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Properties

Label 35.6.j
Level $35$
Weight $6$
Character orbit 35.j
Rep. character $\chi_{35}(4,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $36$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 35.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(35, [\chi])\).

Total New Old
Modular forms 44 44 0
Cusp forms 36 36 0
Eisenstein series 8 8 0

Trace form

\( 36 q + 254 q^{4} - 12 q^{5} + 72 q^{6} + 832 q^{9} - 84 q^{10} - 360 q^{11} + 158 q^{14} + 688 q^{15} - 2630 q^{16} + 3316 q^{19} - 1096 q^{20} + 1594 q^{21} + 3300 q^{24} - 404 q^{25} - 13570 q^{26} + 16004 q^{29}+ \cdots - 120816 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(35, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
35.6.j.a 35.j 35.j $36$ $5.613$ None 35.6.j.a \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{6}]$