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Properties

Label 252.8
Level 252
Weight 8
Dimension 5310
Nonzero newspaces 20
Sturm bound 27648
Trace bound 9

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Defining parameters

Level: \( N \) = \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(27648\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(252))\).

Total New Old
Modular forms 12336 5402 6934
Cusp forms 11856 5310 6546
Eisenstein series 480 92 388

Trace form

\( 5310 q - 3 q^{2} + 97 q^{4} - 867 q^{5} - 438 q^{6} + 643 q^{7} - 879 q^{8} + 1692 q^{9} + O(q^{10}) \) \( 5310 q - 3 q^{2} + 97 q^{4} - 867 q^{5} - 438 q^{6} + 643 q^{7} - 879 q^{8} + 1692 q^{9} + 4388 q^{10} - 5859 q^{11} + 37632 q^{12} + 31406 q^{13} - 63135 q^{14} + 5250 q^{15} + 53845 q^{16} + 35955 q^{17} + 144276 q^{18} - 119511 q^{19} - 261630 q^{20} - 124419 q^{21} - 7932 q^{22} + 66591 q^{23} + 660366 q^{24} - 53896 q^{25} + 203574 q^{26} - 530694 q^{27} - 73647 q^{28} - 1352238 q^{29} + 268122 q^{30} + 910257 q^{31} + 2474997 q^{32} + 2036406 q^{33} + 899336 q^{34} - 1499559 q^{35} - 3495042 q^{36} - 1813265 q^{37} - 103248 q^{38} + 778074 q^{39} - 1340974 q^{40} - 211878 q^{41} + 5157282 q^{42} + 375518 q^{43} + 1324644 q^{44} - 945678 q^{45} - 3819054 q^{46} - 4380957 q^{47} - 1332690 q^{48} + 16695945 q^{49} + 607311 q^{50} + 13752648 q^{51} - 646678 q^{52} + 5413485 q^{53} - 1011420 q^{54} + 910962 q^{55} - 2449035 q^{56} - 5084064 q^{57} + 17206568 q^{58} - 3727953 q^{59} - 6893310 q^{60} - 12726601 q^{61} + 14812227 q^{63} - 34177163 q^{64} - 384306 q^{65} + 7208910 q^{66} - 10528469 q^{67} - 7475064 q^{68} - 8048922 q^{69} - 24516330 q^{70} + 18492456 q^{71} - 3728784 q^{72} + 4900439 q^{73} + 55157340 q^{74} + 28251864 q^{75} - 5751000 q^{76} - 11990610 q^{77} - 2087556 q^{78} - 7593911 q^{79} - 20699082 q^{80} + 30539568 q^{81} - 2574616 q^{82} - 5303658 q^{83} - 60783846 q^{84} - 7718606 q^{85} - 67055202 q^{86} + 56259360 q^{87} - 10285482 q^{88} - 40164429 q^{89} + 107824518 q^{90} - 16506930 q^{91} + 68652606 q^{92} + 60781032 q^{93} + 120895302 q^{94} + 29060967 q^{95} - 7895616 q^{96} + 115077182 q^{97} - 167093529 q^{98} - 90279570 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(252))\)

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
252.8.a \(\chi_{252}(1, \cdot)\) 252.8.a.a 1 1
252.8.a.b 1
252.8.a.c 2
252.8.a.d 2
252.8.a.e 2
252.8.a.f 2
252.8.a.g 4
252.8.a.h 4
252.8.b \(\chi_{252}(55, \cdot)\) n/a 138 1
252.8.e \(\chi_{252}(71, \cdot)\) 252.8.e.a 84 1
252.8.f \(\chi_{252}(125, \cdot)\) 252.8.f.a 20 1
252.8.i \(\chi_{252}(25, \cdot)\) n/a 112 2
252.8.j \(\chi_{252}(85, \cdot)\) 252.8.j.a 42 2
252.8.j.b 42
252.8.k \(\chi_{252}(37, \cdot)\) 252.8.k.a 2 2
252.8.k.b 8
252.8.k.c 10
252.8.k.d 10
252.8.k.e 16
252.8.l \(\chi_{252}(193, \cdot)\) n/a 112 2
252.8.n \(\chi_{252}(31, \cdot)\) n/a 664 2
252.8.o \(\chi_{252}(95, \cdot)\) n/a 664 2
252.8.t \(\chi_{252}(17, \cdot)\) 252.8.t.a 36 2
252.8.w \(\chi_{252}(5, \cdot)\) n/a 112 2
252.8.x \(\chi_{252}(41, \cdot)\) n/a 112 2
252.8.ba \(\chi_{252}(155, \cdot)\) n/a 504 2
252.8.bb \(\chi_{252}(11, \cdot)\) n/a 664 2
252.8.be \(\chi_{252}(107, \cdot)\) n/a 224 2
252.8.bf \(\chi_{252}(19, \cdot)\) n/a 276 2
252.8.bi \(\chi_{252}(139, \cdot)\) n/a 664 2
252.8.bj \(\chi_{252}(103, \cdot)\) n/a 664 2
252.8.bm \(\chi_{252}(173, \cdot)\) n/a 112 2

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(252))\) into lower level spaces

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