Properties

Label 140.2.e
Level $140$
Weight $2$
Character orbit 140.e
Rep. character $\chi_{140}(29,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $48$
Trace bound $5$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 30 4 26
Cusp forms 18 4 14
Eisenstein series 12 0 12

Trace form

\( 4q - 2q^{5} - 6q^{9} + O(q^{10}) \) \( 4q - 2q^{5} - 6q^{9} + 6q^{11} - 6q^{15} + 8q^{19} + 6q^{21} - 2q^{29} - 20q^{31} - 2q^{35} - 6q^{39} + 30q^{45} - 4q^{49} - 30q^{51} - 12q^{55} + 28q^{59} - 12q^{61} + 14q^{65} - 12q^{69} + 24q^{71} + 24q^{75} + 22q^{79} + 36q^{81} - 26q^{85} + 4q^{89} + 10q^{91} - 40q^{95} - 36q^{99} + O(q^{100}) \)

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.e.a \(2\) \(1.118\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+3iq^{3}+(-2+i)q^{5}-iq^{7}-6q^{9}+\cdots\)
140.2.e.b \(2\) \(1.118\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(1+2i)q^{5}+iq^{7}+3q^{9}-4iq^{13}+\cdots\)

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

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