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Properties

Label 32.5
Level 32
Weight 5
Dimension 67
Nonzero newspaces 3
Newform subspaces 5
Sturm bound 320
Trace bound 1

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Defining parameters

Level: \( N \) = \( 32 = 2^{5} \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 5 \)
Sturm bound: \(320\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(32))\).

Total New Old
Modular forms 144 77 67
Cusp forms 112 67 45
Eisenstein series 32 10 22

Trace form

\( 67 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - 28 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} + 25 q^{9} + O(q^{10}) \) \( 67 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - 28 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} + 25 q^{9} - 204 q^{10} + 94 q^{11} + 716 q^{12} + 228 q^{13} + 428 q^{14} - 8 q^{15} - 624 q^{16} - 434 q^{17} - 1624 q^{18} - 706 q^{19} - 1204 q^{20} - 900 q^{21} + 1888 q^{22} - 1156 q^{23} + 2512 q^{24} + 1691 q^{25} - 2704 q^{26} + 5632 q^{27} - 2824 q^{28} + 1892 q^{29} - 2428 q^{30} + 1256 q^{32} - 3964 q^{33} + 3600 q^{34} - 9028 q^{35} + 2928 q^{36} - 3484 q^{37} + 2516 q^{38} - 2692 q^{39} + 6760 q^{40} + 6378 q^{41} + 3656 q^{42} + 12830 q^{43} + 6212 q^{44} + 7840 q^{45} + 2908 q^{46} - 8 q^{47} - 4944 q^{48} - 6489 q^{49} - 3436 q^{50} - 2364 q^{51} - 8156 q^{52} - 13276 q^{53} - 25952 q^{54} - 11780 q^{55} - 23512 q^{56} + 5704 q^{57} - 14624 q^{58} - 2786 q^{59} + 824 q^{60} + 17764 q^{61} + 15288 q^{62} - 11368 q^{64} - 11768 q^{65} + 2252 q^{66} + 7998 q^{67} + 18960 q^{68} - 21252 q^{69} + 49688 q^{70} + 19964 q^{71} + 60308 q^{72} + 19562 q^{73} + 35372 q^{74} + 12570 q^{75} + 6652 q^{76} + 23612 q^{77} + 14068 q^{78} - 50184 q^{79} - 1480 q^{80} - 13965 q^{81} - 16004 q^{82} + 3838 q^{83} - 83296 q^{84} - 20208 q^{85} - 70144 q^{86} + 49276 q^{87} - 73184 q^{88} - 4566 q^{89} - 99928 q^{90} + 35708 q^{91} - 60376 q^{92} - 15552 q^{93} - 34712 q^{94} + 45952 q^{96} + 15878 q^{97} + 85656 q^{98} - 43970 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(32))\)

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
32.5.c \(\chi_{32}(31, \cdot)\) 32.5.c.a 2 1
32.5.c.b 2
32.5.d \(\chi_{32}(15, \cdot)\) 32.5.d.a 1 1
32.5.d.b 2
32.5.f \(\chi_{32}(7, \cdot)\) None 0 2
32.5.h \(\chi_{32}(3, \cdot)\) 32.5.h.a 60 4

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(32))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(32)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)