Properties

Label 140.2.a
Level $140$
Weight $2$
Character orbit 140.a
Rep. character $\chi_{140}(1,\cdot)$
Character field $\Q$
Dimension $2$
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.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(48\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(140))\).

Total New Old
Modular forms 30 2 28
Cusp forms 19 2 17
Eisenstein series 11 0 11

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(5\)\(7\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(2\)

Trace form

\( 2 q + 4 q^{3} + 4 q^{9} + O(q^{10}) \) \( 2 q + 4 q^{3} + 4 q^{9} - 2 q^{11} - 4 q^{13} - 2 q^{15} - 4 q^{17} + 8 q^{19} - 2 q^{21} + 2 q^{25} + 4 q^{27} - 18 q^{29} + 4 q^{31} - 12 q^{33} + 2 q^{35} - 8 q^{37} - 10 q^{39} - 4 q^{41} + 12 q^{43} - 8 q^{45} - 4 q^{47} + 2 q^{49} - 6 q^{51} + 4 q^{53} + 8 q^{55} + 20 q^{57} + 4 q^{59} - 8 q^{63} + 2 q^{65} + 20 q^{67} + 12 q^{69} + 8 q^{71} + 16 q^{73} + 4 q^{75} + 8 q^{77} + 18 q^{79} + 10 q^{81} - 16 q^{83} - 2 q^{85} - 36 q^{87} + 16 q^{89} + 2 q^{91} - 4 q^{93} - 4 q^{95} + 4 q^{97} - 36 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(140))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 7
140.2.a.a $1$ $1.118$ \(\Q\) None \(0\) \(1\) \(1\) \(1\) $-$ $-$ $-$ \(q+q^{3}+q^{5}+q^{7}-2q^{9}+3q^{11}-q^{13}+\cdots\)
140.2.a.b $1$ $1.118$ \(\Q\) None \(0\) \(3\) \(-1\) \(-1\) $-$ $+$ $+$ \(q+3q^{3}-q^{5}-q^{7}+6q^{9}-5q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(140))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(140)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 2}\)