Properties

Label 140.2.c
Level $140$
Weight $2$
Character orbit 140.c
Rep. character $\chi_{140}(139,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $2$
Sturm bound $48$
Trace bound $1$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 28 28 0
Cusp forms 20 20 0
Eisenstein series 8 8 0

Trace form

\( 20q - 4q^{4} - 20q^{9} + O(q^{10}) \) \( 20q - 4q^{4} - 20q^{9} - 16q^{14} + 4q^{16} + 12q^{21} - 12q^{25} + 36q^{30} - 28q^{36} + 32q^{44} - 40q^{46} + 8q^{49} - 12q^{50} - 44q^{56} + 44q^{60} - 4q^{64} - 32q^{65} + 20q^{70} + 88q^{74} + 28q^{81} + 80q^{84} - 56q^{85} - 32q^{86} + O(q^{100}) \)

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.c.a \(4\) \(1.118\) \(\Q(\sqrt{2}, \sqrt{-5})\) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+(-2\beta _{1}-\beta _{2})q^{3}+2q^{4}+\cdots\)
140.2.c.b \(16\) \(1.118\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}-\beta _{9}q^{3}+(-1+\beta _{6})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)