Properties

Label 35.2.b
Level $35$
Weight $2$
Character orbit 35.b
Rep. character $\chi_{35}(29,\cdot)$
Character field $\Q$
Dimension $2$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
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 6 2 4
Cusp forms 2 2 0
Eisenstein series 4 0 4

Trace form

\( 2 q - 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{9} + O(q^{10}) \) \( 2 q - 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{9} + 4 q^{10} - 6 q^{11} + 4 q^{14} - 2 q^{15} - 8 q^{16} + 8 q^{20} - 2 q^{21} + 6 q^{25} + 4 q^{26} + 10 q^{29} - 8 q^{30} + 4 q^{31} - 28 q^{34} - 2 q^{35} - 8 q^{36} - 2 q^{39} + 4 q^{41} + 12 q^{44} - 8 q^{45} + 24 q^{46} - 2 q^{49} - 16 q^{50} + 14 q^{51} + 20 q^{54} + 12 q^{55} - 20 q^{59} + 4 q^{60} - 16 q^{61} + 16 q^{64} - 2 q^{65} - 12 q^{66} - 12 q^{69} - 8 q^{70} - 16 q^{71} - 8 q^{74} + 8 q^{75} + 10 q^{79} + 16 q^{80} + 2 q^{81} + 4 q^{84} + 14 q^{85} - 16 q^{86} + 8 q^{90} - 2 q^{91} + 12 q^{94} - 16 q^{96} - 12 q^{99} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
35.2.b.a 35.b 5.b $2$ $0.279$ \(\Q(\sqrt{-1}) \) None 35.2.b.a \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}-iq^{3}-2q^{4}+(-2-i)q^{5}+\cdots\)