Properties

Label 140.2.q
Level $140$
Weight $2$
Character orbit 140.q
Rep. character $\chi_{140}(9,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $2$
Sturm bound $48$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 140.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(48\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 60 8 52
Cusp forms 36 8 28
Eisenstein series 24 0 24

Trace form

\( 8 q - q^{5} + O(q^{10}) \) \( 8 q - q^{5} + 6 q^{11} - 6 q^{15} - 2 q^{19} - 9 q^{25} - 4 q^{29} + 2 q^{31} + 5 q^{35} - 12 q^{39} - 60 q^{41} + 10 q^{49} - 18 q^{51} + 54 q^{55} + 2 q^{59} + 24 q^{61} + 16 q^{65} + 48 q^{69} + 24 q^{71} - 27 q^{75} + 14 q^{79} + 36 q^{81} - 10 q^{85} - 28 q^{89} + 20 q^{91} - 29 q^{95} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
140.2.q.a 140.q 35.j $4$ $1.118$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None 140.2.q.a \(0\) \(-6\) \(1\) \(-3\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\beta _{2})q^{3}+\beta _{1}q^{5}+(-\beta _{2}+\beta _{3})q^{7}+\cdots\)
140.2.q.b 140.q 35.j $4$ $1.118$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None 140.2.q.a \(0\) \(6\) \(-2\) \(3\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2-\beta _{2})q^{3}+(-1+\beta _{1}-\beta _{3})q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(140, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)