Properties

Label 736.4
Level 736
Weight 4
Dimension 28194
Nonzero newspaces 12
Sturm bound 135168
Trace bound 9

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Defining parameters

Level: N N = 736=2523 736 = 2^{5} \cdot 23
Weight: k k = 4 4
Nonzero newspaces: 12 12
Sturm bound: 135168135168
Trace bound: 99

Dimensions

The following table gives the dimensions of various subspaces of M4(Γ1(736))M_{4}(\Gamma_1(736)).

Total New Old
Modular forms 51392 28614 22778
Cusp forms 49984 28194 21790
Eisenstein series 1408 420 988

Trace form

28194q80q258q380q484q580q690q780q8214q9320q1058q11+16q12+156q13+336q14+158q15+520q16+320q17+280q18++10782q99+O(q100) 28194 q - 80 q^{2} - 58 q^{3} - 80 q^{4} - 84 q^{5} - 80 q^{6} - 90 q^{7} - 80 q^{8} - 214 q^{9} - 320 q^{10} - 58 q^{11} + 16 q^{12} + 156 q^{13} + 336 q^{14} + 158 q^{15} + 520 q^{16} + 320 q^{17} + 280 q^{18}+ \cdots + 10782 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S4new(Γ1(736))S_{4}^{\mathrm{new}}(\Gamma_1(736))

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
736.4.a χ736(1,)\chi_{736}(1, \cdot) 736.4.a.a 3 1
736.4.a.b 3
736.4.a.c 4
736.4.a.d 4
736.4.a.e 8
736.4.a.f 8
736.4.a.g 9
736.4.a.h 9
736.4.a.i 9
736.4.a.j 9
736.4.b χ736(369,)\chi_{736}(369, \cdot) 736.4.b.a 30 1
736.4.b.b 36
736.4.c χ736(735,)\chi_{736}(735, \cdot) 736.4.c.a 72 1
736.4.h χ736(367,)\chi_{736}(367, \cdot) 736.4.h.a 2 1
736.4.h.b 4
736.4.h.c 64
736.4.i χ736(183,)\chi_{736}(183, \cdot) None 0 2
736.4.j χ736(185,)\chi_{736}(185, \cdot) None 0 2
736.4.m χ736(93,)\chi_{736}(93, \cdot) n/a 1056 4
736.4.n χ736(91,)\chi_{736}(91, \cdot) n/a 1144 4
736.4.q χ736(193,)\chi_{736}(193, \cdot) n/a 720 10
736.4.r χ736(15,)\chi_{736}(15, \cdot) n/a 700 10
736.4.w χ736(63,)\chi_{736}(63, \cdot) n/a 720 10
736.4.x χ736(49,)\chi_{736}(49, \cdot) n/a 700 10
736.4.ba χ736(9,)\chi_{736}(9, \cdot) None 0 20
736.4.bb χ736(7,)\chi_{736}(7, \cdot) None 0 20
736.4.be χ736(11,)\chi_{736}(11, \cdot) n/a 11440 40
736.4.bf χ736(13,)\chi_{736}(13, \cdot) n/a 11440 40

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

Decomposition of S4old(Γ1(736))S_{4}^{\mathrm{old}}(\Gamma_1(736)) into lower level spaces