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Properties

Label 52.3
Level 52
Weight 3
Dimension 86
Nonzero newspaces 6
Newform subspaces 10
Sturm bound 504
Trace bound 2

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Defining parameters

Level: \( N \) = \( 52 = 2^{2} \cdot 13 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 10 \)
Sturm bound: \(504\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(52))\).

Total New Old
Modular forms 198 106 92
Cusp forms 138 86 52
Eisenstein series 60 20 40

Trace form

\( 86 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} + 10 q^{7} - 6 q^{8} + 12 q^{9} + O(q^{10}) \) \( 86 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} + 10 q^{7} - 6 q^{8} + 12 q^{9} - 6 q^{10} + 6 q^{11} - 12 q^{12} - 24 q^{13} - 12 q^{14} - 36 q^{15} - 6 q^{16} - 66 q^{17} - 132 q^{18} - 128 q^{19} - 126 q^{20} - 126 q^{21} - 96 q^{22} - 24 q^{23} - 54 q^{24} - 24 q^{25} + 24 q^{26} + 72 q^{27} + 84 q^{28} + 156 q^{29} + 234 q^{30} + 170 q^{31} + 204 q^{32} + 270 q^{33} + 210 q^{34} + 210 q^{35} + 246 q^{36} + 38 q^{37} - 12 q^{38} - 72 q^{39} + 252 q^{40} - 414 q^{41} + 372 q^{42} - 198 q^{43} + 204 q^{44} - 492 q^{45} + 294 q^{46} - 210 q^{47} + 138 q^{48} - 318 q^{49} + 24 q^{50} - 60 q^{52} + 180 q^{53} - 144 q^{54} + 258 q^{55} - 276 q^{56} + 654 q^{57} - 342 q^{58} + 186 q^{59} - 696 q^{60} + 474 q^{61} - 606 q^{62} - 102 q^{63} - 948 q^{64} - 6 q^{65} - 1032 q^{66} - 248 q^{67} - 708 q^{68} - 510 q^{69} - 660 q^{70} - 372 q^{71} - 396 q^{72} - 332 q^{73} - 258 q^{74} - 240 q^{75} - 66 q^{76} - 24 q^{77} + 108 q^{78} + 132 q^{79} + 336 q^{80} + 318 q^{81} + 294 q^{82} + 486 q^{83} + 876 q^{84} + 606 q^{85} + 1104 q^{86} + 588 q^{87} + 1236 q^{88} + 612 q^{89} + 2016 q^{90} + 310 q^{91} + 1284 q^{92} + 726 q^{93} + 1038 q^{94} + 312 q^{95} + 1092 q^{96} - 40 q^{97} + 558 q^{98} - 18 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(52))\)

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
52.3.b \(\chi_{52}(51, \cdot)\) 52.3.b.a 1 1
52.3.b.b 1
52.3.b.c 2
52.3.b.d 8
52.3.c \(\chi_{52}(27, \cdot)\) 52.3.c.a 12 1
52.3.g \(\chi_{52}(5, \cdot)\) 52.3.g.a 6 2
52.3.i \(\chi_{52}(23, \cdot)\) 52.3.i.a 4 2
52.3.i.b 20
52.3.j \(\chi_{52}(3, \cdot)\) 52.3.j.a 24 2
52.3.k \(\chi_{52}(33, \cdot)\) 52.3.k.a 8 4

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(52))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(52)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 2}\)