Properties

Label 160.3.e
Level $160$
Weight $3$
Character orbit 160.e
Rep. character $\chi_{160}(79,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $3$
Sturm bound $72$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 160.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(72\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

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

Total New Old
Modular forms 56 14 42
Cusp forms 40 10 30
Eisenstein series 16 4 12

Trace form

\( 10 q - 22 q^{9} + O(q^{10}) \) \( 10 q - 22 q^{9} + 4 q^{11} - 28 q^{19} + 10 q^{25} + 100 q^{35} + 36 q^{41} - 18 q^{49} - 128 q^{51} + 68 q^{59} - 60 q^{65} - 320 q^{75} - 6 q^{81} + 148 q^{89} + 392 q^{91} + 164 q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
160.3.e.a $1$ $4.360$ \(\Q\) \(\Q(\sqrt{-10}) \) \(0\) \(0\) \(-5\) \(6\) \(q-5q^{5}+6q^{7}+9q^{9}+18q^{11}+6q^{13}+\cdots\)
160.3.e.b $1$ $4.360$ \(\Q\) \(\Q(\sqrt{-10}) \) \(0\) \(0\) \(5\) \(-6\) \(q+5q^{5}-6q^{7}+9q^{9}+18q^{11}-6q^{13}+\cdots\)
160.3.e.c $8$ $4.360$ 8.0.\(\cdots\).2 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{3}+\beta _{3}q^{5}+(-\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)

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

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