Properties

Label 160.2.c
Level $160$
Weight $2$
Character orbit 160.c
Rep. character $\chi_{160}(129,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $2$
Sturm bound $48$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 160.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
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 \(M_{2}(160, [\chi])\).

Total New Old
Modular forms 32 6 26
Cusp forms 16 6 10
Eisenstein series 16 0 16

Trace form

\( 6q + 2q^{5} - 6q^{9} + O(q^{10}) \) \( 6q + 2q^{5} - 6q^{9} - 8q^{21} + 14q^{25} + 4q^{29} - 20q^{41} - 34q^{45} - 14q^{49} + 20q^{61} - 16q^{65} + 56q^{69} + 62q^{81} + 32q^{85} - 4q^{89} + O(q^{100}) \)

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.c.a \(2\) \(1.278\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(2\) \(0\) \(q+(1+i)q^{5}+3q^{9}+2iq^{13}-4iq^{17}+\cdots\)
160.2.c.b \(4\) \(1.278\) \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{2}q^{5}+\beta _{3}q^{7}+(-3+2\beta _{2}+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(160, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)