Properties

Label 11.3.d
Level $11$
Weight $3$
Character orbit 11.d
Rep. character $\chi_{11}(2,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $4$
Newform subspaces $1$
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: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
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

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

Decomposition of \(S_{3}^{\mathrm{new}}(11, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
11.3.d.a 11.d 11.d $4$ $0.300$ \(\Q(\zeta_{10})\) None \(-5\) \(0\) \(-4\) \(10\) $\mathrm{SU}(2)[C_{10}]$ \(q+(-2\zeta_{10}+2\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-2+\cdots)q^{3}+\cdots\)