Properties

Label 17.6.a
Level 17
Weight 6
Character orbit a
Rep. character \(\chi_{17}(1,\cdot)\)
Character field \(\Q\)
Dimension 6
Newforms 3
Sturm bound 9
Trace bound 2

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Defining parameters

Level: \( N \) = \( 17 \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 17.a (trivial)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(9\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(17))\).

Total New Old
Modular forms 8 6 2
Cusp forms 6 6 0
Eisenstein series 2 0 2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators.

\(17\)Dim.
\(+\)\(2\)
\(-\)\(4\)

Trace form

\(6q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 20q^{3} \) \(\mathstrut +\mathstrut 42q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 106q^{6} \) \(\mathstrut +\mathstrut 116q^{7} \) \(\mathstrut -\mathstrut 66q^{8} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 20q^{3} \) \(\mathstrut +\mathstrut 42q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 106q^{6} \) \(\mathstrut +\mathstrut 116q^{7} \) \(\mathstrut -\mathstrut 66q^{8} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut -\mathstrut 262q^{10} \) \(\mathstrut -\mathstrut 100q^{11} \) \(\mathstrut -\mathstrut 586q^{12} \) \(\mathstrut +\mathstrut 412q^{13} \) \(\mathstrut -\mathstrut 472q^{14} \) \(\mathstrut -\mathstrut 1176q^{15} \) \(\mathstrut -\mathstrut 1166q^{16} \) \(\mathstrut +\mathstrut 578q^{17} \) \(\mathstrut +\mathstrut 1682q^{18} \) \(\mathstrut +\mathstrut 1040q^{19} \) \(\mathstrut +\mathstrut 438q^{20} \) \(\mathstrut +\mathstrut 752q^{21} \) \(\mathstrut -\mathstrut 2702q^{22} \) \(\mathstrut +\mathstrut 4660q^{23} \) \(\mathstrut +\mathstrut 2958q^{24} \) \(\mathstrut +\mathstrut 7474q^{25} \) \(\mathstrut -\mathstrut 5584q^{26} \) \(\mathstrut +\mathstrut 3608q^{27} \) \(\mathstrut +\mathstrut 1424q^{28} \) \(\mathstrut -\mathstrut 4824q^{29} \) \(\mathstrut -\mathstrut 9488q^{30} \) \(\mathstrut -\mathstrut 1956q^{31} \) \(\mathstrut -\mathstrut 4394q^{32} \) \(\mathstrut -\mathstrut 9512q^{33} \) \(\mathstrut +\mathstrut 2312q^{34} \) \(\mathstrut +\mathstrut 8056q^{35} \) \(\mathstrut -\mathstrut 20682q^{36} \) \(\mathstrut -\mathstrut 672q^{37} \) \(\mathstrut -\mathstrut 13352q^{38} \) \(\mathstrut -\mathstrut 19896q^{39} \) \(\mathstrut +\mathstrut 14678q^{40} \) \(\mathstrut +\mathstrut 45108q^{41} \) \(\mathstrut +\mathstrut 49464q^{42} \) \(\mathstrut -\mathstrut 16576q^{43} \) \(\mathstrut +\mathstrut 25758q^{44} \) \(\mathstrut -\mathstrut 24264q^{45} \) \(\mathstrut +\mathstrut 32900q^{46} \) \(\mathstrut -\mathstrut 32720q^{47} \) \(\mathstrut -\mathstrut 42434q^{48} \) \(\mathstrut +\mathstrut 3718q^{49} \) \(\mathstrut +\mathstrut 5110q^{50} \) \(\mathstrut +\mathstrut 10404q^{51} \) \(\mathstrut +\mathstrut 79968q^{52} \) \(\mathstrut -\mathstrut 100180q^{53} \) \(\mathstrut +\mathstrut 17260q^{54} \) \(\mathstrut -\mathstrut 7688q^{55} \) \(\mathstrut -\mathstrut 94032q^{56} \) \(\mathstrut -\mathstrut 880q^{57} \) \(\mathstrut +\mathstrut 162706q^{58} \) \(\mathstrut +\mathstrut 61824q^{59} \) \(\mathstrut -\mathstrut 88480q^{60} \) \(\mathstrut +\mathstrut 62304q^{61} \) \(\mathstrut -\mathstrut 46856q^{62} \) \(\mathstrut +\mathstrut 91316q^{63} \) \(\mathstrut -\mathstrut 76918q^{64} \) \(\mathstrut -\mathstrut 133296q^{65} \) \(\mathstrut -\mathstrut 77764q^{66} \) \(\mathstrut -\mathstrut 26840q^{67} \) \(\mathstrut +\mathstrut 27744q^{68} \) \(\mathstrut +\mathstrut 91680q^{69} \) \(\mathstrut -\mathstrut 257352q^{70} \) \(\mathstrut +\mathstrut 107100q^{71} \) \(\mathstrut -\mathstrut 72822q^{72} \) \(\mathstrut -\mathstrut 145332q^{73} \) \(\mathstrut +\mathstrut 69230q^{74} \) \(\mathstrut +\mathstrut 351820q^{75} \) \(\mathstrut +\mathstrut 248024q^{76} \) \(\mathstrut -\mathstrut 200016q^{77} \) \(\mathstrut +\mathstrut 262836q^{78} \) \(\mathstrut -\mathstrut 51676q^{79} \) \(\mathstrut +\mathstrut 205502q^{80} \) \(\mathstrut -\mathstrut 144354q^{81} \) \(\mathstrut -\mathstrut 269840q^{82} \) \(\mathstrut -\mathstrut 5600q^{83} \) \(\mathstrut -\mathstrut 111640q^{84} \) \(\mathstrut +\mathstrut 48552q^{85} \) \(\mathstrut +\mathstrut 223460q^{86} \) \(\mathstrut -\mathstrut 255768q^{87} \) \(\mathstrut +\mathstrut 142838q^{88} \) \(\mathstrut -\mathstrut 112532q^{89} \) \(\mathstrut -\mathstrut 300814q^{90} \) \(\mathstrut +\mathstrut 264328q^{91} \) \(\mathstrut +\mathstrut 386628q^{92} \) \(\mathstrut +\mathstrut 279952q^{93} \) \(\mathstrut -\mathstrut 329376q^{94} \) \(\mathstrut +\mathstrut 257072q^{95} \) \(\mathstrut -\mathstrut 186978q^{96} \) \(\mathstrut +\mathstrut 150564q^{97} \) \(\mathstrut -\mathstrut 241298q^{98} \) \(\mathstrut -\mathstrut 310948q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(17))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 17
17.6.a.a \(1\) \(2.727\) \(\Q\) None \(-6\) \(10\) \(-72\) \(-196\) \(+\) \(q-6q^{2}+10q^{3}+4q^{4}-72q^{5}-60q^{6}+\cdots\)
17.6.a.b \(1\) \(2.727\) \(\Q\) None \(1\) \(-18\) \(-16\) \(28\) \(+\) \(q+q^{2}-18q^{3}-31q^{4}-2^{4}q^{5}-18q^{6}+\cdots\)
17.6.a.c \(4\) \(2.727\) 4.4.5416116.1 None \(3\) \(28\) \(80\) \(284\) \(-\) \(q+(1+\beta _{1})q^{2}+(7+\beta _{1}-\beta _{3})q^{3}+(18+\cdots)q^{4}+\cdots\)