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Properties

Label 968.2
Level 968
Weight 2
Dimension 15785
Nonzero newspaces 12
Newform subspaces 80
Sturm bound 116160
Trace bound 3

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Defining parameters

Level: \( N \) = \( 968 = 2^{3} \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 80 \)
Sturm bound: \(116160\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(968))\).

Total New Old
Modular forms 30000 16347 13653
Cusp forms 28081 15785 12296
Eisenstein series 1919 562 1357

Trace form

\( 15785 q - 90 q^{2} - 90 q^{3} - 90 q^{4} - 90 q^{6} - 90 q^{7} - 90 q^{8} - 180 q^{9} + O(q^{10}) \) \( 15785 q - 90 q^{2} - 90 q^{3} - 90 q^{4} - 90 q^{6} - 90 q^{7} - 90 q^{8} - 180 q^{9} - 90 q^{10} - 100 q^{11} - 170 q^{12} - 90 q^{14} - 70 q^{15} - 90 q^{16} - 160 q^{17} - 90 q^{18} - 60 q^{19} - 90 q^{20} + 40 q^{21} - 100 q^{22} - 150 q^{23} - 90 q^{24} - 140 q^{25} - 90 q^{26} - 60 q^{27} - 90 q^{28} + 20 q^{29} - 150 q^{30} - 70 q^{31} - 110 q^{32} - 215 q^{33} - 250 q^{34} - 150 q^{35} - 250 q^{36} - 190 q^{38} - 210 q^{39} - 230 q^{40} - 240 q^{41} - 310 q^{42} - 170 q^{43} - 170 q^{44} - 60 q^{45} - 230 q^{46} - 150 q^{47} - 310 q^{48} - 240 q^{49} - 230 q^{50} - 200 q^{51} - 190 q^{52} + 40 q^{53} - 250 q^{54} - 110 q^{55} - 250 q^{56} - 130 q^{57} - 110 q^{58} - 20 q^{59} - 190 q^{60} + 40 q^{61} - 90 q^{62} - 70 q^{63} - 90 q^{64} - 100 q^{65} - 100 q^{66} - 90 q^{67} - 90 q^{68} + 80 q^{69} + 50 q^{70} - 50 q^{71} + 10 q^{72} - 200 q^{73} + 10 q^{74} - 180 q^{75} + 70 q^{76} + 10 q^{77} + 70 q^{78} - 250 q^{79} + 130 q^{80} - 230 q^{81} + 110 q^{82} - 280 q^{83} + 150 q^{84} - 120 q^{85} + 30 q^{86} - 310 q^{87} + 60 q^{88} - 400 q^{89} + 190 q^{90} - 310 q^{91} + 70 q^{92} - 60 q^{93} + 150 q^{94} - 250 q^{95} + 50 q^{96} - 210 q^{97} + 130 q^{98} - 150 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(968))\)

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
968.2.a \(\chi_{968}(1, \cdot)\) 968.2.a.a 1 1
968.2.a.b 1
968.2.a.c 1
968.2.a.d 1
968.2.a.e 1
968.2.a.f 2
968.2.a.g 2
968.2.a.h 2
968.2.a.i 2
968.2.a.j 2
968.2.a.k 2
968.2.a.l 2
968.2.a.m 4
968.2.a.n 4
968.2.c \(\chi_{968}(485, \cdot)\) 968.2.c.a 2 1
968.2.c.b 4
968.2.c.c 8
968.2.c.d 10
968.2.c.e 10
968.2.c.f 10
968.2.c.g 16
968.2.c.h 20
968.2.c.i 20
968.2.e \(\chi_{968}(967, \cdot)\) None 0 1
968.2.g \(\chi_{968}(483, \cdot)\) 968.2.g.a 8 1
968.2.g.b 8
968.2.g.c 20
968.2.g.d 32
968.2.g.e 32
968.2.i \(\chi_{968}(9, \cdot)\) 968.2.i.a 4 4
968.2.i.b 4
968.2.i.c 4
968.2.i.d 4
968.2.i.e 4
968.2.i.f 4
968.2.i.g 4
968.2.i.h 4
968.2.i.i 4
968.2.i.j 4
968.2.i.k 4
968.2.i.l 4
968.2.i.m 4
968.2.i.n 8
968.2.i.o 8
968.2.i.p 8
968.2.i.q 8
968.2.i.r 8
968.2.i.s 8
968.2.i.t 8
968.2.k \(\chi_{968}(403, \cdot)\) 968.2.k.a 8 4
968.2.k.b 8
968.2.k.c 8
968.2.k.d 8
968.2.k.e 32
968.2.k.f 32
968.2.k.g 32
968.2.k.h 32
968.2.k.i 32
968.2.k.j 80
968.2.k.k 128
968.2.m \(\chi_{968}(215, \cdot)\) None 0 4
968.2.o \(\chi_{968}(245, \cdot)\) 968.2.o.a 8 4
968.2.o.b 16
968.2.o.c 32
968.2.o.d 40
968.2.o.e 40
968.2.o.f 40
968.2.o.g 40
968.2.o.h 40
968.2.o.i 40
968.2.o.j 40
968.2.o.k 64
968.2.q \(\chi_{968}(89, \cdot)\) 968.2.q.a 160 10
968.2.q.b 170
968.2.r \(\chi_{968}(87, \cdot)\) None 0 10
968.2.t \(\chi_{968}(45, \cdot)\) 968.2.t.a 1300 10
968.2.w \(\chi_{968}(43, \cdot)\) 968.2.w.a 20 10
968.2.w.b 1280
968.2.y \(\chi_{968}(25, \cdot)\) 968.2.y.a 640 40
968.2.y.b 680
968.2.ba \(\chi_{968}(19, \cdot)\) 968.2.ba.a 80 40
968.2.ba.b 5120
968.2.bd \(\chi_{968}(5, \cdot)\) 968.2.bd.a 5200 40
968.2.bf \(\chi_{968}(7, \cdot)\) None 0 40

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(968))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(968)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(484))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(968))\)\(^{\oplus 1}\)