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Properties

Label 161.4.c
Level $161$
Weight $4$
Character orbit 161.c
Rep. character $\chi_{161}(160,\cdot)$
Character field $\Q$
Dimension $46$
Newform subspaces $3$
Sturm bound $64$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 161 = 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 161.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(64\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(161, [\chi])\).

Total New Old
Modular forms 50 50 0
Cusp forms 46 46 0
Eisenstein series 4 4 0

Trace form

\( 46 q - 6 q^{2} + 162 q^{4} - 18 q^{8} - 438 q^{9} + 674 q^{16} - 78 q^{18} + 40 q^{23} + 586 q^{25} + 236 q^{29} - 110 q^{32} - 1144 q^{35} - 3102 q^{36} + 1432 q^{39} - 964 q^{46} + 462 q^{49} + 1854 q^{50}+ \cdots + 4222 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(161, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
161.4.c.a 161.c 161.c $2$ $9.499$ \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) 161.4.c.a \(10\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+5q^{2}+17q^{4}+7\beta q^{7}+45q^{8}+3^{3}q^{9}+\cdots\)
161.4.c.b 161.c 161.c $8$ $9.499$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 161.4.c.b \(-8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-\beta _{2}q^{3}-7q^{4}+(-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
161.4.c.c 161.c 161.c $36$ $9.499$ None 161.4.c.c \(-8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$