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Properties

Label 207.4
Level 207
Weight 4
Dimension 3653
Nonzero newspaces 8
Newform subspaces 20
Sturm bound 12672
Trace bound 2

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Defining parameters

Level: \( N \) = \( 207 = 3^{2} \cdot 23 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 20 \)
Sturm bound: \(12672\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(207))\).

Total New Old
Modular forms 4928 3841 1087
Cusp forms 4576 3653 923
Eisenstein series 352 188 164

Trace form

\( 3653 q - 27 q^{2} - 38 q^{3} - 7 q^{4} - 3 q^{5} - 62 q^{6} - 59 q^{7} - 165 q^{8} - 134 q^{9} + O(q^{10}) \) \( 3653 q - 27 q^{2} - 38 q^{3} - 7 q^{4} - 3 q^{5} - 62 q^{6} - 59 q^{7} - 165 q^{8} - 134 q^{9} - 123 q^{10} + 99 q^{11} + 268 q^{12} + 85 q^{13} + 87 q^{14} - 98 q^{15} - 615 q^{16} - 517 q^{17} - 476 q^{18} + 207 q^{19} + 647 q^{20} - 86 q^{21} + 374 q^{22} + 484 q^{23} + 110 q^{24} + 327 q^{25} + 1243 q^{26} + 820 q^{27} - 795 q^{28} - 355 q^{29} - 620 q^{30} - 1113 q^{31} - 2375 q^{32} - 440 q^{33} - 1353 q^{34} - 1475 q^{35} + 406 q^{36} - 1307 q^{37} - 1760 q^{38} - 1562 q^{39} + 1815 q^{40} + 781 q^{41} + 928 q^{42} + 2899 q^{43} + 4466 q^{44} + 1306 q^{45} + 4389 q^{46} + 2624 q^{47} - 2 q^{48} + 1005 q^{49} + 1034 q^{50} - 638 q^{51} - 2363 q^{52} - 491 q^{53} + 3774 q^{54} + 2937 q^{55} + 13948 q^{56} + 6622 q^{57} - 714 q^{58} + 1453 q^{59} + 908 q^{60} - 1103 q^{61} - 5637 q^{62} - 5430 q^{63} - 8839 q^{64} - 12639 q^{65} - 8976 q^{66} - 653 q^{67} - 25542 q^{68} - 8415 q^{69} - 16854 q^{70} - 15735 q^{71} - 16610 q^{72} - 3827 q^{73} - 10798 q^{74} - 3322 q^{75} - 13558 q^{76} - 4939 q^{77} + 4840 q^{78} - 723 q^{79} + 16644 q^{80} + 8834 q^{81} + 7755 q^{82} + 16487 q^{83} + 21376 q^{84} + 20009 q^{85} + 22451 q^{86} + 262 q^{87} + 8657 q^{88} + 7161 q^{89} + 1644 q^{90} + 13822 q^{91} + 8118 q^{92} + 338 q^{93} + 12494 q^{94} + 3729 q^{95} - 796 q^{96} + 1789 q^{97} - 981 q^{98} - 638 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(207))\)

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
207.4.a \(\chi_{207}(1, \cdot)\) 207.4.a.a 1 1
207.4.a.b 2
207.4.a.c 2
207.4.a.d 4
207.4.a.e 4
207.4.a.f 4
207.4.a.g 5
207.4.a.h 5
207.4.c \(\chi_{207}(206, \cdot)\) 207.4.c.a 24 1
207.4.e \(\chi_{207}(70, \cdot)\) 207.4.e.a 60 2
207.4.e.b 72
207.4.g \(\chi_{207}(68, \cdot)\) 207.4.g.a 12 2
207.4.g.b 128
207.4.i \(\chi_{207}(55, \cdot)\) 207.4.i.a 50 10
207.4.i.b 60
207.4.i.c 60
207.4.i.d 120
207.4.k \(\chi_{207}(17, \cdot)\) 207.4.k.a 240 10
207.4.m \(\chi_{207}(4, \cdot)\) 207.4.m.a 1400 20
207.4.o \(\chi_{207}(5, \cdot)\) 207.4.o.a 1400 20

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(207))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(207)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 2}\)