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Properties

Label 650.2
Level 650
Weight 2
Dimension 3823
Nonzero newspaces 24
Newform subspaces 123
Sturm bound 50400
Trace bound 9

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Defining parameters

Level: \( N \) = \( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Newform subspaces: \( 123 \)
Sturm bound: \(50400\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(650))\).

Total New Old
Modular forms 13272 3823 9449
Cusp forms 11929 3823 8106
Eisenstein series 1343 0 1343

Trace form

\( 3823 q + 2 q^{2} + 8 q^{3} + 2 q^{4} + 10 q^{5} + 8 q^{6} + 20 q^{7} + 5 q^{8} + 42 q^{9} + O(q^{10}) \) \( 3823 q + 2 q^{2} + 8 q^{3} + 2 q^{4} + 10 q^{5} + 8 q^{6} + 20 q^{7} + 5 q^{8} + 42 q^{9} + 10 q^{10} + 36 q^{11} + 12 q^{12} + 38 q^{13} + 28 q^{14} + 40 q^{15} + 6 q^{16} + 11 q^{17} - 9 q^{18} - 12 q^{19} + 12 q^{21} - 56 q^{22} - 20 q^{23} - 32 q^{24} - 70 q^{25} - 6 q^{26} - 4 q^{27} - 20 q^{28} + 19 q^{29} - 40 q^{30} + 24 q^{31} - 8 q^{32} + 76 q^{33} + 10 q^{34} + 40 q^{35} + 50 q^{36} + 97 q^{37} + 76 q^{38} + 68 q^{39} + 10 q^{40} + 95 q^{41} + 100 q^{42} + 52 q^{43} + 48 q^{44} - 30 q^{45} + 72 q^{46} + 64 q^{47} + 8 q^{48} + 56 q^{49} + 38 q^{50} - 96 q^{51} - 3 q^{52} - 138 q^{53} - 172 q^{54} - 104 q^{55} - 68 q^{56} - 416 q^{57} - 129 q^{58} - 240 q^{59} - 96 q^{60} - 149 q^{61} - 308 q^{62} - 620 q^{63} - 19 q^{64} - 227 q^{65} - 360 q^{66} - 332 q^{67} - 105 q^{68} - 640 q^{69} - 224 q^{70} - 136 q^{71} - 142 q^{72} - 212 q^{73} - 301 q^{74} - 360 q^{75} - 108 q^{76} - 296 q^{77} - 272 q^{78} - 96 q^{79} - 2 q^{80} + 14 q^{81} - 49 q^{82} - 56 q^{83} - 28 q^{84} - 30 q^{85} - 8 q^{86} + 80 q^{87} + 24 q^{88} + 66 q^{89} + 10 q^{90} + 108 q^{91} + 32 q^{92} + 248 q^{93} + 156 q^{94} + 120 q^{95} + 8 q^{96} + 256 q^{97} + 162 q^{98} + 300 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(650))\)

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
650.2.a \(\chi_{650}(1, \cdot)\) 650.2.a.a 1 1
650.2.a.b 1
650.2.a.c 1
650.2.a.d 1
650.2.a.e 1
650.2.a.f 1
650.2.a.g 1
650.2.a.h 1
650.2.a.i 1
650.2.a.j 1
650.2.a.k 1
650.2.a.l 1
650.2.a.m 1
650.2.a.n 3
650.2.a.o 3
650.2.b \(\chi_{650}(599, \cdot)\) 650.2.b.a 2 1
650.2.b.b 2
650.2.b.c 2
650.2.b.d 2
650.2.b.e 2
650.2.b.f 2
650.2.b.g 2
650.2.b.h 2
650.2.b.i 2
650.2.c \(\chi_{650}(649, \cdot)\) 650.2.c.a 2 1
650.2.c.b 2
650.2.c.c 2
650.2.c.d 2
650.2.c.e 6
650.2.c.f 6
650.2.d \(\chi_{650}(51, \cdot)\) 650.2.d.a 2 1
650.2.d.b 2
650.2.d.c 6
650.2.d.d 6
650.2.d.e 8
650.2.e \(\chi_{650}(451, \cdot)\) 650.2.e.a 2 2
650.2.e.b 2
650.2.e.c 2
650.2.e.d 4
650.2.e.e 4
650.2.e.f 4
650.2.e.g 4
650.2.e.h 4
650.2.e.i 4
650.2.e.j 6
650.2.e.k 6
650.2.g \(\chi_{650}(57, \cdot)\) 650.2.g.a 2 2
650.2.g.b 2
650.2.g.c 2
650.2.g.d 2
650.2.g.e 2
650.2.g.f 4
650.2.g.g 4
650.2.g.h 12
650.2.g.i 12
650.2.j \(\chi_{650}(307, \cdot)\) 650.2.j.a 2 2
650.2.j.b 2
650.2.j.c 2
650.2.j.d 2
650.2.j.e 2
650.2.j.f 4
650.2.j.g 4
650.2.j.h 12
650.2.j.i 12
650.2.l \(\chi_{650}(131, \cdot)\) 650.2.l.a 4 4
650.2.l.b 20
650.2.l.c 24
650.2.l.d 36
650.2.l.e 36
650.2.m \(\chi_{650}(101, \cdot)\) 650.2.m.a 4 2
650.2.m.b 8
650.2.m.c 8
650.2.m.d 8
650.2.m.e 16
650.2.n \(\chi_{650}(49, \cdot)\) 650.2.n.a 4 2
650.2.n.b 4
650.2.n.c 8
650.2.n.d 8
650.2.n.e 8
650.2.n.f 8
650.2.o \(\chi_{650}(399, \cdot)\) 650.2.o.a 4 2
650.2.o.b 4
650.2.o.c 4
650.2.o.d 4
650.2.o.e 4
650.2.o.f 8
650.2.o.g 8
650.2.o.h 8
650.2.p \(\chi_{650}(181, \cdot)\) 650.2.p.a 136 4
650.2.q \(\chi_{650}(79, \cdot)\) 650.2.q.a 48 4
650.2.q.b 72
650.2.r \(\chi_{650}(129, \cdot)\) 650.2.r.a 72 4
650.2.r.b 72
650.2.t \(\chi_{650}(7, \cdot)\) 650.2.t.a 4 4
650.2.t.b 4
650.2.t.c 8
650.2.t.d 8
650.2.t.e 12
650.2.t.f 16
650.2.t.g 16
650.2.t.h 16
650.2.w \(\chi_{650}(193, \cdot)\) 650.2.w.a 4 4
650.2.w.b 4
650.2.w.c 8
650.2.w.d 8
650.2.w.e 12
650.2.w.f 16
650.2.w.g 16
650.2.w.h 16
650.2.y \(\chi_{650}(61, \cdot)\) 650.2.y.a 136 8
650.2.y.b 152
650.2.ba \(\chi_{650}(73, \cdot)\) 650.2.ba.a 136 8
650.2.ba.b 144
650.2.bd \(\chi_{650}(47, \cdot)\) 650.2.bd.a 136 8
650.2.bd.b 144
650.2.bf \(\chi_{650}(69, \cdot)\) 650.2.bf.a 144 8
650.2.bf.b 144
650.2.bg \(\chi_{650}(9, \cdot)\) 650.2.bg.a 272 8
650.2.bh \(\chi_{650}(121, \cdot)\) 650.2.bh.a 272 8
650.2.bj \(\chi_{650}(37, \cdot)\) 650.2.bj.a 272 16
650.2.bj.b 288
650.2.bm \(\chi_{650}(33, \cdot)\) 650.2.bm.a 272 16
650.2.bm.b 288

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(650))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(650)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(325))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(650))\)\(^{\oplus 1}\)