Properties

Label 17.4.b
Level 17
Weight 4
Character orbit b
Rep. character \(\chi_{17}(16,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 1
Sturm bound 6
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 17 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 17.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 17 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(17, [\chi])\).

Total New Old
Modular forms 6 6 0
Cusp forms 4 4 0
Eisenstein series 2 2 0

Trace form

\(4q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut -\mathstrut 40q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut -\mathstrut 40q^{9} \) \(\mathstrut +\mathstrut 140q^{13} \) \(\mathstrut +\mathstrut 24q^{15} \) \(\mathstrut -\mathstrut 238q^{16} \) \(\mathstrut +\mathstrut 112q^{17} \) \(\mathstrut +\mathstrut 218q^{18} \) \(\mathstrut -\mathstrut 112q^{19} \) \(\mathstrut +\mathstrut 124q^{21} \) \(\mathstrut -\mathstrut 460q^{25} \) \(\mathstrut -\mathstrut 532q^{26} \) \(\mathstrut +\mathstrut 912q^{30} \) \(\mathstrut +\mathstrut 494q^{32} \) \(\mathstrut -\mathstrut 1036q^{33} \) \(\mathstrut +\mathstrut 406q^{34} \) \(\mathstrut +\mathstrut 936q^{35} \) \(\mathstrut -\mathstrut 218q^{36} \) \(\mathstrut +\mathstrut 56q^{38} \) \(\mathstrut -\mathstrut 1184q^{42} \) \(\mathstrut -\mathstrut 520q^{43} \) \(\mathstrut +\mathstrut 952q^{47} \) \(\mathstrut +\mathstrut 312q^{49} \) \(\mathstrut -\mathstrut 1354q^{50} \) \(\mathstrut +\mathstrut 1160q^{51} \) \(\mathstrut +\mathstrut 532q^{52} \) \(\mathstrut -\mathstrut 576q^{53} \) \(\mathstrut +\mathstrut 168q^{55} \) \(\mathstrut -\mathstrut 1176q^{59} \) \(\mathstrut -\mathstrut 912q^{60} \) \(\mathstrut +\mathstrut 1426q^{64} \) \(\mathstrut +\mathstrut 1904q^{66} \) \(\mathstrut -\mathstrut 240q^{67} \) \(\mathstrut -\mathstrut 406q^{68} \) \(\mathstrut +\mathstrut 1204q^{69} \) \(\mathstrut +\mathstrut 192q^{70} \) \(\mathstrut -\mathstrut 1206q^{72} \) \(\mathstrut -\mathstrut 56q^{76} \) \(\mathstrut +\mathstrut 868q^{77} \) \(\mathstrut -\mathstrut 2408q^{81} \) \(\mathstrut -\mathstrut 2856q^{83} \) \(\mathstrut +\mathstrut 1184q^{84} \) \(\mathstrut +\mathstrut 768q^{85} \) \(\mathstrut -\mathstrut 2248q^{86} \) \(\mathstrut -\mathstrut 168q^{87} \) \(\mathstrut +\mathstrut 1988q^{89} \) \(\mathstrut +\mathstrut 1060q^{93} \) \(\mathstrut +\mathstrut 448q^{94} \) \(\mathstrut +\mathstrut 306q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(17, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
17.4.b.a \(4\) \(1.003\) 4.0.4669632.2 None \(-2\) \(0\) \(0\) \(0\) \(q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}+(1-\beta _{2})q^{4}+\cdots\)