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Properties

Label 252.3
Level 252
Weight 3
Dimension 1486
Nonzero newspaces 20
Newform subspaces 36
Sturm bound 10368
Trace bound 9

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Defining parameters

Level: \( N \) = \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 20 \)
Newform subspaces: \( 36 \)
Sturm bound: \(10368\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(252))\).

Total New Old
Modular forms 3696 1574 2122
Cusp forms 3216 1486 1730
Eisenstein series 480 88 392

Trace form

\( 1486 q - 11 q^{2} - 6 q^{3} - 15 q^{4} - 37 q^{5} + 6 q^{6} - 3 q^{7} + 43 q^{8} + 6 q^{9} + O(q^{10}) \) \( 1486 q - 11 q^{2} - 6 q^{3} - 15 q^{4} - 37 q^{5} + 6 q^{6} - 3 q^{7} + 43 q^{8} + 6 q^{9} - 6 q^{10} + 45 q^{11} + 60 q^{12} - 26 q^{13} + 3 q^{14} + 30 q^{15} - 3 q^{16} + 29 q^{17} - 36 q^{18} - 5 q^{19} + 38 q^{20} - 75 q^{21} + 54 q^{22} - 141 q^{23} - 270 q^{24} + 4 q^{25} - 286 q^{26} + 126 q^{27} - 63 q^{28} + 278 q^{29} - 174 q^{30} + 277 q^{31} + 19 q^{32} + 324 q^{33} + 174 q^{34} + 363 q^{35} + 366 q^{36} + 567 q^{37} + 612 q^{38} - 42 q^{39} + 318 q^{40} + 152 q^{41} + 276 q^{42} + 36 q^{43} + 510 q^{44} - 222 q^{45} + 42 q^{46} - 195 q^{47} + 234 q^{48} - 197 q^{49} - 165 q^{50} + 90 q^{51} - 438 q^{52} - 631 q^{53} - 540 q^{54} - 684 q^{55} - 897 q^{56} - 318 q^{57} - 876 q^{58} - 303 q^{59} - 1314 q^{60} - 371 q^{61} - 1476 q^{62} - 225 q^{63} - 939 q^{64} - 440 q^{65} - 1302 q^{66} + 35 q^{67} - 1654 q^{68} - 30 q^{69} - 1230 q^{70} + 192 q^{71} - 360 q^{72} + 865 q^{73} - 274 q^{74} + 102 q^{75} - 414 q^{76} + 1098 q^{77} + 936 q^{78} + 449 q^{79} + 1382 q^{80} + 894 q^{81} + 534 q^{82} + 162 q^{83} + 738 q^{84} + 294 q^{85} + 972 q^{86} - 324 q^{87} + 276 q^{88} - 931 q^{89} + 426 q^{90} - 722 q^{91} + 480 q^{92} + 84 q^{93} + 828 q^{94} - 1173 q^{95} - 720 q^{96} - 620 q^{97} + 571 q^{98} - 966 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(252))\)

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
252.3.c \(\chi_{252}(197, \cdot)\) 252.3.c.a 4 1
252.3.d \(\chi_{252}(181, \cdot)\) 252.3.d.a 2 1
252.3.d.b 2
252.3.d.c 2
252.3.g \(\chi_{252}(127, \cdot)\) 252.3.g.a 6 1
252.3.g.b 12
252.3.g.c 12
252.3.h \(\chi_{252}(251, \cdot)\) 252.3.h.a 8 1
252.3.h.b 24
252.3.m \(\chi_{252}(65, \cdot)\) 252.3.m.a 32 2
252.3.p \(\chi_{252}(61, \cdot)\) 252.3.p.a 32 2
252.3.q \(\chi_{252}(143, \cdot)\) 252.3.q.a 8 2
252.3.q.b 56
252.3.r \(\chi_{252}(131, \cdot)\) 252.3.r.a 184 2
252.3.s \(\chi_{252}(83, \cdot)\) 252.3.s.a 184 2
252.3.u \(\chi_{252}(151, \cdot)\) 252.3.u.a 184 2
252.3.v \(\chi_{252}(43, \cdot)\) 252.3.v.a 144 2
252.3.y \(\chi_{252}(163, \cdot)\) 252.3.y.a 2 2
252.3.y.b 2
252.3.y.c 12
252.3.y.d 14
252.3.y.e 14
252.3.y.f 32
252.3.z \(\chi_{252}(73, \cdot)\) 252.3.z.a 2 2
252.3.z.b 2
252.3.z.c 2
252.3.z.d 4
252.3.z.e 4
252.3.bc \(\chi_{252}(13, \cdot)\) 252.3.bc.a 32 2
252.3.bd \(\chi_{252}(229, \cdot)\) 252.3.bd.a 32 2
252.3.bg \(\chi_{252}(29, \cdot)\) 252.3.bg.a 24 2
252.3.bh \(\chi_{252}(137, \cdot)\) 252.3.bh.a 32 2
252.3.bk \(\chi_{252}(53, \cdot)\) 252.3.bk.a 4 2
252.3.bk.b 8
252.3.bl \(\chi_{252}(67, \cdot)\) 252.3.bl.a 184 2
252.3.bn \(\chi_{252}(47, \cdot)\) 252.3.bn.a 184 2

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(252))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(252)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 2}\)