Properties

Label 7.10
Level 7
Weight 10
Dimension 15
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 40
Trace bound 1

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Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(40\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(7))\).

Total New Old
Modular forms 21 19 2
Cusp forms 15 15 0
Eisenstein series 6 4 2

Trace form

\( 15 q - 3 q^{2} + 159 q^{3} - 3 q^{4} + 849 q^{5} - 7782 q^{6} + 1365 q^{7} + 50943 q^{8} - 50697 q^{9} + O(q^{10}) \) \( 15 q - 3 q^{2} + 159 q^{3} - 3 q^{4} + 849 q^{5} - 7782 q^{6} + 1365 q^{7} + 50943 q^{8} - 50697 q^{9} - 50178 q^{10} + 74085 q^{11} + 81354 q^{12} - 365988 q^{13} + 25305 q^{14} + 44562 q^{15} + 804273 q^{16} + 877455 q^{17} - 954093 q^{18} - 718695 q^{19} - 1798944 q^{20} - 1149687 q^{21} - 1731852 q^{22} + 5302623 q^{23} + 10301394 q^{24} + 3850851 q^{25} - 8733228 q^{26} - 20578290 q^{27} - 16929339 q^{28} + 9370734 q^{29} + 32707014 q^{30} + 24515937 q^{31} + 20243007 q^{32} - 34211217 q^{33} - 69138018 q^{34} - 34642167 q^{35} + 30467433 q^{36} + 71698155 q^{37} + 114349800 q^{38} - 5872230 q^{39} - 109547520 q^{40} - 86960958 q^{41} - 161756154 q^{42} + 44269920 q^{43} + 178065924 q^{44} + 137211210 q^{45} + 87626046 q^{46} - 60054321 q^{47} - 197149314 q^{48} - 20200593 q^{49} - 11659107 q^{50} + 77993031 q^{51} + 56451612 q^{52} - 13401909 q^{53} - 13843902 q^{54} - 168072438 q^{55} + 142817871 q^{56} - 81458118 q^{57} - 139251342 q^{58} - 2882805 q^{59} + 29006124 q^{60} + 122988189 q^{61} + 475392360 q^{62} + 229140891 q^{63} - 36739647 q^{64} - 343809606 q^{65} - 927999018 q^{66} - 623805003 q^{67} + 941394258 q^{68} + 1386338886 q^{69} + 358585626 q^{70} - 685727712 q^{71} - 1839019713 q^{72} - 1014197529 q^{73} - 95367408 q^{74} + 923197398 q^{75} + 2112827346 q^{76} + 1818829131 q^{77} + 894536160 q^{78} - 1018942977 q^{79} - 2340781872 q^{80} - 69910596 q^{81} - 389441682 q^{82} - 801356430 q^{83} + 105840882 q^{84} - 585705750 q^{85} - 1976461080 q^{86} - 934468602 q^{87} + 1123814592 q^{88} + 2804638671 q^{89} + 3997968636 q^{90} + 742843332 q^{91} - 940148952 q^{92} + 478677063 q^{93} + 963200754 q^{94} - 2295446583 q^{95} - 2823517662 q^{96} - 1410444126 q^{97} - 2318361843 q^{98} - 2392338492 q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(7))\)

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
7.10.a \(\chi_{7}(1, \cdot)\) 7.10.a.a 2 1
7.10.a.b 3
7.10.c \(\chi_{7}(2, \cdot)\) 7.10.c.a 10 2