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Properties

Label 140.2.s
Level $140$
Weight $2$
Character orbit 140.s
Rep. character $\chi_{140}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $40$
Newform subspaces $2$
Sturm bound $48$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 140.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 140 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(48\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(140, [\chi])\).

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

Trace form

\( 40 q - 2 q^{4} - 6 q^{5} + 8 q^{9} + O(q^{10}) \) \( 40 q - 2 q^{4} - 6 q^{5} + 8 q^{9} - 12 q^{10} - 2 q^{14} + 2 q^{16} - 24 q^{21} - 24 q^{24} - 6 q^{25} - 18 q^{26} - 24 q^{29} - 6 q^{30} - 44 q^{36} + 42 q^{40} - 26 q^{44} - 24 q^{45} - 26 q^{46} - 8 q^{49} + 36 q^{50} + 84 q^{54} + 8 q^{56} + 4 q^{60} - 12 q^{61} + 100 q^{64} - 4 q^{65} - 24 q^{66} + 46 q^{70} + 14 q^{74} + 72 q^{80} + 56 q^{81} + 16 q^{84} + 20 q^{85} - 28 q^{86} - 72 q^{89} + 30 q^{94} + 12 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(140, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
140.2.s.a 140.s 140.s $8$ $1.118$ 8.0.3317760000.3 \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+\beta _{5}q^{2}+(\beta _{1}-\beta _{5})q^{3}-2\beta _{4}q^{4}-\beta _{7}q^{5}+\cdots\)
140.2.s.b 140.s 140.s $32$ $1.118$ None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{6}]$