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Properties

Label 35.10.j
Level $35$
Weight $10$
Character orbit 35.j
Rep. character $\chi_{35}(4,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $68$
Newform subspaces $1$
Sturm bound $40$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 10 \)
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: \(40\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(35, [\chi])\).

Total New Old
Modular forms 76 76 0
Cusp forms 68 68 0
Eisenstein series 8 8 0

Trace form

\( 68 q + 8190 q^{4} + 283 q^{5} + 3768 q^{6} + 212878 q^{9} - 35564 q^{10} + 20580 q^{11} + 245558 q^{14} - 251762 q^{15} - 1565382 q^{16} + 1617200 q^{19} + 384184 q^{20} - 392432 q^{21} + 1749444 q^{24}+ \cdots + 3178969668 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{10}^{\mathrm{new}}(35, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
35.10.j.a 35.j 35.j $68$ $18.026$ None 35.10.j.a \(0\) \(0\) \(283\) \(0\) $\mathrm{SU}(2)[C_{6}]$