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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
35.2.e.a 35.e 7.c $4$ $0.279$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(-2\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1}-\beta _{2})q^{2}+(\beta _{1}+\beta _{2}+\beta _{3})q^{3}+\cdots\)