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Properties

Label 54.5
Level 54
Weight 5
Dimension 86
Nonzero newspaces 3
Newform subspaces 4
Sturm bound 810
Trace bound 1

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Defining parameters

Level: \( N \) = \( 54 = 2 \cdot 3^{3} \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 4 \)
Sturm bound: \(810\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(54))\).

Total New Old
Modular forms 354 86 268
Cusp forms 294 86 208
Eisenstein series 60 0 60

Trace form

\( 86 q - 16 q^{4} - 36 q^{5} - 96 q^{6} - 104 q^{7} + 204 q^{9} + O(q^{10}) \) \( 86 q - 16 q^{4} - 36 q^{5} - 96 q^{6} - 104 q^{7} + 204 q^{9} + 288 q^{10} + 1440 q^{11} + 96 q^{12} - 320 q^{13} - 576 q^{14} - 1422 q^{15} + 128 q^{16} - 1344 q^{18} + 562 q^{19} + 144 q^{20} + 4308 q^{21} - 672 q^{22} + 3438 q^{23} - 1846 q^{25} - 2808 q^{27} + 208 q^{28} - 4230 q^{29} - 6336 q^{30} + 748 q^{31} - 1026 q^{33} + 3072 q^{34} + 5346 q^{35} + 2976 q^{36} - 1874 q^{37} - 6192 q^{38} - 4974 q^{39} - 2304 q^{40} - 13320 q^{41} - 3840 q^{42} - 812 q^{43} + 9558 q^{45} + 2112 q^{46} + 14364 q^{47} + 1920 q^{48} + 17274 q^{49} + 31104 q^{50} + 20898 q^{51} + 2560 q^{52} - 4896 q^{54} - 15552 q^{55} - 4608 q^{56} - 34218 q^{57} - 19680 q^{58} - 49212 q^{59} - 4176 q^{60} + 1168 q^{61} - 4110 q^{63} + 11264 q^{64} + 2880 q^{65} - 10368 q^{66} - 13418 q^{67} + 21312 q^{68} + 47106 q^{69} + 31392 q^{70} + 39528 q^{71} + 15360 q^{72} + 30160 q^{73} + 17856 q^{74} + 41682 q^{75} + 6496 q^{76} - 6228 q^{77} - 4608 q^{78} - 18548 q^{79} + 6804 q^{81} + 4032 q^{82} - 26244 q^{83} - 2592 q^{84} - 77580 q^{85} - 33696 q^{86} - 111690 q^{87} - 18816 q^{88} - 102222 q^{89} - 66240 q^{90} - 9844 q^{91} - 37728 q^{92} - 11958 q^{93} - 20064 q^{94} + 25848 q^{95} + 6144 q^{96} + 102466 q^{97} + 82944 q^{98} + 179622 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(54))\)

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
54.5.b \(\chi_{54}(53, \cdot)\) 54.5.b.a 2 1
54.5.b.b 4
54.5.d \(\chi_{54}(17, \cdot)\) 54.5.d.a 8 2
54.5.f \(\chi_{54}(5, \cdot)\) 54.5.f.a 72 6

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(54))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(54)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 1}\)