Properties

Label 14.3.d
Level 14
Weight 3
Character orbit d
Rep. character \(\chi_{14}(3,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 4
Newforms 1
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 14.d (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newforms: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(14, [\chi])\).

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

Trace form

\(4q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 24q^{10} \) \(\mathstrut +\mathstrut 18q^{11} \) \(\mathstrut +\mathstrut 12q^{12} \) \(\mathstrut -\mathstrut 36q^{14} \) \(\mathstrut -\mathstrut 36q^{15} \) \(\mathstrut -\mathstrut 8q^{16} \) \(\mathstrut -\mathstrut 30q^{17} \) \(\mathstrut -\mathstrut 24q^{18} \) \(\mathstrut +\mathstrut 6q^{19} \) \(\mathstrut +\mathstrut 54q^{21} \) \(\mathstrut +\mathstrut 24q^{22} \) \(\mathstrut +\mathstrut 30q^{23} \) \(\mathstrut +\mathstrut 24q^{24} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut +\mathstrut 24q^{26} \) \(\mathstrut -\mathstrut 20q^{28} \) \(\mathstrut +\mathstrut 48q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut -\mathstrut 42q^{31} \) \(\mathstrut -\mathstrut 90q^{33} \) \(\mathstrut -\mathstrut 42q^{35} \) \(\mathstrut -\mathstrut 62q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut +\mathstrut 12q^{39} \) \(\mathstrut -\mathstrut 48q^{40} \) \(\mathstrut +\mathstrut 72q^{42} \) \(\mathstrut -\mathstrut 8q^{43} \) \(\mathstrut +\mathstrut 36q^{44} \) \(\mathstrut +\mathstrut 144q^{45} \) \(\mathstrut +\mathstrut 36q^{46} \) \(\mathstrut +\mathstrut 174q^{47} \) \(\mathstrut -\mathstrut 20q^{49} \) \(\mathstrut -\mathstrut 96q^{50} \) \(\mathstrut +\mathstrut 54q^{51} \) \(\mathstrut -\mathstrut 72q^{52} \) \(\mathstrut -\mathstrut 78q^{53} \) \(\mathstrut -\mathstrut 36q^{54} \) \(\mathstrut +\mathstrut 48q^{56} \) \(\mathstrut +\mathstrut 12q^{57} \) \(\mathstrut +\mathstrut 24q^{58} \) \(\mathstrut -\mathstrut 78q^{59} \) \(\mathstrut +\mathstrut 36q^{60} \) \(\mathstrut -\mathstrut 42q^{61} \) \(\mathstrut -\mathstrut 216q^{63} \) \(\mathstrut +\mathstrut 32q^{64} \) \(\mathstrut -\mathstrut 84q^{65} \) \(\mathstrut -\mathstrut 144q^{66} \) \(\mathstrut -\mathstrut 58q^{67} \) \(\mathstrut +\mathstrut 60q^{68} \) \(\mathstrut +\mathstrut 84q^{70} \) \(\mathstrut -\mathstrut 24q^{71} \) \(\mathstrut -\mathstrut 48q^{72} \) \(\mathstrut +\mathstrut 318q^{73} \) \(\mathstrut +\mathstrut 96q^{74} \) \(\mathstrut +\mathstrut 132q^{75} \) \(\mathstrut +\mathstrut 126q^{77} \) \(\mathstrut +\mathstrut 96q^{78} \) \(\mathstrut +\mathstrut 110q^{79} \) \(\mathstrut +\mathstrut 24q^{80} \) \(\mathstrut +\mathstrut 18q^{81} \) \(\mathstrut -\mathstrut 120q^{82} \) \(\mathstrut +\mathstrut 12q^{84} \) \(\mathstrut -\mathstrut 36q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut -\mathstrut 144q^{87} \) \(\mathstrut -\mathstrut 24q^{88} \) \(\mathstrut -\mathstrut 378q^{89} \) \(\mathstrut +\mathstrut 24q^{91} \) \(\mathstrut -\mathstrut 120q^{92} \) \(\mathstrut -\mathstrut 138q^{93} \) \(\mathstrut -\mathstrut 12q^{94} \) \(\mathstrut -\mathstrut 30q^{95} \) \(\mathstrut -\mathstrut 48q^{96} \) \(\mathstrut -\mathstrut 120q^{98} \) \(\mathstrut +\mathstrut 144q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(14, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
14.3.d.a \(4\) \(0.381\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-6\) \(-6\) \(8\) \(q+\beta _{1}q^{2}+(-2-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+\cdots\)