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Properties

Label 160.3.b
Level $160$
Weight $3$
Character orbit 160.b
Rep. character $\chi_{160}(31,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $2$
Sturm bound $72$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 160.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(72\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(160, [\chi])\).

Total New Old
Modular forms 56 8 48
Cusp forms 40 8 32
Eisenstein series 16 0 16

Trace form

\( 8 q - 8 q^{9} + 32 q^{13} - 48 q^{17} - 112 q^{21} + 40 q^{25} + 48 q^{29} + 32 q^{33} + 160 q^{37} + 160 q^{41} - 80 q^{45} - 136 q^{49} - 32 q^{53} - 256 q^{57} - 128 q^{61} + 80 q^{65} + 48 q^{69} - 112 q^{73}+ \cdots + 368 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(160, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
160.3.b.a 160.b 4.b $4$ $4.360$ \(\Q(i, \sqrt{5})\) None 160.3.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}-\beta _{3}q^{5}+(-\beta _{1}+4\beta _{2})q^{7}+\cdots\)
160.3.b.b 160.b 4.b $4$ $4.360$ \(\Q(i, \sqrt{5})\) None 160.3.b.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+\beta _{1}q^{7}+(3+2\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(160, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(160, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)