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Properties

Label 55.4
Level 55
Weight 4
Dimension 298
Nonzero newspaces 6
Newform subspaces 12
Sturm bound 960
Trace bound 1

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Defining parameters

Level: \( N \) = \( 55 = 5 \cdot 11 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 12 \)
Sturm bound: \(960\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(55))\).

Total New Old
Modular forms 400 354 46
Cusp forms 320 298 22
Eisenstein series 80 56 24

Trace form

\( 298 q - 2 q^{2} - 14 q^{3} - 26 q^{4} - 5 q^{5} + 86 q^{6} - 2 q^{7} - 90 q^{8} - 124 q^{9} + O(q^{10}) \) \( 298 q - 2 q^{2} - 14 q^{3} - 26 q^{4} - 5 q^{5} + 86 q^{6} - 2 q^{7} - 90 q^{8} - 124 q^{9} - 150 q^{10} - 162 q^{11} - 372 q^{12} + 26 q^{13} + 428 q^{14} + 315 q^{15} + 858 q^{16} + 238 q^{17} - 184 q^{18} - 660 q^{19} - 370 q^{20} - 884 q^{21} - 1142 q^{22} + 336 q^{23} + 370 q^{24} - 5 q^{25} + 16 q^{26} + 400 q^{27} + 224 q^{28} + 190 q^{29} + 280 q^{30} + 966 q^{31} - 972 q^{32} + 336 q^{33} + 868 q^{34} - 25 q^{35} + 248 q^{36} - 822 q^{37} + 20 q^{38} - 1398 q^{39} - 1340 q^{40} - 1094 q^{41} - 4064 q^{42} - 2604 q^{43} - 2516 q^{44} - 3310 q^{45} - 3884 q^{46} - 282 q^{47} - 684 q^{48} + 1024 q^{49} + 2190 q^{50} + 4036 q^{51} + 10568 q^{52} + 7066 q^{53} + 14220 q^{54} + 6065 q^{55} + 11120 q^{56} + 6240 q^{57} + 3900 q^{58} - 1600 q^{59} + 2280 q^{60} + 1326 q^{61} - 6224 q^{62} - 1904 q^{63} - 6146 q^{64} - 4670 q^{65} - 8624 q^{66} - 8092 q^{67} - 13376 q^{68} - 7788 q^{69} - 7840 q^{70} - 1794 q^{71} - 4690 q^{72} + 6846 q^{73} + 5048 q^{74} - 65 q^{75} - 2020 q^{76} + 4258 q^{77} + 2912 q^{78} - 130 q^{79} + 2800 q^{80} + 1758 q^{81} + 6126 q^{82} - 1624 q^{83} + 148 q^{84} - 2595 q^{85} + 1686 q^{86} - 6840 q^{87} - 9370 q^{88} - 3620 q^{89} - 13530 q^{90} - 11734 q^{91} - 13492 q^{92} - 13718 q^{93} - 21892 q^{94} - 8735 q^{95} - 22104 q^{96} - 8132 q^{97} - 11276 q^{98} - 2714 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(55))\)

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
55.4.a \(\chi_{55}(1, \cdot)\) 55.4.a.a 1 1
55.4.a.b 2
55.4.a.c 3
55.4.a.d 4
55.4.b \(\chi_{55}(34, \cdot)\) 55.4.b.a 6 1
55.4.b.b 10
55.4.e \(\chi_{55}(32, \cdot)\) 55.4.e.a 4 2
55.4.e.b 28
55.4.g \(\chi_{55}(16, \cdot)\) 55.4.g.a 24 4
55.4.g.b 24
55.4.j \(\chi_{55}(4, \cdot)\) 55.4.j.a 64 4
55.4.l \(\chi_{55}(2, \cdot)\) 55.4.l.a 128 8

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(55))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(55)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 1}\)