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Properties

Label 56.5
Level 56
Weight 5
Dimension 198
Nonzero newspaces 6
Newform subspaces 11
Sturm bound 960
Trace bound 2

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Defining parameters

Level: \( N \) = \( 56 = 2^{3} \cdot 7 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 11 \)
Sturm bound: \(960\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(56))\).

Total New Old
Modular forms 420 218 202
Cusp forms 348 198 150
Eisenstein series 72 20 52

Trace form

\( 198 q - 10 q^{2} - 2 q^{3} + 18 q^{4} + 130 q^{6} - 6 q^{7} - 316 q^{8} - 110 q^{9} + O(q^{10}) \) \( 198 q - 10 q^{2} - 2 q^{3} + 18 q^{4} + 130 q^{6} - 6 q^{7} - 316 q^{8} - 110 q^{9} - 486 q^{10} - 26 q^{11} + 778 q^{12} + 474 q^{14} + 612 q^{15} - 1062 q^{16} + 664 q^{17} - 1592 q^{18} - 2586 q^{19} - 180 q^{20} - 840 q^{21} + 3102 q^{22} + 2154 q^{23} + 4942 q^{24} + 1734 q^{25} + 2004 q^{26} + 3964 q^{27} - 3606 q^{28} - 10230 q^{30} - 2142 q^{31} - 4000 q^{32} - 4108 q^{33} + 702 q^{34} - 8382 q^{35} - 3782 q^{36} - 1224 q^{37} + 5968 q^{38} + 1596 q^{39} + 9504 q^{40} - 1496 q^{41} + 10650 q^{42} + 8136 q^{43} + 8722 q^{44} + 5304 q^{45} - 7776 q^{46} + 14898 q^{47} - 15842 q^{48} + 3222 q^{49} - 22102 q^{50} - 502 q^{51} - 16356 q^{52} - 1800 q^{53} - 8306 q^{54} - 1104 q^{56} + 5312 q^{57} + 8292 q^{58} - 1202 q^{59} + 45168 q^{60} - 17640 q^{61} + 47544 q^{62} - 42726 q^{63} + 10458 q^{64} - 17460 q^{65} - 6298 q^{66} - 35394 q^{67} - 21902 q^{68} - 44862 q^{70} + 24324 q^{71} - 14684 q^{72} - 5328 q^{73} + 23286 q^{74} + 82852 q^{75} + 45522 q^{76} + 38448 q^{77} + 57888 q^{78} + 37770 q^{79} + 24756 q^{80} + 35506 q^{81} + 25674 q^{82} - 13448 q^{83} - 23802 q^{84} - 35952 q^{85} - 32330 q^{86} - 67608 q^{87} - 43902 q^{88} + 2944 q^{89} - 75168 q^{90} - 31920 q^{91} - 48102 q^{92} - 70344 q^{93} - 23898 q^{94} - 726 q^{95} + 56674 q^{96} - 16344 q^{97} - 3322 q^{98} + 19040 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(56))\)

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
56.5.c \(\chi_{56}(41, \cdot)\) 56.5.c.a 8 1
56.5.d \(\chi_{56}(15, \cdot)\) None 0 1
56.5.g \(\chi_{56}(43, \cdot)\) 56.5.g.a 2 1
56.5.g.b 22
56.5.h \(\chi_{56}(13, \cdot)\) 56.5.h.a 1 1
56.5.h.b 1
56.5.h.c 2
56.5.h.d 2
56.5.h.e 24
56.5.j \(\chi_{56}(5, \cdot)\) 56.5.j.a 60 2
56.5.k \(\chi_{56}(11, \cdot)\) 56.5.k.a 60 2
56.5.n \(\chi_{56}(23, \cdot)\) None 0 2
56.5.o \(\chi_{56}(17, \cdot)\) 56.5.o.a 16 2

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(56))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(56)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 2}\)