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

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

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 the 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

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