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Properties

Label 35.6.k
Level $35$
Weight $6$
Character orbit 35.k
Rep. character $\chi_{35}(3,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $72$
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.k (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
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 88 88 0
Cusp forms 72 72 0
Eisenstein series 16 16 0

Trace form

\( 72 q - 2 q^{2} - 6 q^{3} + 60 q^{5} + 190 q^{7} + 356 q^{8} - 1494 q^{10} - 364 q^{11} + 186 q^{12} - 2972 q^{15} + 5380 q^{16} - 1608 q^{17} - 1916 q^{18} + 6132 q^{21} + 1048 q^{22} - 9670 q^{23} + 328 q^{25}+ \cdots + 345498 q^{98}+O(q^{100}) \) 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.k.a 35.k 35.k $72$ $5.613$ None 35.6.k.a \(-2\) \(-6\) \(60\) \(190\) $\mathrm{SU}(2)[C_{12}]$