Properties

Label 11.3.d
Level 11
Weight 3
Character orbit d
Rep. character \(\chi_{11}(2,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 4
Newforms 1
Sturm bound 3
Trace bound 0

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Defining parameters

Level: \( N \) = \( 11 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 11.d (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 11 \)
Character field: \(\Q(\zeta_{10})\)
Newforms: \( 1 \)
Sturm bound: \(3\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(11, [\chi])\).

Total New Old
Modular forms 12 12 0
Cusp forms 4 4 0
Eisenstein series 8 8 0

Trace form

\(4q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 9q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 15q^{6} \) \(\mathstrut +\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut -\mathstrut 11q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 9q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 15q^{6} \) \(\mathstrut +\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut -\mathstrut 11q^{9} \) \(\mathstrut +\mathstrut q^{11} \) \(\mathstrut -\mathstrut 30q^{12} \) \(\mathstrut -\mathstrut 20q^{13} \) \(\mathstrut -\mathstrut 10q^{14} \) \(\mathstrut +\mathstrut 19q^{16} \) \(\mathstrut +\mathstrut 30q^{18} \) \(\mathstrut +\mathstrut 25q^{19} \) \(\mathstrut +\mathstrut 44q^{20} \) \(\mathstrut -\mathstrut 35q^{22} \) \(\mathstrut -\mathstrut 20q^{23} \) \(\mathstrut +\mathstrut 5q^{24} \) \(\mathstrut +\mathstrut 9q^{25} \) \(\mathstrut -\mathstrut 10q^{26} \) \(\mathstrut +\mathstrut 15q^{27} \) \(\mathstrut -\mathstrut 60q^{28} \) \(\mathstrut -\mathstrut 40q^{29} \) \(\mathstrut -\mathstrut 80q^{30} \) \(\mathstrut -\mathstrut 58q^{31} \) \(\mathstrut +\mathstrut 65q^{33} \) \(\mathstrut +\mathstrut 130q^{34} \) \(\mathstrut +\mathstrut 80q^{35} \) \(\mathstrut +\mathstrut 26q^{36} \) \(\mathstrut +\mathstrut 90q^{37} \) \(\mathstrut -\mathstrut 60q^{38} \) \(\mathstrut +\mathstrut 50q^{39} \) \(\mathstrut -\mathstrut 60q^{40} \) \(\mathstrut -\mathstrut 80q^{41} \) \(\mathstrut -\mathstrut 10q^{42} \) \(\mathstrut +\mathstrut 24q^{44} \) \(\mathstrut -\mathstrut 24q^{45} \) \(\mathstrut +\mathstrut 30q^{46} \) \(\mathstrut -\mathstrut 30q^{47} \) \(\mathstrut -\mathstrut 40q^{48} \) \(\mathstrut -\mathstrut 109q^{49} \) \(\mathstrut -\mathstrut 45q^{50} \) \(\mathstrut -\mathstrut 195q^{51} \) \(\mathstrut +\mathstrut 110q^{52} \) \(\mathstrut +\mathstrut 120q^{53} \) \(\mathstrut -\mathstrut 76q^{55} \) \(\mathstrut +\mathstrut 100q^{56} \) \(\mathstrut +\mathstrut 45q^{57} \) \(\mathstrut +\mathstrut 40q^{58} \) \(\mathstrut +\mathstrut 23q^{59} \) \(\mathstrut +\mathstrut 140q^{60} \) \(\mathstrut +\mathstrut 10q^{61} \) \(\mathstrut +\mathstrut 200q^{62} \) \(\mathstrut +\mathstrut 90q^{63} \) \(\mathstrut -\mathstrut 149q^{64} \) \(\mathstrut +\mathstrut 90q^{66} \) \(\mathstrut -\mathstrut 230q^{67} \) \(\mathstrut -\mathstrut 260q^{68} \) \(\mathstrut -\mathstrut 10q^{69} \) \(\mathstrut -\mathstrut 40q^{70} \) \(\mathstrut +\mathstrut 148q^{71} \) \(\mathstrut -\mathstrut 95q^{72} \) \(\mathstrut +\mathstrut 300q^{73} \) \(\mathstrut -\mathstrut 270q^{74} \) \(\mathstrut +\mathstrut 45q^{75} \) \(\mathstrut -\mathstrut 200q^{77} \) \(\mathstrut -\mathstrut 200q^{78} \) \(\mathstrut +\mathstrut 70q^{79} \) \(\mathstrut -\mathstrut 84q^{80} \) \(\mathstrut -\mathstrut 116q^{81} \) \(\mathstrut +\mathstrut 25q^{82} \) \(\mathstrut +\mathstrut 225q^{83} \) \(\mathstrut +\mathstrut 90q^{84} \) \(\mathstrut +\mathstrut 260q^{85} \) \(\mathstrut +\mathstrut 175q^{86} \) \(\mathstrut +\mathstrut 55q^{88} \) \(\mathstrut +\mathstrut 122q^{89} \) \(\mathstrut -\mathstrut 20q^{90} \) \(\mathstrut -\mathstrut 80q^{91} \) \(\mathstrut +\mathstrut 40q^{92} \) \(\mathstrut -\mathstrut 200q^{93} \) \(\mathstrut +\mathstrut 120q^{94} \) \(\mathstrut -\mathstrut 100q^{95} \) \(\mathstrut +\mathstrut 340q^{96} \) \(\mathstrut -\mathstrut 165q^{97} \) \(\mathstrut +\mathstrut 31q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(11, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
11.3.d.a \(4\) \(0.300\) \(\Q(\zeta_{10})\) None \(-5\) \(0\) \(-4\) \(10\) \(q+(-2\zeta_{10}+2\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-2+\cdots)q^{3}+\cdots\)