Properties

Label 7.6
Level 7
Weight 6
Dimension 7
Nonzero newspaces 2
Newforms 3
Sturm bound 24
Trace bound 1

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 3 \)
Sturm bound: \(24\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(7))\).

Total New Old
Modular forms 13 11 2
Cusp forms 7 7 0
Eisenstein series 6 4 2

Trace form

\(7q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 61q^{4} \) \(\mathstrut -\mathstrut 36q^{5} \) \(\mathstrut -\mathstrut 222q^{6} \) \(\mathstrut -\mathstrut 119q^{7} \) \(\mathstrut -\mathstrut 177q^{8} \) \(\mathstrut +\mathstrut 891q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(7q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 61q^{4} \) \(\mathstrut -\mathstrut 36q^{5} \) \(\mathstrut -\mathstrut 222q^{6} \) \(\mathstrut -\mathstrut 119q^{7} \) \(\mathstrut -\mathstrut 177q^{8} \) \(\mathstrut +\mathstrut 891q^{9} \) \(\mathstrut +\mathstrut 1542q^{10} \) \(\mathstrut +\mathstrut 204q^{11} \) \(\mathstrut -\mathstrut 2310q^{12} \) \(\mathstrut -\mathstrut 2338q^{13} \) \(\mathstrut -\mathstrut 1743q^{14} \) \(\mathstrut +\mathstrut 912q^{15} \) \(\mathstrut +\mathstrut 3601q^{16} \) \(\mathstrut +\mathstrut 2424q^{17} \) \(\mathstrut +\mathstrut 3795q^{18} \) \(\mathstrut -\mathstrut 3004q^{19} \) \(\mathstrut -\mathstrut 4704q^{20} \) \(\mathstrut -\mathstrut 1134q^{21} \) \(\mathstrut +\mathstrut 180q^{22} \) \(\mathstrut +\mathstrut 3924q^{23} \) \(\mathstrut +\mathstrut 1794q^{24} \) \(\mathstrut -\mathstrut 5099q^{25} \) \(\mathstrut +\mathstrut 2268q^{26} \) \(\mathstrut +\mathstrut 3432q^{27} \) \(\mathstrut -\mathstrut 539q^{28} \) \(\mathstrut -\mathstrut 3990q^{29} \) \(\mathstrut -\mathstrut 19866q^{30} \) \(\mathstrut -\mathstrut 11212q^{31} \) \(\mathstrut -\mathstrut 753q^{32} \) \(\mathstrut +\mathstrut 20166q^{33} \) \(\mathstrut +\mathstrut 37998q^{34} \) \(\mathstrut +\mathstrut 29358q^{35} \) \(\mathstrut +\mathstrut 5241q^{36} \) \(\mathstrut -\mathstrut 15256q^{37} \) \(\mathstrut -\mathstrut 34368q^{38} \) \(\mathstrut -\mathstrut 20160q^{39} \) \(\mathstrut +\mathstrut 7440q^{40} \) \(\mathstrut -\mathstrut 17010q^{41} \) \(\mathstrut -\mathstrut 20034q^{42} \) \(\mathstrut -\mathstrut 17500q^{43} \) \(\mathstrut -\mathstrut 20988q^{44} \) \(\mathstrut +\mathstrut 6570q^{45} \) \(\mathstrut +\mathstrut 12462q^{46} \) \(\mathstrut +\mathstrut 43980q^{47} \) \(\mathstrut +\mathstrut 43710q^{48} \) \(\mathstrut +\mathstrut 12103q^{49} \) \(\mathstrut +\mathstrut 40173q^{50} \) \(\mathstrut +\mathstrut 32088q^{51} \) \(\mathstrut +\mathstrut 23324q^{52} \) \(\mathstrut +\mathstrut 8688q^{53} \) \(\mathstrut -\mathstrut 111054q^{54} \) \(\mathstrut -\mathstrut 102048q^{55} \) \(\mathstrut -\mathstrut 40593q^{56} \) \(\mathstrut -\mathstrut 23868q^{57} \) \(\mathstrut +\mathstrut 61986q^{58} \) \(\mathstrut +\mathstrut 19140q^{59} \) \(\mathstrut +\mathstrut 41244q^{60} \) \(\mathstrut +\mathstrut 3380q^{61} \) \(\mathstrut -\mathstrut 6984q^{62} \) \(\mathstrut +\mathstrut 24885q^{63} \) \(\mathstrut -\mathstrut 18239q^{64} \) \(\mathstrut +\mathstrut 50064q^{65} \) \(\mathstrut +\mathstrut 125190q^{66} \) \(\mathstrut -\mathstrut 65932q^{67} \) \(\mathstrut -\mathstrut 137550q^{68} \) \(\mathstrut -\mathstrut 118620q^{69} \) \(\mathstrut -\mathstrut 130494q^{70} \) \(\mathstrut +\mathstrut 34440q^{71} \) \(\mathstrut +\mathstrut 58143q^{72} \) \(\mathstrut +\mathstrut 136040q^{73} \) \(\mathstrut +\mathstrut 194784q^{74} \) \(\mathstrut +\mathstrut 75948q^{75} \) \(\mathstrut +\mathstrut 58226q^{76} \) \(\mathstrut +\mathstrut 73374q^{77} \) \(\mathstrut -\mathstrut 37632q^{78} \) \(\mathstrut +\mathstrut 74036q^{79} \) \(\mathstrut -\mathstrut 218832q^{80} \) \(\mathstrut -\mathstrut 157671q^{81} \) \(\mathstrut +\mathstrut 53550q^{82} \) \(\mathstrut -\mathstrut 111636q^{83} \) \(\mathstrut +\mathstrut 14994q^{84} \) \(\mathstrut -\mathstrut 47640q^{85} \) \(\mathstrut -\mathstrut 345624q^{86} \) \(\mathstrut -\mathstrut 191040q^{87} \) \(\mathstrut -\mathstrut 103680q^{88} \) \(\mathstrut +\mathstrut 60360q^{89} \) \(\mathstrut +\mathstrut 328836q^{90} \) \(\mathstrut +\mathstrut 125342q^{91} \) \(\mathstrut +\mathstrut 254376q^{92} \) \(\mathstrut -\mathstrut 23982q^{93} \) \(\mathstrut -\mathstrut 31806q^{94} \) \(\mathstrut +\mathstrut 227892q^{95} \) \(\mathstrut +\mathstrut 239106q^{96} \) \(\mathstrut +\mathstrut 380534q^{97} \) \(\mathstrut +\mathstrut 96285q^{98} \) \(\mathstrut -\mathstrut 161532q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)

We only show spaces with even 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
7.6.a \(\chi_{7}(1, \cdot)\) 7.6.a.a 1 1
7.6.a.b 2
7.6.c \(\chi_{7}(2, \cdot)\) 7.6.c.a 4 2