Properties

Label 11.5.b
Level 11
Weight 5
Character orbit b
Rep. character \(\chi_{11}(10,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 2
Sturm bound 5
Trace bound 1

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Defining parameters

Level: \( N \) = \( 11 \)
Weight: \( k \) = \( 5 \)
Character orbit: \([\chi]\) = 11.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 11 \)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(5\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(11, [\chi])\).

Total New Old
Modular forms 5 5 0
Cusp forms 3 3 0
Eisenstein series 2 2 0

Trace form

\( 3q + q^{3} - 12q^{4} + 13q^{5} - 176q^{9} + O(q^{10}) \) \( 3q + q^{3} - 12q^{4} + 13q^{5} - 176q^{9} + 143q^{11} + 196q^{12} + 600q^{14} - 529q^{15} - 312q^{16} - 1652q^{20} + 1320q^{22} + 721q^{23} + 2448q^{25} - 2040q^{26} + 127q^{27} - 3279q^{31} + 781q^{33} + 2520q^{34} + 1504q^{36} - 1779q^{37} - 1080q^{38} - 1800q^{42} + 1628q^{44} - 2896q^{45} + 1486q^{47} + 3496q^{48} + 1203q^{49} + 8326q^{53} - 5247q^{55} + 1200q^{56} - 13920q^{58} - 239q^{59} - 2884q^{60} + 10128q^{64} - 3960q^{66} - 13359q^{67} - 493q^{69} + 18600q^{70} + 14401q^{71} + 10416q^{75} - 13200q^{77} + 6120q^{78} - 30152q^{80} + 5965q^{81} - 11640q^{82} + 13200q^{86} + 2640q^{88} - 15779q^{89} + 20400q^{91} - 5084q^{92} + 4307q^{93} - 1299q^{97} - 5456q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(11, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
11.5.b.a \(1\) \(1.137\) \(\Q\) \(\Q(\sqrt{-11}) \) \(0\) \(7\) \(-49\) \(0\) \(q+7q^{3}+2^{4}q^{4}-7^{2}q^{5}-2^{5}q^{9}+11^{2}q^{11}+\cdots\)
11.5.b.b \(2\) \(1.137\) \(\Q(\sqrt{-30}) \) None \(0\) \(-6\) \(62\) \(0\) \(q+\beta q^{2}-3q^{3}-14q^{4}+31q^{5}-3\beta q^{6}+\cdots\)