Properties

Label 161.4.c
Level 161161
Weight 44
Character orbit 161.c
Rep. character χ161(160,)\chi_{161}(160,\cdot)
Character field Q\Q
Dimension 4646
Newform subspaces 33
Sturm bound 6464
Trace bound 11

Related objects

Downloads

Learn more

Defining parameters

Level: N N == 161=723 161 = 7 \cdot 23
Weight: k k == 4 4
Character orbit: [χ][\chi] == 161.c (of order 22 and degree 11)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 161 161
Character field: Q\Q
Newform subspaces: 3 3
Sturm bound: 6464
Trace bound: 11
Distinguishing TpT_p: 22

Dimensions

The following table gives the dimensions of various subspaces of M4(161,[χ])M_{4}(161, [\chi]).

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

Trace form

46q6q2+162q418q8438q9+674q1678q18+40q23+586q25+236q29110q321144q353102q36+1432q39964q46+462q49+1854q50++4222q98+O(q100) 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 S4new(161,[χ])S_{4}^{\mathrm{new}}(161, [\chi]) into newform subspaces

Label Char Prim Dim AA Field CM Minimal twist Traces Sato-Tate qq-expansion
a2a_{2} a3a_{3} a5a_{5} a7a_{7}
161.4.c.a 161.c 161.c 22 9.4999.499 Q(7)\Q(\sqrt{-7}) Q(7)\Q(\sqrt{-7}) 161.4.c.a 1010 00 00 00 U(1)[D2]\mathrm{U}(1)[D_{2}] q+5q2+17q4+7βq7+45q8+33q9+q+5q^{2}+17q^{4}+7\beta q^{7}+45q^{8}+3^{3}q^{9}+\cdots
161.4.c.b 161.c 161.c 88 9.4999.499 Q[x]/(x8)\mathbb{Q}[x]/(x^{8} - \cdots) None 161.4.c.b 8-8 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] qq2β2q37q4+(β1β3+)q5+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 3636 9.4999.499 None 161.4.c.c 8-8 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}]