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Properties

Label 160.3.h
Level $160$
Weight $3$
Character orbit 160.h
Rep. character $\chi_{160}(159,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $2$
Sturm bound $72$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 160.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(72\)
Trace bound: \(3\)
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 12 44
Cusp forms 40 12 28
Eisenstein series 16 0 16

Trace form

\( 12 q - 4 q^{5} + 36 q^{9} + O(q^{10}) \) \( 12 q - 4 q^{5} + 36 q^{9} + 16 q^{21} - 20 q^{25} + 88 q^{29} - 136 q^{41} - 12 q^{45} - 124 q^{49} - 200 q^{61} - 368 q^{69} + 476 q^{81} - 64 q^{85} + 152 q^{89} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
160.3.h.a 160.h 20.d $6$ $4.360$ 6.0.1827904.1 None \(0\) \(-4\) \(-2\) \(-12\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{1})q^{3}-\beta _{4}q^{5}+(-2-\beta _{3}+\cdots)q^{7}+\cdots\)
160.3.h.b 160.h 20.d $6$ $4.360$ 6.0.1827904.1 None \(0\) \(4\) \(-2\) \(12\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta _{1})q^{3}+(-1-\beta _{1}+\beta _{4})q^{5}+\cdots\)

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

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