Properties

Label 140.1.p
Level 140
Weight 1
Character orbit p
Rep. character \(\chi_{140}(39,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 4
Newforms 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: \(\Q(\zeta_{6})\)
Newforms: \( 2 \)
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

\( 4q - 2q^{4} - 2q^{5} - 4q^{6} + O(q^{10}) \) \( 4q - 2q^{4} - 2q^{5} - 4q^{6} + 4q^{14} - 2q^{16} + 4q^{20} + 2q^{21} + 2q^{24} - 2q^{25} - 4q^{29} + 2q^{30} - 4q^{41} + 2q^{46} - 2q^{49} - 2q^{54} - 2q^{56} + 2q^{61} + 4q^{64} + 4q^{69} - 2q^{70} - 2q^{80} + 2q^{81} - 4q^{84} + 2q^{86} + 2q^{89} - 4q^{94} + 2q^{96} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(140, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
140.1.p.a \(2\) \(0.070\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-5}) \) None \(-1\) \(1\) \(-1\) \(-1\) \(q-\zeta_{6}q^{2}-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+\cdots\)
140.1.p.b \(2\) \(0.070\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-5}) \) None \(1\) \(-1\) \(-1\) \(1\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+\cdots\)