Properties

Label 163.3.b
Level $163$
Weight $3$
Character orbit 163.b
Rep. character $\chi_{163}(162,\cdot)$
Character field $\Q$
Dimension $27$
Newform subspaces $2$
Sturm bound $41$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 163 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 163.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 163 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(41\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(163, [\chi])\).

Total New Old
Modular forms 29 29 0
Cusp forms 27 27 0
Eisenstein series 2 2 0

Trace form

\( 27 q - 52 q^{4} + 28 q^{6} - 77 q^{9} + O(q^{10}) \) \( 27 q - 52 q^{4} + 28 q^{6} - 77 q^{9} - 12 q^{10} + 34 q^{14} + 56 q^{15} + 92 q^{16} - 102 q^{21} + 104 q^{22} - 128 q^{24} - 113 q^{25} + 72 q^{26} - 72 q^{33} + 20 q^{34} - 50 q^{35} + 120 q^{36} + 48 q^{38} - 2 q^{39} - 14 q^{40} + 117 q^{41} + 85 q^{43} + 276 q^{46} + 177 q^{47} - 181 q^{49} - 148 q^{51} + 237 q^{53} - 356 q^{54} + 340 q^{55} - 132 q^{56} - 184 q^{57} - 40 q^{58} - 374 q^{60} + 25 q^{61} - 218 q^{62} - 168 q^{64} + 104 q^{65} - 100 q^{69} - 51 q^{71} - 490 q^{74} + 10 q^{77} + 259 q^{81} + 209 q^{83} + 672 q^{84} + 360 q^{85} - 262 q^{87} - 516 q^{88} + 1076 q^{90} + 140 q^{91} - 78 q^{93} - 498 q^{95} + 770 q^{96} + 49 q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(163, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
163.3.b.a 163.b 163.b $1$ $4.441$ \(\Q\) \(\Q(\sqrt{-163}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+4q^{4}+9q^{9}+2^{4}q^{16}+5^{2}q^{25}+\cdots\)
163.3.b.b 163.b 163.b $26$ $4.441$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$