Properties

Label 108.4
Level 108
Weight 4
Dimension 432
Nonzero newspaces 6
Newform subspaces 11
Sturm bound 2592
Trace bound 1

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Defining parameters

Level: \( N \) = \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 11 \)
Sturm bound: \(2592\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(108))\).

Total New Old
Modular forms 1047 464 583
Cusp forms 897 432 465
Eisenstein series 150 32 118

Trace form

\( 432 q - 3 q^{2} - 13 q^{4} - 6 q^{6} - 28 q^{7} - 9 q^{8} - 60 q^{9} + O(q^{10}) \) \( 432 q - 3 q^{2} - 13 q^{4} - 6 q^{6} - 28 q^{7} - 9 q^{8} - 60 q^{9} + 43 q^{10} - 138 q^{11} - 123 q^{12} - 24 q^{13} + 147 q^{14} + 234 q^{15} + 131 q^{16} + 408 q^{17} + 351 q^{18} + 170 q^{19} + 459 q^{20} - 24 q^{21} + 195 q^{22} - 114 q^{23} - 300 q^{24} - 887 q^{25} + 27 q^{27} - 6 q^{28} - 312 q^{29} - 207 q^{30} + 92 q^{31} - 1383 q^{32} + 921 q^{33} - 905 q^{34} + 1110 q^{35} - 1056 q^{36} + 828 q^{37} - 1791 q^{38} + 66 q^{39} - 725 q^{40} + 264 q^{41} + 2574 q^{42} - 1492 q^{43} + 2655 q^{44} - 978 q^{45} + 1101 q^{46} - 2070 q^{47} - 435 q^{48} + 407 q^{49} - 852 q^{50} - 1368 q^{51} + 2167 q^{52} + 1140 q^{53} - 4458 q^{54} + 918 q^{55} + 81 q^{56} - 609 q^{57} + 2455 q^{58} - 1671 q^{59} + 966 q^{60} - 2040 q^{61} + 1872 q^{62} + 30 q^{63} - 163 q^{64} - 2412 q^{65} + 3093 q^{66} - 3502 q^{67} - 2634 q^{68} - 96 q^{69} - 6333 q^{70} - 240 q^{71} - 4524 q^{72} - 360 q^{73} - 11757 q^{74} + 732 q^{75} - 5121 q^{76} + 378 q^{77} - 2976 q^{78} + 3356 q^{79} + 3792 q^{81} + 2614 q^{82} + 5076 q^{83} + 6324 q^{84} + 5018 q^{85} + 16653 q^{86} + 4824 q^{87} + 10251 q^{88} + 9165 q^{89} - 1104 q^{90} + 2278 q^{91} + 5469 q^{92} + 8568 q^{93} + 6351 q^{94} + 534 q^{95} + 582 q^{96} - 504 q^{97} + 2898 q^{98} - 5076 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(108))\)

We only show spaces with even 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
108.4.a \(\chi_{108}(1, \cdot)\) 108.4.a.a 1 1
108.4.a.b 1
108.4.a.c 1
108.4.a.d 1
108.4.b \(\chi_{108}(107, \cdot)\) 108.4.b.a 12 1
108.4.b.b 12
108.4.e \(\chi_{108}(37, \cdot)\) 108.4.e.a 6 2
108.4.h \(\chi_{108}(35, \cdot)\) 108.4.h.a 8 2
108.4.h.b 24
108.4.i \(\chi_{108}(13, \cdot)\) 108.4.i.a 54 6
108.4.l \(\chi_{108}(11, \cdot)\) 108.4.l.a 312 6

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(108))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(108)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 1}\)