Properties

Label 555.2
Level 555
Weight 2
Dimension 7307
Nonzero newspaces 30
Newform subspaces 56
Sturm bound 43776
Trace bound 8

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Defining parameters

Level: \( N \) = \( 555 = 3 \cdot 5 \cdot 37 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 30 \)
Newform subspaces: \( 56 \)
Sturm bound: \(43776\)
Trace bound: \(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(555))\).

Total New Old
Modular forms 11520 7723 3797
Cusp forms 10369 7307 3062
Eisenstein series 1151 416 735

Trace form

\( 7307q + 5q^{2} - 33q^{3} - 63q^{4} - q^{5} - 107q^{6} - 64q^{7} + 9q^{8} - 37q^{9} + O(q^{10}) \) \( 7307q + 5q^{2} - 33q^{3} - 63q^{4} - q^{5} - 107q^{6} - 64q^{7} + 9q^{8} - 37q^{9} - 103q^{10} + 20q^{11} - 31q^{12} - 54q^{13} + 24q^{14} - 51q^{15} - 183q^{16} + 14q^{17} - 31q^{18} - 60q^{19} + 9q^{20} - 100q^{21} - 44q^{22} + 24q^{23} - 15q^{24} - 109q^{25} + 2q^{26} - 45q^{27} - 256q^{28} - 38q^{29} - 125q^{30} - 400q^{31} - 215q^{32} - 104q^{33} - 302q^{34} - 100q^{35} - 243q^{36} - 193q^{37} - 76q^{38} - 110q^{39} - 369q^{40} - 194q^{41} - 156q^{42} - 180q^{43} - 212q^{44} - 55q^{45} - 432q^{46} - 40q^{47} - 127q^{48} - 97q^{49} - 13q^{50} - 86q^{51} + 22q^{52} + 74q^{53} - 35q^{54} - 88q^{55} + 120q^{56} - 8q^{57} - 58q^{58} - 76q^{59} - 175q^{60} - 330q^{61} - 264q^{62} - 244q^{63} - 463q^{64} - 144q^{65} - 568q^{66} - 172q^{67} - 302q^{68} - 300q^{69} - 480q^{70} - 200q^{71} - 459q^{72} - 378q^{73} - 475q^{74} - 285q^{75} - 788q^{76} - 192q^{77} - 494q^{78} - 280q^{79} - 363q^{80} - 397q^{81} - 358q^{82} - 84q^{83} - 484q^{84} - 256q^{85} - 364q^{86} - 226q^{87} - 228q^{88} - 78q^{89} - 175q^{90} - 248q^{91} + 96q^{92} + 104q^{93} + 88q^{94} + 12q^{95} + 305q^{96} + 22q^{97} + 157q^{98} + 164q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(555))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
555.2.a \(\chi_{555}(1, \cdot)\) 555.2.a.a 1 1
555.2.a.b 1
555.2.a.c 2
555.2.a.d 2
555.2.a.e 2
555.2.a.f 2
555.2.a.g 2
555.2.a.h 3
555.2.a.i 3
555.2.a.j 5
555.2.c \(\chi_{555}(334, \cdot)\) 555.2.c.a 2 1
555.2.c.b 8
555.2.c.c 26
555.2.e \(\chi_{555}(406, \cdot)\) 555.2.e.a 2 1
555.2.e.b 10
555.2.e.c 12
555.2.g \(\chi_{555}(184, \cdot)\) 555.2.g.a 40 1
555.2.i \(\chi_{555}(121, \cdot)\) 555.2.i.a 2 2
555.2.i.b 4
555.2.i.c 4
555.2.i.d 10
555.2.i.e 14
555.2.i.f 14
555.2.j \(\chi_{555}(43, \cdot)\) 555.2.j.a 76 2
555.2.m \(\chi_{555}(179, \cdot)\) 555.2.m.a 16 2
555.2.m.b 128
555.2.n \(\chi_{555}(332, \cdot)\) 555.2.n.a 32 2
555.2.n.b 112
555.2.o \(\chi_{555}(38, \cdot)\) 555.2.o.a 144 2
555.2.s \(\chi_{555}(191, \cdot)\) 555.2.s.a 104 2
555.2.t \(\chi_{555}(253, \cdot)\) 555.2.t.a 76 2
555.2.x \(\chi_{555}(64, \cdot)\) 555.2.x.a 80 2
555.2.z \(\chi_{555}(196, \cdot)\) 555.2.z.a 20 2
555.2.z.b 28
555.2.bb \(\chi_{555}(454, \cdot)\) 555.2.bb.a 72 2
555.2.bc \(\chi_{555}(16, \cdot)\) 555.2.bc.a 6 6
555.2.bc.b 36
555.2.bc.c 36
555.2.bc.d 36
555.2.bc.e 42
555.2.bd \(\chi_{555}(82, \cdot)\) 555.2.bd.a 152 4
555.2.bg \(\chi_{555}(236, \cdot)\) 555.2.bg.a 208 4
555.2.bh \(\chi_{555}(122, \cdot)\) 555.2.bh.a 288 4
555.2.bi \(\chi_{555}(47, \cdot)\) 555.2.bi.a 288 4
555.2.bm \(\chi_{555}(14, \cdot)\) 555.2.bm.a 288 4
555.2.bn \(\chi_{555}(193, \cdot)\) 555.2.bn.a 152 4
555.2.bp \(\chi_{555}(4, \cdot)\) 555.2.bp.a 240 6
555.2.bs \(\chi_{555}(34, \cdot)\) 555.2.bs.a 216 6
555.2.bt \(\chi_{555}(136, \cdot)\) 555.2.bt.a 72 6
555.2.bt.b 84
555.2.bx \(\chi_{555}(22, \cdot)\) 555.2.bx.a 456 12
555.2.bz \(\chi_{555}(56, \cdot)\) 555.2.bz.a 600 12
555.2.ca \(\chi_{555}(59, \cdot)\) 555.2.ca.a 864 12
555.2.cc \(\chi_{555}(53, \cdot)\) 555.2.cc.a 864 12
555.2.cf \(\chi_{555}(62, \cdot)\) 555.2.cf.a 864 12
555.2.ch \(\chi_{555}(13, \cdot)\) 555.2.ch.a 456 12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(555))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(555)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(185))\)\(^{\oplus 2}\)