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 $3$

Related objects

Downloads

Learn more

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

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

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.i.a \(2\) \(1.118\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(1\) \(5\) \(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}+\cdots\)
140.2.i.b \(2\) \(1.118\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(1\) \(1\) \(q+(3-3\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)

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

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