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Properties

Label 656.4
Level 656
Weight 4
Dimension 22478
Nonzero newspaces 20
Sturm bound 107520
Trace bound 5

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Defining parameters

Level: N N = 656=24⋅41 656 = 2^{4} \cdot 41
Weight: k k = 4 4
Nonzero newspaces: 20 20
Sturm bound: 107520107520
Trace bound: 55

Dimensions

The following table gives the dimensions of various subspaces of M4(Γ1(656))M_{4}(\Gamma_1(656)).

Total New Old
Modular forms 40880 22828 18052
Cusp forms 39760 22478 17282
Eisenstein series 1120 350 770

Trace form

22478q−76q2−64q3−96q4−92q5−16q6−12q7+8q8+2q9+56q10−184q11−280q12−140q13−456q14+204q15−640q16−272q17−428q18+⋯−9008q99+O(q100) 22478 q - 76 q^{2} - 64 q^{3} - 96 q^{4} - 92 q^{5} - 16 q^{6} - 12 q^{7} + 8 q^{8} + 2 q^{9} + 56 q^{10} - 184 q^{11} - 280 q^{12} - 140 q^{13} - 456 q^{14} + 204 q^{15} - 640 q^{16} - 272 q^{17} - 428 q^{18}+ \cdots - 9008 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S4new(Γ1(656))S_{4}^{\mathrm{new}}(\Gamma_1(656))

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space Sknew(N,χ) S_k^{\mathrm{new}}(N, \chi) we list available newforms together with their dimension.

Label χ\chi Newforms Dimension χ\chi degree
656.4.a χ656(1,⋅)\chi_{656}(1, \cdot) 656.4.a.a 1 1
656.4.a.b 1
656.4.a.c 2
656.4.a.d 3
656.4.a.e 3
656.4.a.f 3
656.4.a.g 3
656.4.a.h 6
656.4.a.i 7
656.4.a.j 7
656.4.a.k 7
656.4.a.l 8
656.4.a.m 9
656.4.b χ656(329,⋅)\chi_{656}(329, \cdot) None 0 1
656.4.d χ656(81,⋅)\chi_{656}(81, \cdot) 656.4.d.a 4 1
656.4.d.b 4
656.4.d.c 6
656.4.d.d 10
656.4.d.e 10
656.4.d.f 12
656.4.d.g 16
656.4.g χ656(409,⋅)\chi_{656}(409, \cdot) None 0 1
656.4.i χ656(173,⋅)\chi_{656}(173, \cdot) n/a 500 2
656.4.l χ656(337,⋅)\chi_{656}(337, \cdot) n/a 124 2
656.4.n χ656(165,⋅)\chi_{656}(165, \cdot) n/a 480 2
656.4.o χ656(245,⋅)\chi_{656}(245, \cdot) n/a 500 2
656.4.r χ656(9,⋅)\chi_{656}(9, \cdot) None 0 2
656.4.t χ656(237,⋅)\chi_{656}(237, \cdot) n/a 500 2
656.4.u χ656(305,⋅)\chi_{656}(305, \cdot) n/a 248 4
656.4.v χ656(331,⋅)\chi_{656}(331, \cdot) n/a 1000 4
656.4.z χ656(55,⋅)\chi_{656}(55, \cdot) None 0 4
656.4.ba χ656(79,⋅)\chi_{656}(79, \cdot) n/a 252 4
656.4.bb χ656(3,⋅)\chi_{656}(3, \cdot) n/a 1000 4
656.4.be χ656(113,⋅)\chi_{656}(113, \cdot) n/a 248 4
656.4.bg χ656(57,⋅)\chi_{656}(57, \cdot) None 0 4
656.4.bi χ656(25,⋅)\chi_{656}(25, \cdot) None 0 4
656.4.bl χ656(197,⋅)\chi_{656}(197, \cdot) n/a 2000 8
656.4.bm χ656(121,⋅)\chi_{656}(121, \cdot) None 0 8
656.4.bp χ656(45,⋅)\chi_{656}(45, \cdot) n/a 2000 8
656.4.bq χ656(37,⋅)\chi_{656}(37, \cdot) n/a 2000 8
656.4.bs χ656(33,⋅)\chi_{656}(33, \cdot) n/a 496 8
656.4.bu χ656(5,⋅)\chi_{656}(5, \cdot) n/a 2000 8
656.4.bx χ656(259,⋅)\chi_{656}(259, \cdot) n/a 4000 16
656.4.by χ656(15,⋅)\chi_{656}(15, \cdot) n/a 1008 16
656.4.bz χ656(7,⋅)\chi_{656}(7, \cdot) None 0 16
656.4.cd χ656(11,⋅)\chi_{656}(11, \cdot) n/a 4000 16

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of S4old(Γ1(656))S_{4}^{\mathrm{old}}(\Gamma_1(656)) into lower level spaces

S4old(Γ1(656))≅ S_{4}^{\mathrm{old}}(\Gamma_1(656)) \cong S4new(Γ1(1))S_{4}^{\mathrm{new}}(\Gamma_1(1))⊕10^{\oplus 10}⊕\oplusS4new(Γ1(2))S_{4}^{\mathrm{new}}(\Gamma_1(2))⊕8^{\oplus 8}⊕\oplusS4new(Γ1(4))S_{4}^{\mathrm{new}}(\Gamma_1(4))⊕6^{\oplus 6}⊕\oplusS4new(Γ1(8))S_{4}^{\mathrm{new}}(\Gamma_1(8))⊕4^{\oplus 4}⊕\oplusS4new(Γ1(16))S_{4}^{\mathrm{new}}(\Gamma_1(16))⊕2^{\oplus 2}⊕\oplusS4new(Γ1(41))S_{4}^{\mathrm{new}}(\Gamma_1(41))⊕5^{\oplus 5}⊕\oplusS4new(Γ1(82))S_{4}^{\mathrm{new}}(\Gamma_1(82))⊕4^{\oplus 4}⊕\oplusS4new(Γ1(164))S_{4}^{\mathrm{new}}(\Gamma_1(164))⊕3^{\oplus 3}⊕\oplusS4new(Γ1(328))S_{4}^{\mathrm{new}}(\Gamma_1(328))⊕2^{\oplus 2}