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Properties

Label 47.4
Level 47
Weight 4
Dimension 253
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 736
Trace bound 1

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Defining parameters

Level: \( N \) = \( 47 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(736\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(47))\).

Total New Old
Modular forms 299 297 2
Cusp forms 253 253 0
Eisenstein series 46 44 2

Trace form

\( 253 q - 23 q^{2} - 23 q^{3} - 23 q^{4} - 23 q^{5} - 23 q^{6} - 23 q^{7} - 23 q^{8} - 23 q^{9} + O(q^{10}) \) \( 253 q - 23 q^{2} - 23 q^{3} - 23 q^{4} - 23 q^{5} - 23 q^{6} - 23 q^{7} - 23 q^{8} - 23 q^{9} - 23 q^{10} - 23 q^{11} - 23 q^{12} - 23 q^{13} - 23 q^{14} - 23 q^{15} - 23 q^{16} - 23 q^{17} - 23 q^{18} - 23 q^{19} - 23 q^{20} - 23 q^{21} - 23 q^{22} - 23 q^{23} - 23 q^{24} - 23 q^{25} - 23 q^{26} - 23 q^{27} - 23 q^{28} - 23 q^{29} - 23 q^{30} - 23 q^{31} - 23 q^{32} - 23 q^{33} - 23 q^{34} - 2001 q^{35} - 5911 q^{36} - 1035 q^{37} - 1219 q^{38} - 713 q^{39} + 529 q^{40} + 1081 q^{41} + 3565 q^{42} + 759 q^{43} + 3657 q^{44} + 5037 q^{45} + 4186 q^{46} + 2093 q^{47} + 10074 q^{48} + 1817 q^{49} + 3105 q^{50} + 2967 q^{51} + 1449 q^{52} + 69 q^{53} - 1403 q^{54} - 1817 q^{55} - 6095 q^{56} - 4439 q^{57} - 3979 q^{58} - 2553 q^{59} - 12535 q^{60} - 3795 q^{61} - 23 q^{62} - 23 q^{63} - 23 q^{64} - 23 q^{65} - 23 q^{66} - 23 q^{67} - 23 q^{68} - 23 q^{69} - 23 q^{70} - 23 q^{71} - 23 q^{72} - 23 q^{73} - 23 q^{74} - 23 q^{75} - 9821 q^{76} - 8257 q^{77} - 20309 q^{78} - 10787 q^{79} - 14352 q^{80} - 8717 q^{81} - 8096 q^{82} - 805 q^{83} + 805 q^{84} + 3841 q^{85} + 6785 q^{86} + 4669 q^{87} + 17365 q^{88} + 6693 q^{89} + 29785 q^{90} + 19987 q^{91} + 18630 q^{92} + 8510 q^{93} + 25645 q^{94} + 16698 q^{95} + 23805 q^{96} + 7429 q^{97} + 15088 q^{98} + 14467 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(47))\)

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
47.4.a \(\chi_{47}(1, \cdot)\) 47.4.a.a 3 1
47.4.a.b 8
47.4.c \(\chi_{47}(2, \cdot)\) 47.4.c.a 242 22