Properties

Label 17.4.c
Level 17
Weight 4
Character orbit c
Rep. character \(\chi_{17}(4,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 8
Newforms 1
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) = \( 17 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 17.c (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 17 \)
Character field: \(\Q(i)\)
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 12 12 0
Cusp forms 8 8 0
Eisenstein series 4 4 0

Trace form

\(8q \) \(\mathstrut -\mathstrut 36q^{4} \) \(\mathstrut +\mathstrut 14q^{5} \) \(\mathstrut +\mathstrut 22q^{6} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut -\mathstrut 36q^{4} \) \(\mathstrut +\mathstrut 14q^{5} \) \(\mathstrut +\mathstrut 22q^{6} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 78q^{10} \) \(\mathstrut -\mathstrut 108q^{11} \) \(\mathstrut -\mathstrut 174q^{12} \) \(\mathstrut -\mathstrut 88q^{13} \) \(\mathstrut +\mathstrut 108q^{14} \) \(\mathstrut +\mathstrut 420q^{16} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut +\mathstrut 428q^{18} \) \(\mathstrut -\mathstrut 306q^{20} \) \(\mathstrut -\mathstrut 260q^{21} \) \(\mathstrut +\mathstrut 30q^{22} \) \(\mathstrut -\mathstrut 22q^{23} \) \(\mathstrut -\mathstrut 862q^{24} \) \(\mathstrut +\mathstrut 540q^{27} \) \(\mathstrut -\mathstrut 764q^{28} \) \(\mathstrut +\mathstrut 46q^{29} \) \(\mathstrut -\mathstrut 120q^{30} \) \(\mathstrut +\mathstrut 610q^{31} \) \(\mathstrut +\mathstrut 816q^{33} \) \(\mathstrut +\mathstrut 1002q^{34} \) \(\mathstrut +\mathstrut 1172q^{35} \) \(\mathstrut -\mathstrut 574q^{37} \) \(\mathstrut -\mathstrut 768q^{38} \) \(\mathstrut -\mathstrut 844q^{39} \) \(\mathstrut -\mathstrut 342q^{40} \) \(\mathstrut -\mathstrut 968q^{41} \) \(\mathstrut +\mathstrut 550q^{44} \) \(\mathstrut -\mathstrut 1154q^{45} \) \(\mathstrut -\mathstrut 944q^{46} \) \(\mathstrut -\mathstrut 368q^{47} \) \(\mathstrut +\mathstrut 2494q^{48} \) \(\mathstrut +\mathstrut 468q^{50} \) \(\mathstrut +\mathstrut 296q^{51} \) \(\mathstrut +\mathstrut 2564q^{52} \) \(\mathstrut -\mathstrut 1592q^{54} \) \(\mathstrut -\mathstrut 1996q^{55} \) \(\mathstrut +\mathstrut 684q^{56} \) \(\mathstrut -\mathstrut 300q^{57} \) \(\mathstrut +\mathstrut 266q^{58} \) \(\mathstrut +\mathstrut 1258q^{61} \) \(\mathstrut -\mathstrut 2516q^{62} \) \(\mathstrut +\mathstrut 122q^{63} \) \(\mathstrut -\mathstrut 3044q^{64} \) \(\mathstrut +\mathstrut 628q^{65} \) \(\mathstrut +\mathstrut 764q^{67} \) \(\mathstrut +\mathstrut 1914q^{68} \) \(\mathstrut +\mathstrut 1812q^{69} \) \(\mathstrut +\mathstrut 1266q^{71} \) \(\mathstrut +\mathstrut 1404q^{72} \) \(\mathstrut -\mathstrut 1732q^{73} \) \(\mathstrut +\mathstrut 1538q^{74} \) \(\mathstrut +\mathstrut 1292q^{75} \) \(\mathstrut -\mathstrut 2836q^{78} \) \(\mathstrut +\mathstrut 914q^{79} \) \(\mathstrut +\mathstrut 498q^{80} \) \(\mathstrut +\mathstrut 280q^{81} \) \(\mathstrut -\mathstrut 280q^{82} \) \(\mathstrut -\mathstrut 2952q^{84} \) \(\mathstrut -\mathstrut 2498q^{85} \) \(\mathstrut -\mathstrut 4244q^{86} \) \(\mathstrut +\mathstrut 442q^{88} \) \(\mathstrut -\mathstrut 2156q^{89} \) \(\mathstrut +\mathstrut 2478q^{90} \) \(\mathstrut -\mathstrut 1632q^{91} \) \(\mathstrut -\mathstrut 1768q^{92} \) \(\mathstrut +\mathstrut 1484q^{95} \) \(\mathstrut +\mathstrut 3998q^{96} \) \(\mathstrut +\mathstrut 1836q^{97} \) \(\mathstrut +\mathstrut 6728q^{98} \) \(\mathstrut -\mathstrut 2088q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.c.a \(8\) \(1.003\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(14\) \(2\) \(q+(\beta _{1}-\beta _{3})q^{2}+\beta _{4}q^{3}+(-5-\beta _{2}+\cdots)q^{4}+\cdots\)