Properties

Label 140.2.k
Level $140$
Weight $2$
Character orbit 140.k
Rep. character $\chi_{140}(43,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $36$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 140.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 56 36 20
Cusp forms 40 36 4
Eisenstein series 16 0 16

Trace form

\( 36 q - 8 q^{6} + O(q^{10}) \) \( 36 q - 8 q^{6} - 16 q^{10} - 16 q^{12} - 4 q^{13} - 8 q^{16} - 20 q^{17} + 28 q^{18} + 20 q^{20} + 4 q^{22} - 20 q^{25} - 32 q^{26} - 4 q^{30} + 20 q^{37} - 36 q^{40} - 20 q^{42} + 20 q^{45} + 16 q^{46} - 24 q^{48} + 40 q^{50} + 16 q^{52} - 44 q^{53} - 24 q^{56} - 16 q^{57} - 4 q^{58} + 40 q^{60} - 64 q^{61} + 40 q^{62} + 4 q^{65} + 32 q^{66} + 80 q^{68} + 80 q^{72} + 52 q^{73} + 8 q^{76} - 76 q^{78} - 20 q^{80} - 36 q^{81} + 56 q^{82} - 20 q^{85} + 56 q^{86} - 40 q^{88} - 16 q^{90} - 56 q^{92} + 32 q^{93} + 120 q^{96} + 20 q^{97} + O(q^{100}) \)

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.k.a 140.k 20.e $36$ $1.118$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(140, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(140, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)