Properties

Label 140.2.m
Level $140$
Weight $2$
Character orbit 140.m
Rep. character $\chi_{140}(13,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $8$
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.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
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 60 8 52
Cusp forms 36 8 28
Eisenstein series 24 0 24

Trace form

\( 8q - 2q^{7} + O(q^{10}) \) \( 8q - 2q^{7} - 12q^{11} + 20q^{15} - 8q^{21} + 4q^{23} - 12q^{25} - 14q^{35} - 4q^{37} - 40q^{43} + 4q^{51} + 40q^{53} - 44q^{57} + 42q^{63} + 20q^{65} + 40q^{67} + 8q^{71} + 44q^{77} + 48q^{85} - 8q^{91} - 52q^{93} - 44q^{95} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
140.2.m.a \(8\) \(1.118\) 8.0.\(\cdots\).3 None \(0\) \(0\) \(0\) \(-2\) \(q+\beta _{1}q^{3}+(-\beta _{2}+\beta _{6})q^{5}+(\beta _{4}-\beta _{7})q^{7}+\cdots\)

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

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