Properties

Label 140.2.c
Level $140$
Weight $2$
Character orbit 140.c
Rep. character $\chi_{140}(139,\cdot)$
Character field $\Q$
Dimension $20$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 140 \)
Character field: \(\Q\)
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 28 28 0
Cusp forms 20 20 0
Eisenstein series 8 8 0

Trace form

\( 20 q - 4 q^{4} - 20 q^{9} + O(q^{10}) \) \( 20 q - 4 q^{4} - 20 q^{9} - 16 q^{14} + 4 q^{16} + 12 q^{21} - 12 q^{25} + 36 q^{30} - 28 q^{36} + 32 q^{44} - 40 q^{46} + 8 q^{49} - 12 q^{50} - 44 q^{56} + 44 q^{60} - 4 q^{64} - 32 q^{65} + 20 q^{70} + 88 q^{74} + 28 q^{81} + 80 q^{84} - 56 q^{85} - 32 q^{86} + O(q^{100}) \)

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.c.a 140.c 140.c $4$ $1.118$ \(\Q(\sqrt{2}, \sqrt{-5})\) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{2}q^{2}+(-2\beta _{1}-\beta _{2})q^{3}+2q^{4}+\cdots\)
140.2.c.b 140.c 140.c $16$ $1.118$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}-\beta _{9}q^{3}+(-1+\beta _{6})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)