Properties

Label 7.17.d
Level 7
Weight 17
Character orbit d
Rep. character \(\chi_{7}(3,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 20
Newforms 1
Sturm bound 11
Trace bound 0

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Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 17 \)
Character orbit: \([\chi]\) = 7.d (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newforms: \( 1 \)
Sturm bound: \(11\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{17}(7, [\chi])\).

Total New Old
Modular forms 24 24 0
Cusp forms 20 20 0
Eisenstein series 4 4 0

Trace form

\(20q \) \(\mathstrut +\mathstrut 92q^{2} \) \(\mathstrut +\mathstrut 6558q^{3} \) \(\mathstrut -\mathstrut 285924q^{4} \) \(\mathstrut +\mathstrut 241890q^{5} \) \(\mathstrut -\mathstrut 1847944q^{7} \) \(\mathstrut +\mathstrut 23873872q^{8} \) \(\mathstrut +\mathstrut 146092512q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(20q \) \(\mathstrut +\mathstrut 92q^{2} \) \(\mathstrut +\mathstrut 6558q^{3} \) \(\mathstrut -\mathstrut 285924q^{4} \) \(\mathstrut +\mathstrut 241890q^{5} \) \(\mathstrut -\mathstrut 1847944q^{7} \) \(\mathstrut +\mathstrut 23873872q^{8} \) \(\mathstrut +\mathstrut 146092512q^{9} \) \(\mathstrut -\mathstrut 567579804q^{10} \) \(\mathstrut +\mathstrut 487037030q^{11} \) \(\mathstrut -\mathstrut 2240722092q^{12} \) \(\mathstrut +\mathstrut 598121216q^{14} \) \(\mathstrut -\mathstrut 2098975212q^{15} \) \(\mathstrut -\mathstrut 13522996616q^{16} \) \(\mathstrut +\mathstrut 16479299850q^{17} \) \(\mathstrut -\mathstrut 21631627512q^{18} \) \(\mathstrut -\mathstrut 29753076894q^{19} \) \(\mathstrut +\mathstrut 30310552398q^{21} \) \(\mathstrut +\mathstrut 143879888720q^{22} \) \(\mathstrut -\mathstrut 199076938822q^{23} \) \(\mathstrut +\mathstrut 613456300512q^{24} \) \(\mathstrut +\mathstrut 212723266388q^{25} \) \(\mathstrut -\mathstrut 1359419612544q^{26} \) \(\mathstrut +\mathstrut 2531834927748q^{28} \) \(\mathstrut +\mathstrut 438309600272q^{29} \) \(\mathstrut -\mathstrut 2296351012392q^{30} \) \(\mathstrut +\mathstrut 1037434908306q^{31} \) \(\mathstrut -\mathstrut 3523947158064q^{32} \) \(\mathstrut +\mathstrut 411779151054q^{33} \) \(\mathstrut -\mathstrut 7248579242478q^{35} \) \(\mathstrut -\mathstrut 2493315404256q^{36} \) \(\mathstrut +\mathstrut 5318067734218q^{37} \) \(\mathstrut -\mathstrut 9079217417208q^{38} \) \(\mathstrut +\mathstrut 13250117821332q^{39} \) \(\mathstrut +\mathstrut 15010293809208q^{40} \) \(\mathstrut +\mathstrut 16256122433712q^{42} \) \(\mathstrut -\mathstrut 621187489400q^{43} \) \(\mathstrut +\mathstrut 25172272315980q^{44} \) \(\mathstrut -\mathstrut 85040191344096q^{45} \) \(\mathstrut -\mathstrut 15614039192704q^{46} \) \(\mathstrut +\mathstrut 106960600327866q^{47} \) \(\mathstrut -\mathstrut 52978127838580q^{49} \) \(\mathstrut +\mathstrut 35872835226128q^{50} \) \(\mathstrut +\mathstrut 4235281588962q^{51} \) \(\mathstrut +\mathstrut 126484190926632q^{52} \) \(\mathstrut +\mathstrut 29048763888218q^{53} \) \(\mathstrut -\mathstrut 635343594055560q^{54} \) \(\mathstrut +\mathstrut 230352840277168q^{56} \) \(\mathstrut +\mathstrut 366396034764636q^{57} \) \(\mathstrut -\mathstrut 279762037805080q^{58} \) \(\mathstrut -\mathstrut 99092116656282q^{59} \) \(\mathstrut -\mathstrut 173605217618196q^{60} \) \(\mathstrut -\mathstrut 904353032308434q^{61} \) \(\mathstrut +\mathstrut 1188663557133192q^{63} \) \(\mathstrut +\mathstrut 2502182430870944q^{64} \) \(\mathstrut -\mathstrut 500211967540404q^{65} \) \(\mathstrut -\mathstrut 951679982792988q^{66} \) \(\mathstrut -\mathstrut 33326890567694q^{67} \) \(\mathstrut -\mathstrut 964537664673492q^{68} \) \(\mathstrut -\mathstrut 569178593140080q^{70} \) \(\mathstrut +\mathstrut 3111156268483352q^{71} \) \(\mathstrut +\mathstrut 936737429904432q^{72} \) \(\mathstrut -\mathstrut 1146801010325370q^{73} \) \(\mathstrut -\mathstrut 2161044304782140q^{74} \) \(\mathstrut -\mathstrut 4935640048894356q^{75} \) \(\mathstrut +\mathstrut 1321278185203718q^{77} \) \(\mathstrut +\mathstrut 13747974994685232q^{78} \) \(\mathstrut +\mathstrut 126874036566250q^{79} \) \(\mathstrut -\mathstrut 18764997660746184q^{80} \) \(\mathstrut -\mathstrut 2081051947014102q^{81} \) \(\mathstrut -\mathstrut 11916006908925168q^{82} \) \(\mathstrut +\mathstrut 17065299612720828q^{84} \) \(\mathstrut +\mathstrut 27928718307758508q^{85} \) \(\mathstrut -\mathstrut 7493915124549152q^{86} \) \(\mathstrut -\mathstrut 4167264363403248q^{87} \) \(\mathstrut -\mathstrut 10398917942882000q^{88} \) \(\mathstrut -\mathstrut 34000447101257730q^{89} \) \(\mathstrut +\mathstrut 6895892767523928q^{91} \) \(\mathstrut +\mathstrut 113018032389709752q^{92} \) \(\mathstrut -\mathstrut 15597881218045122q^{93} \) \(\mathstrut -\mathstrut 7183919979926376q^{94} \) \(\mathstrut -\mathstrut 19569222088313322q^{95} \) \(\mathstrut -\mathstrut 137281944028491360q^{96} \) \(\mathstrut +\mathstrut 65453414234371436q^{98} \) \(\mathstrut +\mathstrut 142672614742345392q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{17}^{\mathrm{new}}(7, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
7.17.d.a \(20\) \(11.363\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(92\) \(6558\) \(241890\) \(-1847944\) \(q+(9-\beta _{1}+9\beta _{2}-\beta _{3})q^{2}+(438+\beta _{1}+\cdots)q^{3}+\cdots\)