Properties

Label 160.2.n
Level $160$
Weight $2$
Character orbit 160.n
Rep. character $\chi_{160}(63,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $12$
Newform subspaces $6$
Sturm bound $48$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 160.n (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 6 \)
Sturm bound: \(48\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

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

Total New Old
Modular forms 64 12 52
Cusp forms 32 12 20
Eisenstein series 32 0 32

Trace form

\( 12 q + O(q^{10}) \) \( 12 q + 4 q^{13} - 12 q^{17} + 16 q^{21} - 12 q^{25} - 16 q^{33} - 20 q^{37} - 16 q^{41} - 20 q^{45} - 52 q^{53} + 32 q^{57} + 44 q^{65} + 28 q^{73} + 48 q^{77} + 36 q^{81} + 68 q^{85} + 80 q^{93} - 36 q^{97} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
160.2.n.a 160.n 20.e $2$ $1.278$ \(\Q(\sqrt{-1}) \) None \(0\) \(-4\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-2-2i)q^{3}+(-2+i)q^{5}+(-2+\cdots)q^{7}+\cdots\)
160.2.n.b 160.n 20.e $2$ $1.278$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-i)q^{3}+(1-2i)q^{5}+(-1+i)q^{7}+\cdots\)
160.2.n.c 160.n 20.e $2$ $1.278$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(2\) \(6\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-i)q^{3}+(1+2i)q^{5}+(3-3i)q^{7}+\cdots\)
160.2.n.d 160.n 20.e $2$ $1.278$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(2\) \(-6\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+i)q^{3}+(1+2i)q^{5}+(-3+3i)q^{7}+\cdots\)
160.2.n.e 160.n 20.e $2$ $1.278$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(2\) \(2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+i)q^{3}+(1-2i)q^{5}+(1-i)q^{7}+\cdots\)
160.2.n.f 160.n 20.e $2$ $1.278$ \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(2+2i)q^{3}+(-2+i)q^{5}+(2-2i)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(160, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)