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Properties

Label 37.4
Level 37
Weight 4
Dimension 153
Nonzero newspaces 6
Newform subspaces 7
Sturm bound 456
Trace bound 1

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Defining parameters

Level: \( N \) = \( 37 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 7 \)
Sturm bound: \(456\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(37))\).

Total New Old
Modular forms 189 187 2
Cusp forms 153 153 0
Eisenstein series 36 34 2

Trace form

\( 153 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} + O(q^{10}) \) \( 153 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 18 q^{18} - 18 q^{19} - 18 q^{20} - 18 q^{21} - 18 q^{22} - 18 q^{23} - 18 q^{24} - 18 q^{25} - 684 q^{26} - 1314 q^{27} - 2178 q^{28} - 378 q^{29} - 450 q^{30} + 306 q^{31} + 1134 q^{32} + 846 q^{33} + 2142 q^{34} + 1818 q^{35} + 4824 q^{36} + 1494 q^{37} + 1188 q^{38} + 1242 q^{39} + 3222 q^{40} + 846 q^{41} + 414 q^{42} - 234 q^{43} - 1458 q^{44} - 1962 q^{45} - 3906 q^{46} - 1350 q^{47} - 5778 q^{48} - 2898 q^{49} - 1332 q^{50} - 18 q^{51} - 18 q^{52} - 18 q^{53} - 18 q^{54} - 18 q^{55} - 18 q^{56} - 18 q^{57} - 3024 q^{58} - 4950 q^{59} - 13752 q^{60} - 3753 q^{61} - 5328 q^{62} - 4014 q^{63} - 2160 q^{64} + 63 q^{65} + 4266 q^{66} + 1098 q^{67} + 4626 q^{68} + 7614 q^{69} + 12060 q^{70} + 4806 q^{71} + 17730 q^{72} + 5220 q^{73} + 10494 q^{74} + 12744 q^{75} + 9486 q^{76} + 4374 q^{77} + 13338 q^{78} + 3078 q^{79} + 6120 q^{80} + 2430 q^{81} + 90 q^{82} - 630 q^{83} - 9342 q^{84} - 4797 q^{85} - 10476 q^{86} - 11790 q^{87} - 12348 q^{88} - 7533 q^{89} - 25092 q^{90} - 10026 q^{91} - 21564 q^{92} - 10602 q^{93} - 11682 q^{94} - 9378 q^{95} - 18018 q^{96} - 5202 q^{97} - 6642 q^{98} - 1998 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(37))\)

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
37.4.a \(\chi_{37}(1, \cdot)\) 37.4.a.a 4 1
37.4.a.b 5
37.4.b \(\chi_{37}(36, \cdot)\) 37.4.b.a 8 1
37.4.c \(\chi_{37}(10, \cdot)\) 37.4.c.a 18 2
37.4.e \(\chi_{37}(11, \cdot)\) 37.4.e.a 16 2
37.4.f \(\chi_{37}(7, \cdot)\) 37.4.f.a 54 6
37.4.h \(\chi_{37}(3, \cdot)\) 37.4.h.a 48 6