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Properties

Label 37.5
Level 37
Weight 5
Dimension 210
Nonzero newspaces 3
Newform subspaces 3
Sturm bound 570
Trace bound 1

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Defining parameters

Level: \( N \) = \( 37 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 3 \)
Sturm bound: \(570\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(37))\).

Total New Old
Modular forms 246 246 0
Cusp forms 210 210 0
Eisenstein series 36 36 0

Trace form

\( 210 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} + O(q^{10}) \) \( 210 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 18 q^{18} - 18 q^{19} - 18 q^{20} - 18 q^{21} - 18 q^{22} - 18 q^{23} - 18 q^{24} - 18 q^{25} + 4302 q^{26} + 5814 q^{27} + 3822 q^{28} - 1152 q^{29} - 10386 q^{30} - 10008 q^{31} - 13842 q^{32} - 6174 q^{33} - 9234 q^{34} - 3744 q^{35} + 3048 q^{37} + 5148 q^{38} + 8676 q^{39} + 34542 q^{40} + 15372 q^{41} + 20718 q^{42} + 9306 q^{43} + 13806 q^{44} + 4356 q^{45} - 5778 q^{46} - 5364 q^{47} - 34578 q^{48} - 22170 q^{49} - 12114 q^{50} - 18 q^{51} - 18 q^{52} - 18 q^{53} - 18 q^{54} - 18 q^{55} - 18 q^{56} - 18 q^{57} + 29412 q^{58} + 39294 q^{59} + 80244 q^{60} + 11862 q^{61} - 2988 q^{62} - 28098 q^{63} - 53316 q^{64} - 42786 q^{65} - 146430 q^{66} - 21186 q^{67} - 59958 q^{68} - 70290 q^{69} - 77832 q^{70} - 19890 q^{71} - 35766 q^{72} + 21150 q^{74} + 52524 q^{75} + 61470 q^{76} + 39726 q^{77} + 165042 q^{78} + 52686 q^{79} + 153828 q^{80} + 112878 q^{81} + 80658 q^{82} + 23742 q^{83} + 130266 q^{84} + 25254 q^{85} + 4896 q^{86} - 33282 q^{87} - 66168 q^{88} - 56178 q^{89} - 233496 q^{90} - 71628 q^{91} + 120888 q^{92} + 94536 q^{93} + 78318 q^{94} + 37782 q^{95} + 10062 q^{96} - 23418 q^{97} - 89874 q^{98} - 76248 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(37))\)

We only show spaces with odd 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
37.5.d \(\chi_{37}(6, \cdot)\) 37.5.d.a 22 2
37.5.g \(\chi_{37}(8, \cdot)\) 37.5.g.a 44 4
37.5.i \(\chi_{37}(2, \cdot)\) 37.5.i.a 144 12