Properties

Label 140.2.g
Level $140$
Weight $2$
Character orbit 140.g
Rep. character $\chi_{140}(111,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $3$
Sturm bound $48$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 140.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(48\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(3\), \(19\)

Dimensions

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

Total New Old
Modular forms 28 16 12
Cusp forms 20 16 4
Eisenstein series 8 0 8

Trace form

\( 16 q - 2 q^{2} + 2 q^{4} - 2 q^{8} + 16 q^{9} + O(q^{10}) \) \( 16 q - 2 q^{2} + 2 q^{4} - 2 q^{8} + 16 q^{9} - 14 q^{14} + 2 q^{16} - 30 q^{18} - 12 q^{21} + 32 q^{22} - 16 q^{25} - 2 q^{28} - 8 q^{29} - 2 q^{32} - 30 q^{36} - 32 q^{37} - 4 q^{42} - 36 q^{44} + 28 q^{46} + 28 q^{49} + 2 q^{50} + 32 q^{53} + 34 q^{56} - 48 q^{57} + 40 q^{58} + 28 q^{60} + 2 q^{64} + 8 q^{65} + 16 q^{70} + 62 q^{72} + 4 q^{74} - 8 q^{77} - 36 q^{78} - 24 q^{81} + 8 q^{84} - 28 q^{86} + 68 q^{88} + 4 q^{92} - 16 q^{93} + 30 q^{98} + O(q^{100}) \)

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.g.a 140.g 28.d $4$ $1.118$ \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
140.2.g.b 140.g 28.d $4$ $1.118$ \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
140.2.g.c 140.g 28.d $8$ $1.118$ 8.0.342102016.5 None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{7}q^{2}+(-\beta _{4}+\beta _{6})q^{3}+(-\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots\)

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

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