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

\( 140q - 20q^{2} - 28q^{4} - 11q^{7} - 16q^{8} + O(q^{10}) \) \( 140q - 20q^{2} - 28q^{4} - 11q^{7} - 16q^{8} - 22q^{11} - 11q^{14} - 22q^{15} - 26q^{16} + 8q^{18} + 22q^{21} - 44q^{23} - 10q^{25} + 33q^{28} - 42q^{29} - 66q^{30} - 6q^{32} - 13q^{35} + 27q^{36} + 22q^{37} - 14q^{39} - 121q^{42} + 22q^{43} + 99q^{44} - 58q^{46} - 55q^{49} + 85q^{50} + 22q^{51} - 22q^{53} - 132q^{56} + 22q^{57} + 81q^{58} - 22q^{60} - 66q^{63} + 48q^{64} + 132q^{65} - 22q^{67} - 54q^{70} - 6q^{71} + 262q^{72} - 33q^{74} - 130q^{77} + 162q^{78} + 66q^{79} - 96q^{81} - 77q^{84} + 110q^{85} + 22q^{86} - 99q^{88} + 244q^{92} - 108q^{93} - 80q^{95} + 7q^{98} + 132q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
161.2.k.a \(20\) \(1.286\) 20.0.\(\cdots\).2 \(\Q(\sqrt{-7}) \) \(2\) \(0\) \(0\) \(0\) \(q+(\beta _{4}+\beta _{6}-\beta _{14})q^{2}+(-\beta _{2}+\beta _{13}+\cdots)q^{4}+\cdots\)
161.2.k.b \(120\) \(1.286\) None \(-22\) \(0\) \(0\) \(-11\)