Properties

Label 35.4.k
Level $35$
Weight $4$
Character orbit 35.k
Rep. character $\chi_{35}(3,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $40$
Newform subspaces $1$
Sturm bound $16$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
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: \(16\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(35, [\chi])\).

Total New Old
Modular forms 56 56 0
Cusp forms 40 40 0
Eisenstein series 16 16 0

Trace form

\( 40 q - 2 q^{2} - 6 q^{3} - 30 q^{5} + 4 q^{7} - 124 q^{8} + 66 q^{10} - 40 q^{11} + 42 q^{12} + 328 q^{15} + 68 q^{16} - 150 q^{17} + 4 q^{18} + 36 q^{21} - 600 q^{22} + 134 q^{23} - 42 q^{25} - 468 q^{26}+ \cdots - 7782 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(35, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
35.4.k.a 35.k 35.k $40$ $2.065$ None 35.4.k.a \(-2\) \(-6\) \(-30\) \(4\) $\mathrm{SU}(2)[C_{12}]$