↑

Properties

Label 549.2
Level 549
Weight 2
Dimension 8565
Nonzero newspaces 30
Newform subspaces 86
Sturm bound 44640
Trace bound 5

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 549 = 3^{2} \cdot 61 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 30 \)
Newform subspaces: \( 86 \)
Sturm bound: \(44640\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(549))\).

Total New Old
Modular forms 11640 9095 2545
Cusp forms 10681 8565 2116
Eisenstein series 959 530 429

Trace form

\( 8565 q - 90 q^{2} - 120 q^{3} - 90 q^{4} - 90 q^{5} - 120 q^{6} - 90 q^{7} - 90 q^{8} - 120 q^{9} + O(q^{10}) \) \( 8565 q - 90 q^{2} - 120 q^{3} - 90 q^{4} - 90 q^{5} - 120 q^{6} - 90 q^{7} - 90 q^{8} - 120 q^{9} - 270 q^{10} - 90 q^{11} - 120 q^{12} - 90 q^{13} - 90 q^{14} - 120 q^{15} - 90 q^{16} - 90 q^{17} - 120 q^{18} - 270 q^{19} - 90 q^{20} - 120 q^{21} - 90 q^{22} - 90 q^{23} - 120 q^{24} - 90 q^{25} - 90 q^{26} - 120 q^{27} - 270 q^{28} - 90 q^{29} - 120 q^{30} - 90 q^{31} - 90 q^{32} - 120 q^{33} - 90 q^{34} - 90 q^{35} - 120 q^{36} - 270 q^{37} - 90 q^{38} - 120 q^{39} - 90 q^{40} - 90 q^{41} - 120 q^{42} - 90 q^{43} - 90 q^{44} - 120 q^{45} - 270 q^{46} - 120 q^{47} - 120 q^{48} - 160 q^{49} - 165 q^{50} - 120 q^{51} - 315 q^{52} - 120 q^{53} - 120 q^{54} - 390 q^{55} - 270 q^{56} - 120 q^{57} - 210 q^{58} - 150 q^{59} - 120 q^{60} - 220 q^{61} - 360 q^{62} - 120 q^{63} - 510 q^{64} - 150 q^{65} - 120 q^{66} - 210 q^{67} - 270 q^{68} - 120 q^{69} - 270 q^{70} - 120 q^{71} - 120 q^{72} - 330 q^{73} - 165 q^{74} - 120 q^{75} - 190 q^{76} - 120 q^{77} - 120 q^{78} - 90 q^{79} - 90 q^{80} - 120 q^{81} - 270 q^{82} - 90 q^{83} - 120 q^{84} - 90 q^{85} - 90 q^{86} - 120 q^{87} - 90 q^{88} - 90 q^{89} - 120 q^{90} - 270 q^{91} - 90 q^{92} - 120 q^{93} - 90 q^{94} - 90 q^{95} - 120 q^{96} - 90 q^{97} - 90 q^{98} - 120 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(549))\)

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
549.2.a \(\chi_{549}(1, \cdot)\) 549.2.a.a 1 1
549.2.a.b 1
549.2.a.c 1
549.2.a.d 2
549.2.a.e 2
549.2.a.f 3
549.2.a.g 3
549.2.a.h 6
549.2.a.i 6
549.2.c \(\chi_{549}(487, \cdot)\) 549.2.c.a 2 1
549.2.c.b 2
549.2.c.c 4
549.2.c.d 4
549.2.c.e 6
549.2.c.f 8
549.2.e \(\chi_{549}(352, \cdot)\) 549.2.e.a 2 2
549.2.e.b 2
549.2.e.c 4
549.2.e.d 4
549.2.e.e 6
549.2.e.f 6
549.2.e.g 8
549.2.e.h 16
549.2.f \(\chi_{549}(184, \cdot)\) 549.2.f.a 2 2
549.2.f.b 2
549.2.f.c 4
549.2.f.d 54
549.2.f.e 58
549.2.g \(\chi_{549}(196, \cdot)\) 549.2.g.a 10 2
549.2.g.b 110
549.2.h \(\chi_{549}(13, \cdot)\) 549.2.h.a 10 2
549.2.h.b 110
549.2.j \(\chi_{549}(233, \cdot)\) 549.2.j.a 44 2
549.2.k \(\chi_{549}(217, \cdot)\) 549.2.k.a 12 4
549.2.k.b 20
549.2.k.c 28
549.2.k.d 40
549.2.l \(\chi_{549}(292, \cdot)\) 549.2.l.a 2 2
549.2.l.b 4
549.2.l.c 114
549.2.r \(\chi_{549}(121, \cdot)\) 549.2.r.a 4 2
549.2.r.b 116
549.2.s \(\chi_{549}(109, \cdot)\) 549.2.s.a 2 2
549.2.s.b 2
549.2.s.c 2
549.2.s.d 4
549.2.s.e 4
549.2.s.f 4
549.2.s.g 8
549.2.s.h 8
549.2.s.i 8
549.2.s.j 8
549.2.v \(\chi_{549}(319, \cdot)\) 549.2.v.a 2 2
549.2.v.b 4
549.2.v.c 114
549.2.y \(\chi_{549}(64, \cdot)\) 549.2.y.a 16 4
549.2.y.b 16
549.2.y.c 24
549.2.y.d 48
549.2.ba \(\chi_{549}(29, \cdot)\) 549.2.ba.a 240 4
549.2.bd \(\chi_{549}(11, \cdot)\) 549.2.bd.a 4 4
549.2.bd.b 236
549.2.be \(\chi_{549}(143, \cdot)\) 549.2.be.a 80 4
549.2.bh \(\chi_{549}(32, \cdot)\) 549.2.bh.a 240 4
549.2.bi \(\chi_{549}(22, \cdot)\) 549.2.bi.a 480 8
549.2.bj \(\chi_{549}(16, \cdot)\) 549.2.bj.a 480 8
549.2.bk \(\chi_{549}(34, \cdot)\) 549.2.bk.a 480 8
549.2.bl \(\chi_{549}(73, \cdot)\) 549.2.bl.a 8 8
549.2.bl.b 32
549.2.bl.c 40
549.2.bl.d 48
549.2.bl.e 64
549.2.bm \(\chi_{549}(8, \cdot)\) 549.2.bm.a 176 8
549.2.bp \(\chi_{549}(4, \cdot)\) 549.2.bp.a 480 8
549.2.bs \(\chi_{549}(19, \cdot)\) 549.2.bs.a 8 8
549.2.bs.b 16
549.2.bs.c 16
549.2.bs.d 40
549.2.bs.e 40
549.2.bs.f 80
549.2.bt \(\chi_{549}(52, \cdot)\) 549.2.bt.a 480 8
549.2.bz \(\chi_{549}(97, \cdot)\) 549.2.bz.a 480 8
549.2.ca \(\chi_{549}(2, \cdot)\) 549.2.ca.a 960 16
549.2.cd \(\chi_{549}(17, \cdot)\) 549.2.cd.a 320 16
549.2.ce \(\chi_{549}(23, \cdot)\) 549.2.ce.a 960 16
549.2.ch \(\chi_{549}(59, \cdot)\) 549.2.ch.a 960 16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(549))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(549)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(61))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(183))\)\(^{\oplus 2}\)