 980414 q^{43} - 942348 q^{44} - 1851892 q^{45} + 4279846 q^{46} - 66568 q^{47} - 7055896 q^{48} + 53706 q^{49} - 3252718 q^{50} + 617266 q^{51} + 1514952 q^{52} + 2715144 q^{53} + 6445090 q^{54} - 1340317 q^{55} - 6062760 q^{56} + 3819120 q^{57} - 1046220 q^{58} - 7119907 q^{59} + 752912 q^{60} - 5708566 q^{61} + 6940534 q^{62} + 859244 q^{63} + 10607904 q^{64} + 5688520 q^{65} - 3000074 q^{66} - 3542943 q^{67} + 18917816 q^{68} + 4250597 q^{69} - 18308116 q^{70} - 4568007 q^{71} - 26184720 q^{72} + 12352174 q^{73} - 13520406 q^{74} + 9979160 q^{75} + 6867104 q^{76} - 1860738 q^{77} + 1427848 q^{78} + 4367742 q^{79} + 1481336 q^{80} - 10193266 q^{81} - 1752916 q^{82} - 6503706 q^{83} + 14049200 q^{84} + 3504482 q^{85} - 5562708 q^{86} - 9064920 q^{87} + 1197900 q^{88} + 4783221 q^{89} + 13795712 q^{90} + 3752424 q^{91} - 7320368 q^{92} - 1131947 q^{93} - 15632 q^{94} - 4528968 q^{95} + 19662920 q^{96} + 11357247 q^{97} + 24721536 q^{98} - 2474329 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(11))\) 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
11.8.a.a 11.a 1.a $2$ $3.436$ \(\Q(\sqrt{15}) \) None \(-8\) \(-6\) \(-470\) \(-1228\) $-$ $\mathrm{SU}(2)$ \(q+(-4+\beta )q^{2}+(-3-6\beta )q^{3}+(-52+\cdots)q^{4}+\cdots\)
11.8.a.b 11.a 1.a $4$ $3.436$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(-35\) \(537\) \(170\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(-9-\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\cdots\)