Properties

Label 37.8
Level 37
Weight 8
Dimension 381
Nonzero newspaces 6
Newform subspaces 7
Sturm bound 912
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 37 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 7 \)
Sturm bound: \(912\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(37))\).

Total New Old
Modular forms 417 415 2
Cusp forms 381 381 0
Eisenstein series 36 34 2

Trace form

\( 381 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} + O(q^{10}) \) \( 381 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 18 q^{18} - 18 q^{19} - 18 q^{20} - 18 q^{21} - 18 q^{22} - 18 q^{23} - 18 q^{24} - 18 q^{25} - 792234 q^{26} + 472374 q^{27} + 1931502 q^{28} + 137340 q^{29} - 1415250 q^{30} - 1787904 q^{31} - 2064402 q^{32} - 368406 q^{33} + 1023534 q^{34} + 1927728 q^{35} + 6298524 q^{36} + 1790148 q^{37} + 834876 q^{38} - 325476 q^{39} - 5736978 q^{40} - 3819384 q^{41} - 5863122 q^{42} - 2359206 q^{43} - 1387026 q^{44} + 2794968 q^{45} + 9196974 q^{46} + 3044916 q^{47} + 6635502 q^{48} - 3511914 q^{49} - 6664842 q^{50} - 18 q^{51} - 18 q^{52} - 18 q^{53} - 18 q^{54} - 18 q^{55} - 18 q^{56} - 18 q^{57} - 19001952 q^{58} - 3063366 q^{59} + 38693448 q^{60} + 15773967 q^{61} + 19325952 q^{62} + 2013858 q^{63} - 20214576 q^{64} - 22576257 q^{65} - 80258742 q^{66} - 10128870 q^{67} - 19687662 q^{68} - 6382530 q^{69} + 20992140 q^{70} + 17463078 q^{71} + 86308434 q^{72} + 28009188 q^{73} + 53674110 q^{74} + 52705944 q^{75} + 22623390 q^{76} - 1309482 q^{77} - 52900614 q^{78} - 28062234 q^{79} - 104316120 q^{80} - 85139586 q^{81} - 60256134 q^{82} - 14818086 q^{83} - 38377854 q^{84} + 16081803 q^{85} + 74457540 q^{86} + 101388546 q^{87} + 100030212 q^{88} + 41607747 q^{89} + 16440588 q^{90} - 86939556 q^{91} - 184444668 q^{92} + 27361080 q^{93} + 92389806 q^{94} + 95750982 q^{95} + 172235502 q^{96} + 28600038 q^{97} - 26209170 q^{98} - 60254388 q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(37))\)

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
37.8.a \(\chi_{37}(1, \cdot)\) 37.8.a.a 10 1
37.8.a.b 11
37.8.b \(\chi_{37}(36, \cdot)\) 37.8.b.a 20 1
37.8.c \(\chi_{37}(10, \cdot)\) 37.8.c.a 42 2
37.8.e \(\chi_{37}(11, \cdot)\) 37.8.e.a 40 2
37.8.f \(\chi_{37}(7, \cdot)\) 37.8.f.a 132 6
37.8.h \(\chi_{37}(3, \cdot)\) 37.8.h.a 126 6