Properties

Label 140.2.o
Level $140$
Weight $2$
Character orbit 140.o
Rep. character $\chi_{140}(31,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 140.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 56 32 24
Cusp forms 40 32 8
Eisenstein series 16 0 16

Trace form

\( 32q + 2q^{2} - 2q^{4} - 4q^{8} - 16q^{9} + O(q^{10}) \) \( 32q + 2q^{2} - 2q^{4} - 4q^{8} - 16q^{9} - 30q^{12} + 2q^{14} - 14q^{16} - 12q^{21} - 8q^{22} + 36q^{24} + 16q^{25} + 30q^{26} + 2q^{28} - 40q^{29} + 2q^{32} + 60q^{36} + 8q^{37} - 60q^{38} - 62q^{42} - 18q^{44} + 12q^{45} + 2q^{46} - 16q^{49} + 4q^{50} - 36q^{52} - 8q^{53} + 12q^{54} - 4q^{56} + 48q^{57} + 2q^{58} + 14q^{60} + 24q^{61} + 4q^{64} + 4q^{65} + 24q^{66} + 60q^{68} - 4q^{70} + 4q^{72} - 72q^{73} + 38q^{74} - 40q^{77} + 120q^{78} - 36q^{81} + 42q^{82} - 20q^{84} + 28q^{86} + 4q^{88} - 60q^{89} - 4q^{92} - 8q^{93} + 18q^{94} - 60q^{96} + 78q^{98} + O(q^{100}) \)

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.o.a \(32\) \(1.118\) None \(2\) \(0\) \(0\) \(0\)

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

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