Properties

Label 160.4.c
Level $160$
Weight $4$
Character orbit 160.c
Rep. character $\chi_{160}(129,\cdot)$
Character field $\Q$
Dimension $18$
Newform subspaces $4$
Sturm bound $96$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 160.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(96\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(160, [\chi])\).

Total New Old
Modular forms 80 18 62
Cusp forms 64 18 46
Eisenstein series 16 0 16

Trace form

\( 18 q - 2 q^{5} - 162 q^{9} + O(q^{10}) \) \( 18 q - 2 q^{5} - 162 q^{9} + 136 q^{21} - 102 q^{25} - 228 q^{29} - 412 q^{41} + 1074 q^{45} - 1802 q^{49} + 780 q^{61} + 1616 q^{65} + 2504 q^{69} + 218 q^{81} - 3104 q^{85} + 2260 q^{89} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(160, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
160.4.c.a 160.c 5.b $2$ $9.440$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-22\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-11+i)q^{5}+3^{3}q^{9}-46iq^{13}+\cdots\)
160.4.c.b 160.c 5.b $4$ $9.440$ \(\Q(i, \sqrt{29})\) None \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(-3+\beta _{1})q^{5}+\beta _{2}q^{7}+11q^{9}+\cdots\)
160.4.c.c 160.c 5.b $4$ $9.440$ \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-\beta _{1}+2\beta _{3})q^{3}-5\beta _{2}q^{5}+(-6\beta _{1}+\cdots)q^{7}+\cdots\)
160.4.c.d 160.c 5.b $8$ $9.440$ 8.0.\(\cdots\).22 None \(0\) \(0\) \(32\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(4-\beta _{4})q^{5}+(\beta _{1}-\beta _{3})q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(160, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(160, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)