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Properties

Label 140.1.p
Level $140$
Weight $1$
Character orbit 140.p
Rep. character $\chi_{140}(39,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $2$
Sturm bound $24$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 140.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 140 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(140, [\chi])\).

Total New Old
Modular forms 12 12 0
Cusp forms 4 4 0
Eisenstein series 8 8 0

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4 q - 2 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{14} - 2 q^{16} + 4 q^{20} + 2 q^{21} + 2 q^{24} - 2 q^{25} - 4 q^{29} + 2 q^{30} - 4 q^{41} + 2 q^{46} - 2 q^{49} - 2 q^{54} - 2 q^{56} + 2 q^{61} + 4 q^{64} + 4 q^{69}+ \cdots + 2 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(140, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
140.1.p.a 140.p 140.p $2$ $0.070$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-5}) \) None 140.1.p.a \(-1\) \(1\) \(-1\) \(-1\) \(q-\zeta_{6}q^{2}-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+\cdots\)
140.1.p.b 140.p 140.p $2$ $0.070$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-5}) \) None 140.1.p.a \(1\) \(-1\) \(-1\) \(1\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+\cdots\)