Properties

Label 7.17
Level 7
Weight 17
Dimension 29
Nonzero newspaces 2
Newforms 3
Sturm bound 68
Trace bound 1

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Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 17 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 3 \)
Sturm bound: \(68\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{17}(\Gamma_1(7))\).

Total New Old
Modular forms 35 35 0
Cusp forms 29 29 0
Eisenstein series 6 6 0

Trace form

\( 29q - 3q^{2} + 6558q^{3} - 131075q^{4} + 241890q^{5} + 882385q^{7} + 19677585q^{8} + 147205353q^{9} + O(q^{10}) \) \( 29q - 3q^{2} + 6558q^{3} - 131075q^{4} + 241890q^{5} + 882385q^{7} + 19677585q^{8} + 147205353q^{9} - 567579804q^{10} + 661745688q^{11} - 2240722092q^{12} + 1106282625q^{14} - 2015581932q^{15} - 12578516359q^{16} + 16479299850q^{17} - 9536050647q^{18} - 29753076894q^{19} + 76157787342q^{21} - 5200345902q^{22} - 265495929492q^{23} + 613456300512q^{24} + 427277408093q^{25} - 1359419612544q^{26} + 2939436853157q^{28} - 572914875678q^{29} - 2488369312872q^{30} + 1037434908306q^{31} - 2277219498351q^{32} + 411779151054q^{33} - 6876653860398q^{35} - 1163822710719q^{36} + 8331978501788q^{37} - 9079217417208q^{38} + 5274313813524q^{39} + 15010293809208q^{40} + 3095553897072q^{42} + 17265154638650q^{43} + 35719419327438q^{44} - 85040191344096q^{45} - 49923218253246q^{46} + 106960600327866q^{47} - 47195732058475q^{49} + 7820032448433q^{50} + 62905662180450q^{51} + 126484190926632q^{52} + 32325105686316q^{53} - 635343594055560q^{54} + 397792677871281q^{56} + 170232979269276q^{57} - 72879666444822q^{58} - 99092116656282q^{59} - 509387610363156q^{60} - 904353032308434q^{61} + 1660558387183521q^{63} + 1831167567044641q^{64} + 73067487921036q^{65} - 951679982792988q^{66} - 1316698063189724q^{67} - 964537664673492q^{68} + 699463493737680q^{70} + 3322549304747850q^{71} + 3859927087358385q^{72} - 1146801010325370q^{73} - 8795766307739322q^{74} - 4935640048894356q^{75} + 4332904215015768q^{77} + 13940434568318832q^{78} + 7099477833384220q^{79} - 18764997660746184q^{80} - 14845066689736845q^{81} - 11916006908925168q^{82} + 29990047173869244q^{84} + 22113338793420588q^{85} + 9831157206475746q^{86} - 4167264363403248q^{87} - 43161623036399502q^{88} - 34000447101257730q^{89} + 30825691730796312q^{91} + 92964134706713850q^{92} + 11414270344406718q^{93} - 7183919979926376q^{94} - 72773924945421162q^{95} - 137281944028491360q^{96} + 123653421427420941q^{98} + 115927390544916834q^{99} + O(q^{100}) \)

Decomposition of \(S_{17}^{\mathrm{new}}(\Gamma_1(7))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
7.17.b \(\chi_{7}(6, \cdot)\) 7.17.b.a 1 1
7.17.b.b 8
7.17.d \(\chi_{7}(3, \cdot)\) 7.17.d.a 20 2