Properties

Label 140.2.g
Level $140$
Weight $2$
Character orbit 140.g
Rep. character $\chi_{140}(111,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $3$
Sturm bound $48$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 140.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(48\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(3\), \(19\)

Dimensions

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

Total New Old
Modular forms 28 16 12
Cusp forms 20 16 4
Eisenstein series 8 0 8

Trace form

\( 16q - 2q^{2} + 2q^{4} - 2q^{8} + 16q^{9} + O(q^{10}) \) \( 16q - 2q^{2} + 2q^{4} - 2q^{8} + 16q^{9} - 14q^{14} + 2q^{16} - 30q^{18} - 12q^{21} + 32q^{22} - 16q^{25} - 2q^{28} - 8q^{29} - 2q^{32} - 30q^{36} - 32q^{37} - 4q^{42} - 36q^{44} + 28q^{46} + 28q^{49} + 2q^{50} + 32q^{53} + 34q^{56} - 48q^{57} + 40q^{58} + 28q^{60} + 2q^{64} + 8q^{65} + 16q^{70} + 62q^{72} + 4q^{74} - 8q^{77} - 36q^{78} - 24q^{81} + 8q^{84} - 28q^{86} + 68q^{88} + 4q^{92} - 16q^{93} + 30q^{98} + O(q^{100}) \)

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.g.a \(4\) \(1.118\) \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
140.2.g.b \(4\) \(1.118\) \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
140.2.g.c \(8\) \(1.118\) 8.0.342102016.5 None \(2\) \(0\) \(0\) \(0\) \(q-\beta _{7}q^{2}+(-\beta _{4}+\beta _{6})q^{3}+(-\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots\)

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

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