↑

Properties

Label 37.6
Level 37
Weight 6
Dimension 267
Nonzero newspaces 6
Newform subspaces 7
Sturm bound 684
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 37 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 7 \)
Sturm bound: \(684\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(37))\).

Total New Old
Modular forms 303 301 2
Cusp forms 267 267 0
Eisenstein series 36 34 2

Trace form

\( 267 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} + O(q^{10}) \) \( 267 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 18 q^{18} - 18 q^{19} - 18 q^{20} - 18 q^{21} - 18 q^{22} - 18 q^{23} - 18 q^{24} - 18 q^{25} - 25902 q^{26} - 17514 q^{27} + 29742 q^{28} + 18360 q^{29} + 75150 q^{30} + 39888 q^{31} + 18414 q^{32} - 10062 q^{33} - 55026 q^{34} - 60552 q^{35} - 174996 q^{36} - 52896 q^{37} - 36180 q^{38} - 23076 q^{39} + 8622 q^{40} + 41508 q^{41} + 106254 q^{42} + 74538 q^{43} + 173934 q^{44} + 126828 q^{45} + 121230 q^{46} + 3780 q^{47} - 138258 q^{48} - 146874 q^{49} - 103662 q^{50} - 18 q^{51} - 18 q^{52} - 18 q^{53} - 18 q^{54} - 18 q^{55} - 18 q^{56} - 18 q^{57} - 267120 q^{58} - 259398 q^{59} - 219384 q^{60} + 85257 q^{61} + 361872 q^{62} + 532530 q^{63} + 616752 q^{64} + 336861 q^{65} + 742122 q^{66} + 52218 q^{67} - 16110 q^{68} - 245538 q^{69} - 612036 q^{70} - 302778 q^{71} - 1252782 q^{72} - 383724 q^{73} - 756738 q^{74} - 853416 q^{75} - 548514 q^{76} - 179226 q^{77} - 216486 q^{78} + 71622 q^{79} + 585864 q^{80} + 704862 q^{81} + 717210 q^{82} + 288378 q^{83} + 2216322 q^{84} + 709461 q^{85} + 963252 q^{86} + 558450 q^{87} + 92772 q^{88} - 229743 q^{89} - 1712484 q^{90} - 1133292 q^{91} - 2433852 q^{92} - 623124 q^{93} - 156978 q^{94} + 322182 q^{95} + 1586862 q^{96} + 807030 q^{97} + 1727406 q^{98} + 1034532 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(37))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
37.6.a \(\chi_{37}(1, \cdot)\) 37.6.a.a 7 1
37.6.a.b 8
37.6.b \(\chi_{37}(36, \cdot)\) 37.6.b.a 16 1
37.6.c \(\chi_{37}(10, \cdot)\) 37.6.c.a 30 2
37.6.e \(\chi_{37}(11, \cdot)\) 37.6.e.a 32 2
37.6.f \(\chi_{37}(7, \cdot)\) 37.6.f.a 84 6
37.6.h \(\chi_{37}(3, \cdot)\) 37.6.h.a 90 6