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Properties

Label 108.5
Level 108
Weight 5
Dimension 581
Nonzero newspaces 6
Newform subspaces 9
Sturm bound 3240
Trace bound 1

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Defining parameters

Level: \( N \) = \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 9 \)
Sturm bound: \(3240\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(108))\).

Total New Old
Modular forms 1371 613 758
Cusp forms 1221 581 640
Eisenstein series 150 32 118

Trace form

\( 581 q - 5 q^{2} + 7 q^{4} + 8 q^{5} - 6 q^{6} - 16 q^{7} - 125 q^{8} - 114 q^{9} + O(q^{10}) \) \( 581 q - 5 q^{2} + 7 q^{4} + 8 q^{5} - 6 q^{6} - 16 q^{7} - 125 q^{8} - 114 q^{9} - q^{10} + 36 q^{11} + 39 q^{12} - 554 q^{13} - 1113 q^{14} - 225 q^{15} - 125 q^{16} + 50 q^{17} + 729 q^{18} + 539 q^{19} + 2087 q^{20} - 294 q^{21} + 1083 q^{22} + 441 q^{23} - 354 q^{24} + 2473 q^{25} - 5806 q^{26} + 54 q^{27} + 1626 q^{28} - 2383 q^{29} + 3951 q^{30} - 4234 q^{31} + 5065 q^{32} - 3777 q^{33} - 589 q^{34} - 2673 q^{35} - 2136 q^{36} + 6535 q^{37} - 7479 q^{38} + 6951 q^{39} - 3949 q^{40} + 13478 q^{41} - 19566 q^{42} + 2618 q^{43} - 5205 q^{44} + 4341 q^{45} + 1785 q^{46} - 8586 q^{47} + 31965 q^{48} - 21119 q^{49} + 16788 q^{50} + 1899 q^{51} - 4297 q^{52} + 10064 q^{53} - 8994 q^{54} + 15516 q^{55} - 25659 q^{56} - 6279 q^{57} - 877 q^{58} + 9108 q^{59} - 39102 q^{60} + 4294 q^{61} + 5550 q^{62} - 11985 q^{63} + 14761 q^{64} - 1670 q^{65} + 47157 q^{66} - 7495 q^{67} + 67076 q^{68} + 12027 q^{69} + 8931 q^{70} - 19764 q^{71} + 6276 q^{72} + 18358 q^{73} - 7837 q^{74} - 3453 q^{75} - 40665 q^{76} + 6900 q^{77} - 43746 q^{78} - 4546 q^{79} - 109522 q^{80} - 35358 q^{81} - 46894 q^{82} - 57078 q^{83} - 39846 q^{84} - 10028 q^{85} - 24675 q^{86} + 40545 q^{87} + 8475 q^{88} - 13189 q^{89} + 107706 q^{90} + 28786 q^{91} + 97113 q^{92} + 30087 q^{93} + 62271 q^{94} + 85140 q^{95} - 6870 q^{96} - 34643 q^{97} + 33940 q^{98} + 12177 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(108))\)

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
108.5.c \(\chi_{108}(53, \cdot)\) 108.5.c.a 1 1
108.5.c.b 2
108.5.c.c 2
108.5.d \(\chi_{108}(55, \cdot)\) 108.5.d.a 16 1
108.5.d.b 16
108.5.f \(\chi_{108}(19, \cdot)\) 108.5.f.a 44 2
108.5.g \(\chi_{108}(17, \cdot)\) 108.5.g.a 8 2
108.5.j \(\chi_{108}(7, \cdot)\) 108.5.j.a 420 6
108.5.k \(\chi_{108}(5, \cdot)\) 108.5.k.a 72 6

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(108))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(108)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 2}\)