Properties

Label 35.2.e
Level $35$
Weight $2$
Character orbit 35.e
Rep. character $\chi_{35}(11,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $4$
Newform subspaces $1$
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: \(\Q(\zeta_{3})\)
Newform subspaces: \( 1 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(35, [\chi])\) into newform subspaces

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 \(-2\) \(-2\) \(-2\) \(2\) \(q+(-1+\beta _{1}-\beta _{2})q^{2}+(\beta _{1}+\beta _{2}+\beta _{3})q^{3}+\cdots\)