Properties

Label 160.2.o
Level $160$
Weight $2$
Character orbit 160.o
Rep. character $\chi_{160}(47,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $8$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 160.o (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(160, [\chi])\).

Total New Old
Modular forms 64 16 48
Cusp forms 32 8 24
Eisenstein series 32 8 24

Trace form

\( 8q + 4q^{3} + O(q^{10}) \) \( 8q + 4q^{3} + 8q^{11} - 8q^{17} - 8q^{27} - 16q^{33} - 20q^{35} - 8q^{41} - 28q^{43} - 8q^{51} + 8q^{57} + 28q^{67} + 16q^{73} + 60q^{75} + 32q^{81} + 44q^{83} + 40q^{91} + 16q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(160, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
160.2.o.a \(8\) \(1.278\) \(\Q(\zeta_{20})\) None \(0\) \(4\) \(0\) \(0\) \(q-\zeta_{20}^{3}q^{3}+\zeta_{20}^{5}q^{5}-\zeta_{20}^{6}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(160, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(160, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 3}\)