Properties

Label 17.8.a
Level 17
Weight 8
Character orbit a
Rep. character \(\chi_{17}(1,\cdot)\)
Character field \(\Q\)
Dimension 10
Newforms 3
Sturm bound 12
Trace bound 1

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Defining parameters

Level: \( N \) = \( 17 \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 17.a (trivial)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(12\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(17))\).

Total New Old
Modular forms 12 10 2
Cusp forms 10 10 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.
\(+\)\(6\)
\(-\)\(4\)

Trace form

\(10q \) \(\mathstrut +\mathstrut 14q^{2} \) \(\mathstrut -\mathstrut 28q^{3} \) \(\mathstrut +\mathstrut 586q^{4} \) \(\mathstrut -\mathstrut 392q^{5} \) \(\mathstrut +\mathstrut 322q^{6} \) \(\mathstrut -\mathstrut 396q^{7} \) \(\mathstrut +\mathstrut 2814q^{8} \) \(\mathstrut +\mathstrut 5082q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(10q \) \(\mathstrut +\mathstrut 14q^{2} \) \(\mathstrut -\mathstrut 28q^{3} \) \(\mathstrut +\mathstrut 586q^{4} \) \(\mathstrut -\mathstrut 392q^{5} \) \(\mathstrut +\mathstrut 322q^{6} \) \(\mathstrut -\mathstrut 396q^{7} \) \(\mathstrut +\mathstrut 2814q^{8} \) \(\mathstrut +\mathstrut 5082q^{9} \) \(\mathstrut +\mathstrut 466q^{10} \) \(\mathstrut -\mathstrut 1092q^{11} \) \(\mathstrut -\mathstrut 394q^{12} \) \(\mathstrut +\mathstrut 4516q^{13} \) \(\mathstrut -\mathstrut 19768q^{14} \) \(\mathstrut +\mathstrut 18360q^{15} \) \(\mathstrut +\mathstrut 15282q^{16} \) \(\mathstrut -\mathstrut 9826q^{17} \) \(\mathstrut -\mathstrut 5854q^{18} \) \(\mathstrut -\mathstrut 53664q^{19} \) \(\mathstrut -\mathstrut 131242q^{20} \) \(\mathstrut +\mathstrut 46736q^{21} \) \(\mathstrut +\mathstrut 37322q^{22} \) \(\mathstrut -\mathstrut 144716q^{23} \) \(\mathstrut +\mathstrut 89982q^{24} \) \(\mathstrut +\mathstrut 122238q^{25} \) \(\mathstrut +\mathstrut 250544q^{26} \) \(\mathstrut -\mathstrut 199720q^{27} \) \(\mathstrut -\mathstrut 238704q^{28} \) \(\mathstrut +\mathstrut 161112q^{29} \) \(\mathstrut -\mathstrut 456656q^{30} \) \(\mathstrut +\mathstrut 493292q^{31} \) \(\mathstrut +\mathstrut 760246q^{32} \) \(\mathstrut +\mathstrut 674104q^{33} \) \(\mathstrut -\mathstrut 78608q^{34} \) \(\mathstrut +\mathstrut 55000q^{35} \) \(\mathstrut -\mathstrut 344826q^{36} \) \(\mathstrut -\mathstrut 190528q^{37} \) \(\mathstrut -\mathstrut 199448q^{38} \) \(\mathstrut -\mathstrut 295992q^{39} \) \(\mathstrut -\mathstrut 2330858q^{40} \) \(\mathstrut +\mathstrut 23964q^{41} \) \(\mathstrut +\mathstrut 75672q^{42} \) \(\mathstrut +\mathstrut 1646064q^{43} \) \(\mathstrut -\mathstrut 1157106q^{44} \) \(\mathstrut -\mathstrut 629352q^{45} \) \(\mathstrut -\mathstrut 512540q^{46} \) \(\mathstrut -\mathstrut 717984q^{47} \) \(\mathstrut +\mathstrut 2983822q^{48} \) \(\mathstrut +\mathstrut 886778q^{49} \) \(\mathstrut -\mathstrut 417146q^{50} \) \(\mathstrut -\mathstrut 530604q^{51} \) \(\mathstrut +\mathstrut 938480q^{52} \) \(\mathstrut +\mathstrut 803220q^{53} \) \(\mathstrut -\mathstrut 2944340q^{54} \) \(\mathstrut +\mathstrut 2265992q^{55} \) \(\mathstrut +\mathstrut 1386144q^{56} \) \(\mathstrut -\mathstrut 53920q^{57} \) \(\mathstrut -\mathstrut 3586438q^{58} \) \(\mathstrut -\mathstrut 2281392q^{59} \) \(\mathstrut +\mathstrut 1789280q^{60} \) \(\mathstrut -\mathstrut 1922176q^{61} \) \(\mathstrut +\mathstrut 6003704q^{62} \) \(\mathstrut -\mathstrut 5770684q^{63} \) \(\mathstrut +\mathstrut 11273354q^{64} \) \(\mathstrut -\mathstrut 89600q^{65} \) \(\mathstrut -\mathstrut 1862932q^{66} \) \(\mathstrut +\mathstrut 909784q^{67} \) \(\mathstrut -\mathstrut 1886592q^{68} \) \(\mathstrut -\mathstrut 4111344q^{69} \) \(\mathstrut +\mathstrut 17308440q^{70} \) \(\mathstrut +\mathstrut 643868q^{71} \) \(\mathstrut -\mathstrut 5539878q^{72} \) \(\mathstrut +\mathstrut 2656244q^{73} \) \(\mathstrut +\mathstrut 5908694q^{74} \) \(\mathstrut -\mathstrut 19207316q^{75} \) \(\mathstrut -\mathstrut 17345880q^{76} \) \(\mathstrut -\mathstrut 1420128q^{77} \) \(\mathstrut -\mathstrut 13551036q^{78} \) \(\mathstrut +\mathstrut 10534932q^{79} \) \(\mathstrut -\mathstrut 26016226q^{80} \) \(\mathstrut +\mathstrut 14907522q^{81} \) \(\mathstrut +\mathstrut 20638064q^{82} \) \(\mathstrut -\mathstrut 239920q^{83} \) \(\mathstrut +\mathstrut 1099784q^{84} \) \(\mathstrut -\mathstrut 117912q^{85} \) \(\mathstrut -\mathstrut 19882012q^{86} \) \(\mathstrut +\mathstrut 41992440q^{87} \) \(\mathstrut -\mathstrut 4108970q^{88} \) \(\mathstrut -\mathstrut 5368028q^{89} \) \(\mathstrut +\mathstrut 47657786q^{90} \) \(\mathstrut -\mathstrut 6274200q^{91} \) \(\mathstrut -\mathstrut 56318332q^{92} \) \(\mathstrut -\mathstrut 38834816q^{93} \) \(\mathstrut +\mathstrut 7636896q^{94} \) \(\mathstrut -\mathstrut 16028656q^{95} \) \(\mathstrut +\mathstrut 30349998q^{96} \) \(\mathstrut -\mathstrut 27032980q^{97} \) \(\mathstrut +\mathstrut 39536286q^{98} \) \(\mathstrut +\mathstrut 26005388q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(17))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 17
17.8.a.a \(1\) \(5.311\) \(\Q\) None \(-2\) \(18\) \(-10\) \(-902\) \(-\) \(q-2q^{2}+18q^{3}-124q^{4}-10q^{5}+\cdots\)
17.8.a.b \(3\) \(5.311\) 3.3.694349.1 None \(1\) \(-86\) \(-198\) \(-1558\) \(-\) \(q+\beta _{2}q^{2}+(-28-\beta _{1}-2\beta _{2})q^{3}+(78+\cdots)q^{4}+\cdots\)
17.8.a.c \(6\) \(5.311\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(15\) \(40\) \(-184\) \(2064\) \(+\) \(q+(2+\beta _{1})q^{2}+(6+\beta _{1}+\beta _{4})q^{3}+(78+\cdots)q^{4}+\cdots\)