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Properties

Label 496.2
Level 496
Weight 2
Dimension 4181
Nonzero newspaces 16
Newform subspaces 59
Sturm bound 30720
Trace bound 3

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Defining parameters

Level: \( N \) = \( 496 = 2^{4} \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Newform subspaces: \( 59 \)
Sturm bound: \(30720\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(496))\).

Total New Old
Modular forms 8100 4441 3659
Cusp forms 7261 4181 3080
Eisenstein series 839 260 579

Trace form

\( 4181 q - 56 q^{2} - 41 q^{3} - 60 q^{4} - 71 q^{5} - 68 q^{6} - 45 q^{7} - 68 q^{8} - 15 q^{9} + O(q^{10}) \) \( 4181 q - 56 q^{2} - 41 q^{3} - 60 q^{4} - 71 q^{5} - 68 q^{6} - 45 q^{7} - 68 q^{8} - 15 q^{9} - 60 q^{10} - 49 q^{11} - 52 q^{12} - 71 q^{13} - 52 q^{14} - 53 q^{15} - 44 q^{16} - 127 q^{17} - 64 q^{18} - 57 q^{19} - 68 q^{20} - 83 q^{21} - 60 q^{22} - 45 q^{23} - 60 q^{24} - 15 q^{25} - 68 q^{26} - 29 q^{27} - 76 q^{28} - 87 q^{29} - 52 q^{30} - 29 q^{31} - 136 q^{32} - 127 q^{33} - 68 q^{34} - 37 q^{35} - 52 q^{36} - 87 q^{37} - 36 q^{38} - 45 q^{39} - 44 q^{40} - 15 q^{41} - 60 q^{42} - 65 q^{43} - 52 q^{44} - 79 q^{45} - 84 q^{46} - 77 q^{47} - 76 q^{48} - 147 q^{49} - 48 q^{50} - 53 q^{51} - 52 q^{52} - 55 q^{53} - 60 q^{54} - 45 q^{55} - 44 q^{56} - 15 q^{57} - 36 q^{58} - 33 q^{59} - 60 q^{60} - 54 q^{61} - 76 q^{62} - 98 q^{63} - 60 q^{64} - 143 q^{65} - 68 q^{66} - 25 q^{67} - 60 q^{68} - 51 q^{69} - 76 q^{70} - 45 q^{71} - 68 q^{72} - 15 q^{73} - 60 q^{74} - 57 q^{75} - 84 q^{76} - 83 q^{77} - 52 q^{78} - 45 q^{79} - 76 q^{80} - 155 q^{81} - 60 q^{82} - 41 q^{83} - 44 q^{84} - 83 q^{85} - 60 q^{86} - 45 q^{87} - 76 q^{88} - 15 q^{89} - 52 q^{90} - 53 q^{91} - 12 q^{92} - 91 q^{93} - 88 q^{94} - 21 q^{95} - 28 q^{96} - 127 q^{97} - 48 q^{98} - 41 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(496))\)

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
496.2.a \(\chi_{496}(1, \cdot)\) 496.2.a.a 1 1
496.2.a.b 1
496.2.a.c 1
496.2.a.d 1
496.2.a.e 1
496.2.a.f 1
496.2.a.g 2
496.2.a.h 2
496.2.a.i 2
496.2.a.j 3
496.2.b \(\chi_{496}(247, \cdot)\) None 0 1
496.2.c \(\chi_{496}(249, \cdot)\) None 0 1
496.2.h \(\chi_{496}(495, \cdot)\) 496.2.h.a 2 1
496.2.h.b 2
496.2.h.c 4
496.2.h.d 8
496.2.i \(\chi_{496}(129, \cdot)\) 496.2.i.a 2 2
496.2.i.b 2
496.2.i.c 2
496.2.i.d 2
496.2.i.e 2
496.2.i.f 2
496.2.i.g 2
496.2.i.h 4
496.2.i.i 6
496.2.i.j 6
496.2.k \(\chi_{496}(125, \cdot)\) 496.2.k.a 2 2
496.2.k.b 4
496.2.k.c 48
496.2.k.d 66
496.2.m \(\chi_{496}(123, \cdot)\) 496.2.m.a 12 2
496.2.m.b 112
496.2.n \(\chi_{496}(33, \cdot)\) 496.2.n.a 4 4
496.2.n.b 4
496.2.n.c 4
496.2.n.d 8
496.2.n.e 8
496.2.n.f 16
496.2.n.g 16
496.2.o \(\chi_{496}(223, \cdot)\) 496.2.o.a 2 2
496.2.o.b 2
496.2.o.c 8
496.2.o.d 8
496.2.o.e 12
496.2.t \(\chi_{496}(25, \cdot)\) None 0 2
496.2.u \(\chi_{496}(119, \cdot)\) None 0 2
496.2.x \(\chi_{496}(15, \cdot)\) 496.2.x.a 16 4
496.2.x.b 48
496.2.y \(\chi_{496}(233, \cdot)\) None 0 4
496.2.z \(\chi_{496}(23, \cdot)\) None 0 4
496.2.bd \(\chi_{496}(99, \cdot)\) 496.2.bd.a 248 4
496.2.bf \(\chi_{496}(5, \cdot)\) 496.2.bf.a 248 4
496.2.bg \(\chi_{496}(49, \cdot)\) 496.2.bg.a 8 8
496.2.bg.b 8
496.2.bg.c 16
496.2.bg.d 24
496.2.bg.e 32
496.2.bg.f 32
496.2.bh \(\chi_{496}(27, \cdot)\) 496.2.bh.a 496 8
496.2.bj \(\chi_{496}(101, \cdot)\) 496.2.bj.a 496 8
496.2.bn \(\chi_{496}(55, \cdot)\) None 0 8
496.2.bo \(\chi_{496}(9, \cdot)\) None 0 8
496.2.bp \(\chi_{496}(79, \cdot)\) 496.2.bp.a 40 8
496.2.bp.b 40
496.2.bp.c 48
496.2.bs \(\chi_{496}(45, \cdot)\) 496.2.bs.a 992 16
496.2.bu \(\chi_{496}(3, \cdot)\) 496.2.bu.a 992 16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(496))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(496)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(124))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(248))\)\(^{\oplus 2}\)