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

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

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.q.a \(4\) \(1.118\) \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(0\) \(-6\) \(1\) \(-3\) \(q+(-1-\beta _{2})q^{3}+\beta _{1}q^{5}+(-\beta _{2}+\beta _{3})q^{7}+\cdots\)
140.2.q.b \(4\) \(1.118\) \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(0\) \(6\) \(-2\) \(3\) \(q+(2-\beta _{2})q^{3}+(-1+\beta _{1}-\beta _{3})q^{5}+\cdots\)

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

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