Properties

Label 140.2.i
Level $140$
Weight $2$
Character orbit 140.i
Rep. character $\chi_{140}(81,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $4$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
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 4 56
Cusp forms 36 4 32
Eisenstein series 24 0 24

Trace form

\( 4 q + 2 q^{3} + 2 q^{5} + 6 q^{7} - 4 q^{9} + O(q^{10}) \) \( 4 q + 2 q^{3} + 2 q^{5} + 6 q^{7} - 4 q^{9} - 4 q^{11} - 8 q^{13} + 4 q^{15} + 4 q^{17} - 8 q^{19} + 14 q^{21} + 6 q^{23} - 2 q^{25} - 28 q^{27} + 12 q^{29} - 4 q^{31} - 12 q^{33} - 16 q^{37} - 20 q^{39} + 4 q^{41} + 12 q^{43} + 4 q^{45} - 8 q^{47} - 2 q^{49} + 12 q^{51} - 16 q^{53} - 8 q^{55} + 16 q^{57} + 8 q^{59} - 6 q^{61} + 32 q^{63} - 4 q^{65} + 10 q^{67} + 60 q^{69} + 16 q^{71} - 4 q^{73} + 2 q^{75} + 4 q^{77} - 10 q^{81} + 4 q^{83} + 8 q^{85} + 6 q^{87} - 10 q^{89} + 4 q^{91} + 4 q^{93} + 8 q^{95} - 40 q^{97} - 48 q^{99} + O(q^{100}) \)

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.i.a 140.i 7.c $2$ $1.118$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(1\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}+\cdots\)
140.2.i.b 140.i 7.c $2$ $1.118$ \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(3-3\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(140, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)