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Properties

Label 52.6
Level 52
Weight 6
Dimension 231
Nonzero newspaces 6
Newform subspaces 10
Sturm bound 1008
Trace bound 1

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Defining parameters

Level: \( N \) = \( 52 = 2^{2} \cdot 13 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 10 \)
Sturm bound: \(1008\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(52))\).

Total New Old
Modular forms 450 255 195
Cusp forms 390 231 159
Eisenstein series 60 24 36

Trace form

\( 231 q - 6 q^{2} + 24 q^{3} - 6 q^{4} - 120 q^{5} - 6 q^{6} - 122 q^{7} - 6 q^{8} + 834 q^{9} + O(q^{10}) \) \( 231 q - 6 q^{2} + 24 q^{3} - 6 q^{4} - 120 q^{5} - 6 q^{6} - 122 q^{7} - 6 q^{8} + 834 q^{9} - 6 q^{10} - 1614 q^{11} - 1166 q^{13} - 12 q^{14} + 2484 q^{15} - 6 q^{16} + 4329 q^{17} + 1416 q^{18} - 6164 q^{19} - 11406 q^{20} - 13386 q^{21} - 876 q^{22} + 11436 q^{23} + 24234 q^{24} + 9793 q^{25} + 17964 q^{26} + 6948 q^{27} + 3264 q^{28} - 7509 q^{29} - 34806 q^{30} - 4874 q^{31} - 38376 q^{32} - 978 q^{33} - 13086 q^{34} + 7374 q^{35} + 50178 q^{36} + 1321 q^{37} - 17100 q^{39} - 41316 q^{40} - 70611 q^{41} + 69168 q^{42} - 2262 q^{43} + 63924 q^{44} + 7095 q^{45} + 42534 q^{46} + 52818 q^{47} - 52278 q^{48} + 167548 q^{49} - 126768 q^{50} - 50640 q^{51} - 137652 q^{52} + 61260 q^{53} - 82920 q^{54} + 25086 q^{55} + 23700 q^{56} - 20514 q^{57} + 132522 q^{58} - 23934 q^{59} + 283884 q^{60} - 162451 q^{61} + 347766 q^{62} - 88218 q^{63} - 40575 q^{65} - 548016 q^{66} - 170276 q^{67} - 416448 q^{68} - 265446 q^{69} - 233964 q^{70} + 65796 q^{71} + 31896 q^{72} + 18916 q^{73} + 298950 q^{74} + 409464 q^{75} + 332934 q^{76} + 543396 q^{77} + 667008 q^{78} + 425828 q^{79} + 492588 q^{80} + 126204 q^{81} + 71934 q^{82} - 129774 q^{83} - 343692 q^{84} - 445959 q^{85} - 933924 q^{86} - 614580 q^{87} - 657324 q^{88} - 523776 q^{89} - 408482 q^{91} + 189804 q^{92} + 261858 q^{93} + 748278 q^{94} + 368976 q^{95} + 909696 q^{96} + 52768 q^{97} - 54630 q^{98} + 249138 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(52))\)

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
52.6.a \(\chi_{52}(1, \cdot)\) 52.6.a.a 1 1
52.6.a.b 1
52.6.a.c 3
52.6.d \(\chi_{52}(25, \cdot)\) 52.6.d.a 6 1
52.6.e \(\chi_{52}(9, \cdot)\) 52.6.e.a 12 2
52.6.f \(\chi_{52}(31, \cdot)\) 52.6.f.a 2 2
52.6.f.b 64
52.6.h \(\chi_{52}(17, \cdot)\) 52.6.h.a 10 2
52.6.l \(\chi_{52}(7, \cdot)\) 52.6.l.a 4 4
52.6.l.b 128

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(52))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(52)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 2}\)