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Properties

Label 558.2
Level 558
Weight 2
Dimension 2276
Nonzero newspaces 20
Newform subspaces 63
Sturm bound 34560
Trace bound 12

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Defining parameters

Level: \( N \) = \( 558 = 2 \cdot 3^{2} \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Newform subspaces: \( 63 \)
Sturm bound: \(34560\)
Trace bound: \(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(558))\).

Total New Old
Modular forms 9120 2276 6844
Cusp forms 8161 2276 5885
Eisenstein series 959 0 959

Trace form

\( 2276 q + 2 q^{2} + 6 q^{3} + 2 q^{4} - 6 q^{6} + 4 q^{7} - 4 q^{8} - 6 q^{9} + O(q^{10}) \) \( 2276 q + 2 q^{2} + 6 q^{3} + 2 q^{4} - 6 q^{6} + 4 q^{7} - 4 q^{8} - 6 q^{9} - 6 q^{11} + 4 q^{13} + 4 q^{14} + 2 q^{16} + 12 q^{17} + 12 q^{18} + 4 q^{19} - 12 q^{21} + 24 q^{22} + 18 q^{23} + 6 q^{24} + 60 q^{25} + 22 q^{26} + 32 q^{28} + 72 q^{29} + 56 q^{31} + 2 q^{32} + 18 q^{33} + 54 q^{34} + 60 q^{35} - 6 q^{36} + 106 q^{37} + 28 q^{38} + 48 q^{41} + 8 q^{43} + 12 q^{44} + 24 q^{46} - 12 q^{47} - 6 q^{48} + 24 q^{49} - 10 q^{50} - 18 q^{51} + 4 q^{52} - 18 q^{53} - 18 q^{54} + 60 q^{55} + 4 q^{56} - 6 q^{57} + 12 q^{58} + 36 q^{59} + 106 q^{61} + 8 q^{62} + 24 q^{63} - 4 q^{64} + 90 q^{65} + 40 q^{67} - 6 q^{68} + 108 q^{71} - 6 q^{72} - 14 q^{73} - 8 q^{74} - 30 q^{75} - 32 q^{76} - 252 q^{77} - 168 q^{78} - 218 q^{79} - 90 q^{80} - 222 q^{81} - 216 q^{82} - 606 q^{83} - 108 q^{84} - 360 q^{85} - 362 q^{86} - 276 q^{87} - 186 q^{88} - 474 q^{89} - 360 q^{90} - 406 q^{91} - 12 q^{92} - 480 q^{93} - 192 q^{94} - 720 q^{95} - 380 q^{97} - 528 q^{98} - 336 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(558))\)

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
558.2.a \(\chi_{558}(1, \cdot)\) 558.2.a.a 1 1
558.2.a.b 1
558.2.a.c 1
558.2.a.d 1
558.2.a.e 1
558.2.a.f 1
558.2.a.g 1
558.2.a.h 1
558.2.a.i 2
558.2.a.j 2
558.2.c \(\chi_{558}(557, \cdot)\) 558.2.c.a 8 1
558.2.e \(\chi_{558}(253, \cdot)\) 558.2.e.a 2 2
558.2.e.b 2
558.2.e.c 2
558.2.e.d 2
558.2.e.e 4
558.2.e.f 4
558.2.e.g 6
558.2.e.h 6
558.2.f \(\chi_{558}(187, \cdot)\) 558.2.f.a 2 2
558.2.f.b 2
558.2.f.c 4
558.2.f.d 8
558.2.f.e 8
558.2.f.f 16
558.2.f.g 20
558.2.g \(\chi_{558}(211, \cdot)\) 558.2.g.a 32 2
558.2.g.b 32
558.2.h \(\chi_{558}(25, \cdot)\) 558.2.h.a 32 2
558.2.h.b 32
558.2.i \(\chi_{558}(109, \cdot)\) 558.2.i.a 4 4
558.2.i.b 4
558.2.i.c 4
558.2.i.d 4
558.2.i.e 4
558.2.i.f 4
558.2.i.g 8
558.2.i.h 8
558.2.i.i 8
558.2.j \(\chi_{558}(491, \cdot)\) 558.2.j.a 64 2
558.2.p \(\chi_{558}(161, \cdot)\) 558.2.p.a 24 2
558.2.q \(\chi_{558}(185, \cdot)\) 558.2.q.a 64 2
558.2.t \(\chi_{558}(119, \cdot)\) 558.2.t.a 64 2
558.2.v \(\chi_{558}(89, \cdot)\) 558.2.v.a 32 4
558.2.y \(\chi_{558}(121, \cdot)\) 558.2.y.a 128 8
558.2.y.b 128
558.2.z \(\chi_{558}(97, \cdot)\) 558.2.z.a 128 8
558.2.z.b 128
558.2.ba \(\chi_{558}(19, \cdot)\) 558.2.ba.a 8 8
558.2.ba.b 8
558.2.ba.c 8
558.2.ba.d 8
558.2.ba.e 8
558.2.ba.f 8
558.2.ba.g 16
558.2.ba.h 24
558.2.ba.i 24
558.2.bb \(\chi_{558}(7, \cdot)\) 558.2.bb.a 128 8
558.2.bb.b 128
558.2.bd \(\chi_{558}(65, \cdot)\) 558.2.bd.a 256 8
558.2.bh \(\chi_{558}(11, \cdot)\) 558.2.bh.a 256 8
558.2.bk \(\chi_{558}(23, \cdot)\) 558.2.bk.a 256 8
558.2.bl \(\chi_{558}(17, \cdot)\) 558.2.bl.a 96 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(558))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(558)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(186))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(279))\)\(^{\oplus 2}\)