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Properties

Label 252.12
Level 252
Weight 12
Dimension 8372
Nonzero newspaces 20
Sturm bound 41472
Trace bound 9

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Defining parameters

Level: \( N \) = \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(41472\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(252))\).

Total New Old
Modular forms 19248 8464 10784
Cusp forms 18768 8372 10396
Eisenstein series 480 92 388

Trace form

\( 8372 q - 3 q^{2} - 1032 q^{3} + 7905 q^{4} - 13497 q^{5} + 26250 q^{6} - 14601 q^{7} - 168447 q^{8} + 459816 q^{9} + O(q^{10}) \) \( 8372 q - 3 q^{2} - 1032 q^{3} + 7905 q^{4} - 13497 q^{5} + 26250 q^{6} - 14601 q^{7} - 168447 q^{8} + 459816 q^{9} + 122628 q^{10} - 851595 q^{11} - 3365760 q^{12} + 6328322 q^{13} - 2160303 q^{14} - 22910550 q^{15} + 25092885 q^{16} + 26013345 q^{17} + 26540532 q^{18} + 18153209 q^{19} - 116040510 q^{20} - 71122341 q^{21} + 212503860 q^{22} + 220782939 q^{23} - 242096850 q^{24} - 650920126 q^{25} + 84329574 q^{26} - 54800262 q^{27} + 220513809 q^{28} + 319931922 q^{29} - 777269478 q^{30} + 1676020421 q^{31} + 312149637 q^{32} - 773121618 q^{33} + 2779666632 q^{34} + 2257225281 q^{35} - 1555537026 q^{36} - 1484020071 q^{37} - 792152928 q^{38} + 1065610146 q^{39} + 4526921826 q^{40} + 9026130390 q^{41} + 1899412962 q^{42} - 3793825650 q^{43} - 14367720156 q^{44} - 11216093658 q^{45} + 478132050 q^{46} + 1243816335 q^{47} - 2658332178 q^{48} + 73324550909 q^{49} - 12390178449 q^{50} - 22322199744 q^{51} - 29581137558 q^{52} - 2040496389 q^{53} + 43746876036 q^{54} + 9937997802 q^{55} - 24855955083 q^{56} - 54105011580 q^{57} - 11231928312 q^{58} - 4968702993 q^{59} + 89556238530 q^{60} + 223406453 q^{61} + 47347954263 q^{63} - 2491295211 q^{64} + 21848726994 q^{65} + 22010825838 q^{66} + 19540645459 q^{67} - 70960776792 q^{68} - 55606018998 q^{69} + 175115967990 q^{70} + 101107757064 q^{71} - 136637833968 q^{72} + 182316824477 q^{73} - 61633926756 q^{74} - 176754057936 q^{75} - 118531796952 q^{76} - 138603879378 q^{77} + 274270766652 q^{78} - 275858183147 q^{79} + 66528889398 q^{80} - 192245537940 q^{81} - 24022438632 q^{82} + 562191482910 q^{83} - 351325982358 q^{84} + 472234989174 q^{85} + 106776316590 q^{86} - 220094222544 q^{87} - 92629960746 q^{88} - 931445381295 q^{89} + 93692595558 q^{90} + 35714520206 q^{91} + 31579570494 q^{92} - 165263800200 q^{93} + 556862694390 q^{94} - 512502500373 q^{95} - 335442811104 q^{96} - 279557642974 q^{97} + 1041082343223 q^{98} + 204710686350 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(252))\)

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
252.12.a \(\chi_{252}(1, \cdot)\) 252.12.a.a 1 1
252.12.a.b 2
252.12.a.c 2
252.12.a.d 2
252.12.a.e 3
252.12.a.f 3
252.12.a.g 3
252.12.a.h 6
252.12.a.i 6
252.12.b \(\chi_{252}(55, \cdot)\) n/a 218 1
252.12.e \(\chi_{252}(71, \cdot)\) n/a 132 1
252.12.f \(\chi_{252}(125, \cdot)\) 252.12.f.a 28 1
252.12.i \(\chi_{252}(25, \cdot)\) n/a 176 2
252.12.j \(\chi_{252}(85, \cdot)\) n/a 132 2
252.12.k \(\chi_{252}(37, \cdot)\) 252.12.k.a 2 2
252.12.k.b 14
252.12.k.c 14
252.12.k.d 16
252.12.k.e 28
252.12.l \(\chi_{252}(193, \cdot)\) n/a 176 2
252.12.n \(\chi_{252}(31, \cdot)\) n/a 1048 2
252.12.o \(\chi_{252}(95, \cdot)\) n/a 1048 2
252.12.t \(\chi_{252}(17, \cdot)\) 252.12.t.a 60 2
252.12.w \(\chi_{252}(5, \cdot)\) n/a 176 2
252.12.x \(\chi_{252}(41, \cdot)\) n/a 176 2
252.12.ba \(\chi_{252}(155, \cdot)\) n/a 792 2
252.12.bb \(\chi_{252}(11, \cdot)\) n/a 1048 2
252.12.be \(\chi_{252}(107, \cdot)\) n/a 352 2
252.12.bf \(\chi_{252}(19, \cdot)\) n/a 436 2
252.12.bi \(\chi_{252}(139, \cdot)\) n/a 1048 2
252.12.bj \(\chi_{252}(103, \cdot)\) n/a 1048 2
252.12.bm \(\chi_{252}(173, \cdot)\) n/a 176 2

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(252))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(252)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 9}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 2}\)