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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
140.2.s.a \(8\) \(1.118\) 8.0.3317760000.3 \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{2}+(\beta _{1}-\beta _{5})q^{3}-2\beta _{4}q^{4}-\beta _{7}q^{5}+\cdots\)
140.2.s.b \(32\) \(1.118\) None \(0\) \(0\) \(-6\) \(0\)