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Properties

Label 161.2.k
Level $161$
Weight $2$
Character orbit 161.k
Rep. character $\chi_{161}(20,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $140$
Newform subspaces $2$
Sturm bound $32$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 161 = 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 161.k (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 2 \)
Sturm bound: \(32\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(161, [\chi])\).

Total New Old
Modular forms 180 180 0
Cusp forms 140 140 0
Eisenstein series 40 40 0

Trace form

\( 140 q - 20 q^{2} - 28 q^{4} - 11 q^{7} - 16 q^{8} - 22 q^{11} - 11 q^{14} - 22 q^{15} - 26 q^{16} + 8 q^{18} + 22 q^{21} - 44 q^{23} - 10 q^{25} + 33 q^{28} - 42 q^{29} - 66 q^{30} - 6 q^{32} - 13 q^{35}+ \cdots + 132 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(161, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
161.2.k.a 161.k 161.k $20$ $1.286$ 20.0.\(\cdots\).2 \(\Q(\sqrt{-7}) \) 161.2.k.a \(2\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{22}]$ \(q+(\beta _{4}+\beta _{6}-\beta _{14})q^{2}+(-\beta _{2}+\beta _{13}+\cdots)q^{4}+\cdots\)
161.2.k.b 161.k 161.k $120$ $1.286$ None 161.2.k.b \(-22\) \(0\) \(0\) \(-11\) $\mathrm{SU}(2)[C_{22}]$