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Properties

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

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Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 17 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
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

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

Display 100 coefficients 10 coefficients

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 available 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