Properties

Label 35.2.e
Level 35
Weight 2
Character orbit e
Rep. character \(\chi_{35}(11,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 4
Newforms 1
Sturm bound 8
Trace bound 0

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Defining parameters

Level: \( N \) = \( 35 = 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 35.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newforms: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(35, [\chi])\).

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

Trace form

\(4q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut 6q^{12} \) \(\mathstrut -\mathstrut 8q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 4q^{15} \) \(\mathstrut -\mathstrut 6q^{16} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut +\mathstrut 8q^{18} \) \(\mathstrut +\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 14q^{21} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut +\mathstrut 2q^{23} \) \(\mathstrut -\mathstrut 2q^{24} \) \(\mathstrut -\mathstrut 2q^{25} \) \(\mathstrut +\mathstrut 12q^{26} \) \(\mathstrut +\mathstrut 4q^{27} \) \(\mathstrut -\mathstrut 22q^{28} \) \(\mathstrut -\mathstrut 4q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 12q^{31} \) \(\mathstrut +\mathstrut 6q^{32} \) \(\mathstrut -\mathstrut 12q^{33} \) \(\mathstrut +\mathstrut 24q^{34} \) \(\mathstrut -\mathstrut 4q^{35} \) \(\mathstrut -\mathstrut 32q^{36} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut -\mathstrut 6q^{40} \) \(\mathstrut -\mathstrut 20q^{41} \) \(\mathstrut -\mathstrut 2q^{42} \) \(\mathstrut +\mathstrut 20q^{43} \) \(\mathstrut +\mathstrut 12q^{44} \) \(\mathstrut -\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 4q^{47} \) \(\mathstrut +\mathstrut 12q^{48} \) \(\mathstrut +\mathstrut 10q^{49} \) \(\mathstrut +\mathstrut 4q^{50} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut +\mathstrut 20q^{52} \) \(\mathstrut +\mathstrut 8q^{53} \) \(\mathstrut -\mathstrut 6q^{54} \) \(\mathstrut +\mathstrut 8q^{55} \) \(\mathstrut +\mathstrut 18q^{56} \) \(\mathstrut -\mathstrut 16q^{57} \) \(\mathstrut +\mathstrut 2q^{58} \) \(\mathstrut +\mathstrut 8q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut +\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 24q^{62} \) \(\mathstrut -\mathstrut 28q^{64} \) \(\mathstrut +\mathstrut 4q^{65} \) \(\mathstrut +\mathstrut 4q^{66} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 20q^{68} \) \(\mathstrut -\mathstrut 12q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 16q^{71} \) \(\mathstrut +\mathstrut 8q^{72} \) \(\mathstrut -\mathstrut 4q^{73} \) \(\mathstrut -\mathstrut 2q^{75} \) \(\mathstrut +\mathstrut 32q^{76} \) \(\mathstrut +\mathstrut 28q^{77} \) \(\mathstrut +\mathstrut 8q^{78} \) \(\mathstrut -\mathstrut 24q^{79} \) \(\mathstrut -\mathstrut 6q^{80} \) \(\mathstrut +\mathstrut 2q^{81} \) \(\mathstrut +\mathstrut 18q^{82} \) \(\mathstrut +\mathstrut 4q^{83} \) \(\mathstrut +\mathstrut 12q^{84} \) \(\mathstrut +\mathstrut 8q^{85} \) \(\mathstrut -\mathstrut 6q^{86} \) \(\mathstrut +\mathstrut 2q^{87} \) \(\mathstrut -\mathstrut 4q^{88} \) \(\mathstrut +\mathstrut 6q^{89} \) \(\mathstrut -\mathstrut 16q^{90} \) \(\mathstrut -\mathstrut 28q^{91} \) \(\mathstrut +\mathstrut 12q^{92} \) \(\mathstrut +\mathstrut 12q^{93} \) \(\mathstrut -\mathstrut 4q^{94} \) \(\mathstrut +\mathstrut 10q^{96} \) \(\mathstrut +\mathstrut 24q^{97} \) \(\mathstrut -\mathstrut 14q^{98} \) \(\mathstrut +\mathstrut 32q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(35, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
35.2.e.a \(4\) \(0.279\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(-2\) \(-2\) \(2\) \(q+(-1+\beta _{1}-\beta _{2})q^{2}+(\beta _{1}+\beta _{2}+\beta _{3})q^{3}+\cdots\)