↑

Properties

Label 56.3
Level 56
Weight 3
Dimension 94
Nonzero newspaces 6
Newform subspaces 13
Sturm bound 576
Trace bound 2

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 56 = 2^{3} \cdot 7 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 13 \)
Sturm bound: \(576\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(56))\).

Total New Old
Modular forms 228 114 114
Cusp forms 156 94 62
Eisenstein series 72 20 52

Trace form

\( 94 q - 2 q^{2} - 2 q^{3} - 14 q^{4} - 14 q^{6} - 6 q^{7} + 4 q^{8} + 22 q^{9} + O(q^{10}) \) \( 94 q - 2 q^{2} - 2 q^{3} - 14 q^{4} - 14 q^{6} - 6 q^{7} + 4 q^{8} + 22 q^{9} - 6 q^{10} - 22 q^{11} + 10 q^{12} - 6 q^{14} - 36 q^{15} - 38 q^{16} - 40 q^{17} - 80 q^{18} - 22 q^{19} - 132 q^{20} - 84 q^{21} - 106 q^{22} - 78 q^{23} - 146 q^{24} - 98 q^{25} - 36 q^{26} - 68 q^{27} + 42 q^{28} + 138 q^{30} + 150 q^{31} + 208 q^{32} + 248 q^{33} + 254 q^{34} + 246 q^{35} + 298 q^{36} + 108 q^{37} + 56 q^{38} + 48 q^{39} + 144 q^{40} + 80 q^{41} + 210 q^{42} - 208 q^{43} + 146 q^{44} - 276 q^{45} + 264 q^{46} - 402 q^{47} + 478 q^{48} - 314 q^{49} + 298 q^{50} - 418 q^{51} + 156 q^{52} - 180 q^{53} + 166 q^{54} - 48 q^{56} + 56 q^{57} - 108 q^{58} + 470 q^{59} - 480 q^{60} + 252 q^{61} - 384 q^{62} + 618 q^{63} - 518 q^{64} + 240 q^{65} - 994 q^{66} + 254 q^{67} - 862 q^{68} - 990 q^{70} - 276 q^{71} - 1196 q^{72} + 116 q^{73} - 762 q^{74} - 332 q^{75} - 238 q^{76} - 360 q^{77} - 432 q^{78} - 414 q^{79} - 348 q^{80} - 158 q^{81} - 262 q^{82} - 328 q^{83} + 102 q^{84} + 168 q^{85} + 374 q^{86} + 396 q^{87} + 578 q^{88} - 100 q^{89} + 1008 q^{90} + 696 q^{91} + 858 q^{92} + 396 q^{93} + 1398 q^{94} + 1266 q^{95} + 1858 q^{96} - 496 q^{97} + 1726 q^{98} + 1328 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(56))\)

We only show spaces with odd 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
56.3.c \(\chi_{56}(41, \cdot)\) 56.3.c.a 4 1
56.3.d \(\chi_{56}(15, \cdot)\) None 0 1
56.3.g \(\chi_{56}(43, \cdot)\) 56.3.g.a 4 1
56.3.g.b 8
56.3.h \(\chi_{56}(13, \cdot)\) 56.3.h.a 2 1
56.3.h.b 2
56.3.h.c 2
56.3.h.d 8
56.3.j \(\chi_{56}(5, \cdot)\) 56.3.j.a 28 2
56.3.k \(\chi_{56}(11, \cdot)\) 56.3.k.a 2 2
56.3.k.b 2
56.3.k.c 12
56.3.k.d 12
56.3.n \(\chi_{56}(23, \cdot)\) None 0 2
56.3.o \(\chi_{56}(17, \cdot)\) 56.3.o.a 8 2

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(56))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(56)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 2}\)