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Properties

Label 279.2
Level 279
Weight 2
Dimension 2145
Nonzero newspaces 20
Newform subspaces 37
Sturm bound 11520
Trace bound 5

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Defining parameters

Level: \( N \) = \( 279 = 3^{2} \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Newform subspaces: \( 37 \)
Sturm bound: \(11520\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(279))\).

Total New Old
Modular forms 3120 2405 715
Cusp forms 2641 2145 496
Eisenstein series 479 260 219

Trace form

\( 2145 q - 45 q^{2} - 60 q^{3} - 45 q^{4} - 45 q^{5} - 60 q^{6} - 45 q^{7} - 45 q^{8} - 60 q^{9} + O(q^{10}) \) \( 2145 q - 45 q^{2} - 60 q^{3} - 45 q^{4} - 45 q^{5} - 60 q^{6} - 45 q^{7} - 45 q^{8} - 60 q^{9} - 135 q^{10} - 45 q^{11} - 60 q^{12} - 45 q^{13} - 45 q^{14} - 60 q^{15} - 45 q^{16} - 45 q^{17} - 60 q^{18} - 135 q^{19} - 45 q^{20} - 60 q^{21} - 75 q^{22} - 60 q^{23} - 60 q^{24} - 80 q^{25} - 75 q^{26} - 60 q^{27} - 215 q^{28} - 75 q^{29} - 60 q^{30} - 75 q^{31} - 180 q^{32} - 60 q^{33} - 105 q^{34} - 75 q^{35} - 60 q^{36} - 180 q^{37} - 75 q^{38} - 60 q^{39} - 105 q^{40} - 60 q^{41} - 60 q^{42} - 50 q^{43} - 45 q^{44} - 60 q^{45} - 135 q^{46} - 45 q^{47} - 60 q^{48} - 75 q^{49} - 120 q^{50} - 60 q^{51} - 120 q^{52} - 75 q^{53} - 60 q^{54} - 195 q^{55} - 180 q^{56} - 60 q^{57} - 150 q^{58} - 75 q^{59} - 150 q^{61} - 135 q^{62} - 120 q^{63} - 255 q^{64} - 135 q^{65} - 60 q^{66} - 75 q^{67} - 150 q^{68} - 60 q^{69} - 180 q^{70} - 105 q^{71} - 60 q^{72} - 165 q^{73} - 120 q^{74} - 30 q^{75} + 30 q^{76} + 60 q^{77} + 120 q^{78} + 60 q^{79} + 405 q^{80} + 60 q^{81} + 45 q^{82} + 270 q^{83} + 300 q^{84} + 135 q^{85} + 315 q^{86} + 60 q^{87} + 495 q^{88} + 180 q^{89} + 300 q^{90} + 60 q^{91} + 540 q^{92} + 180 q^{93} + 90 q^{94} + 315 q^{95} + 300 q^{96} + 150 q^{97} + 495 q^{98} + 90 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(279))\)

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
279.2.a \(\chi_{279}(1, \cdot)\) 279.2.a.a 2 1
279.2.a.b 2
279.2.a.c 3
279.2.a.d 6
279.2.c \(\chi_{279}(278, \cdot)\) 279.2.c.a 12 1
279.2.e \(\chi_{279}(160, \cdot)\) 279.2.e.a 60 2
279.2.f \(\chi_{279}(94, \cdot)\) 279.2.f.a 30 2
279.2.f.b 30
279.2.g \(\chi_{279}(25, \cdot)\) 279.2.g.a 60 2
279.2.h \(\chi_{279}(118, \cdot)\) 279.2.h.a 2 2
279.2.h.b 4
279.2.h.c 4
279.2.h.d 6
279.2.h.e 8
279.2.i \(\chi_{279}(64, \cdot)\) 279.2.i.a 4 4
279.2.i.b 8
279.2.i.c 16
279.2.i.d 24
279.2.j \(\chi_{279}(26, \cdot)\) 279.2.j.a 4 2
279.2.j.b 4
279.2.j.c 12
279.2.o \(\chi_{279}(212, \cdot)\) 279.2.o.a 60 2
279.2.r \(\chi_{279}(68, \cdot)\) 279.2.r.a 60 2
279.2.s \(\chi_{279}(92, \cdot)\) 279.2.s.a 60 2
279.2.w \(\chi_{279}(89, \cdot)\) 279.2.w.a 48 4
279.2.y \(\chi_{279}(10, \cdot)\) 279.2.y.a 8 8
279.2.y.b 16
279.2.y.c 16
279.2.y.d 24
279.2.y.e 32
279.2.z \(\chi_{279}(4, \cdot)\) 279.2.z.a 240 8
279.2.ba \(\chi_{279}(76, \cdot)\) 279.2.ba.a 240 8
279.2.bb \(\chi_{279}(7, \cdot)\) 279.2.bb.a 240 8
279.2.be \(\chi_{279}(65, \cdot)\) 279.2.be.a 240 8
279.2.bg \(\chi_{279}(23, \cdot)\) 279.2.bg.a 240 8
279.2.bh \(\chi_{279}(11, \cdot)\) 279.2.bh.a 240 8
279.2.bn \(\chi_{279}(17, \cdot)\) 279.2.bn.a 80 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(279))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(279)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 2}\)