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Properties

Label 35.3.l
Level $35$
Weight $3$
Character orbit 35.l
Rep. character $\chi_{35}(2,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $24$
Newform subspaces $1$
Sturm bound $12$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 35.l (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(35, [\chi])\).

Total New Old
Modular forms 40 40 0
Cusp forms 24 24 0
Eisenstein series 16 16 0

Trace form

\( 24 q - 2 q^{2} - 2 q^{3} - 4 q^{5} - 6 q^{7} - 36 q^{8} + 14 q^{10} - 24 q^{11} - 46 q^{12} - 8 q^{13} + 52 q^{15} + 20 q^{16} - 48 q^{17} - 4 q^{18} - 72 q^{20} + 56 q^{21} + 104 q^{22} - 86 q^{23} - 16 q^{25}+ \cdots + 482 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(35, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
35.3.l.a 35.l 35.l $24$ $0.954$ None 35.3.l.a \(-2\) \(-2\) \(-4\) \(-6\) $\mathrm{SU}(2)[C_{12}]$