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Properties

Label 528.6
Level 528
Weight 6
Dimension 15848
Nonzero newspaces 16
Sturm bound 92160
Trace bound 11

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Defining parameters

Level: \( N \) = \( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(92160\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(528))\).

Total New Old
Modular forms 38960 16012 22948
Cusp forms 37840 15848 21992
Eisenstein series 1120 164 956

Trace form

\( 15848 q - 29 q^{3} - 120 q^{4} - 76 q^{5} + 212 q^{6} + 306 q^{7} + 984 q^{8} - 947 q^{9} + O(q^{10}) \) \( 15848 q - 29 q^{3} - 120 q^{4} - 76 q^{5} + 212 q^{6} + 306 q^{7} + 984 q^{8} - 947 q^{9} - 1768 q^{10} - 1812 q^{11} - 24 q^{12} + 434 q^{13} - 648 q^{14} + 4485 q^{15} - 8392 q^{16} - 404 q^{17} + 8780 q^{18} - 19390 q^{19} + 15200 q^{20} - 3964 q^{21} - 1248 q^{22} + 9328 q^{23} - 15596 q^{24} + 3900 q^{25} + 25960 q^{26} + 5995 q^{27} + 3800 q^{28} + 16708 q^{29} + 1460 q^{30} - 40702 q^{31} - 88320 q^{32} + 16143 q^{33} - 62304 q^{34} - 45588 q^{35} + 64716 q^{36} - 27798 q^{37} + 144176 q^{38} + 74633 q^{39} + 180808 q^{40} + 118156 q^{41} + 5908 q^{42} + 66548 q^{43} - 43768 q^{44} + 24934 q^{45} - 244008 q^{46} - 57732 q^{47} - 71252 q^{48} - 289640 q^{49} - 212424 q^{50} - 244695 q^{51} + 329720 q^{52} + 99996 q^{53} + 68100 q^{54} + 99070 q^{55} + 317184 q^{56} + 248175 q^{57} + 70728 q^{58} + 61064 q^{59} + 71868 q^{60} - 114254 q^{61} - 382200 q^{62} - 37599 q^{63} - 715944 q^{64} - 60552 q^{65} - 155232 q^{66} - 403356 q^{67} + 244672 q^{68} - 202386 q^{69} + 75664 q^{70} - 381764 q^{71} - 197956 q^{72} - 401686 q^{73} + 886192 q^{74} + 398687 q^{75} + 1810232 q^{76} + 1112336 q^{77} + 1087832 q^{78} + 897886 q^{79} + 55224 q^{80} + 997037 q^{81} - 145864 q^{82} - 26300 q^{83} - 1158388 q^{84} - 1175978 q^{85} - 1122144 q^{86} - 705016 q^{87} - 4197864 q^{88} - 909476 q^{89} - 332724 q^{90} - 1325910 q^{91} - 674976 q^{92} - 975993 q^{93} + 217000 q^{94} + 272652 q^{95} + 1529876 q^{96} + 1286922 q^{97} + 4029288 q^{98} + 385693 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(528))\)

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
528.6.a \(\chi_{528}(1, \cdot)\) 528.6.a.a 1 1
528.6.a.b 1
528.6.a.c 1
528.6.a.d 1
528.6.a.e 1
528.6.a.f 1
528.6.a.g 1
528.6.a.h 1
528.6.a.i 1
528.6.a.j 1
528.6.a.k 2
528.6.a.l 2
528.6.a.m 2
528.6.a.n 2
528.6.a.o 2
528.6.a.p 2
528.6.a.q 2
528.6.a.r 2
528.6.a.s 2
528.6.a.t 3
528.6.a.u 3
528.6.a.v 3
528.6.a.w 3
528.6.a.x 3
528.6.a.y 3
528.6.a.z 4
528.6.b \(\chi_{528}(65, \cdot)\) n/a 118 1
528.6.d \(\chi_{528}(287, \cdot)\) 528.6.d.a 16 1
528.6.d.b 16
528.6.d.c 34
528.6.d.d 34
528.6.f \(\chi_{528}(265, \cdot)\) None 0 1
528.6.h \(\chi_{528}(439, \cdot)\) None 0 1
528.6.k \(\chi_{528}(23, \cdot)\) None 0 1
528.6.m \(\chi_{528}(329, \cdot)\) None 0 1
528.6.o \(\chi_{528}(175, \cdot)\) 528.6.o.a 20 1
528.6.o.b 40
528.6.q \(\chi_{528}(43, \cdot)\) n/a 480 2
528.6.t \(\chi_{528}(133, \cdot)\) n/a 400 2
528.6.u \(\chi_{528}(155, \cdot)\) n/a 800 2
528.6.x \(\chi_{528}(197, \cdot)\) n/a 952 2
528.6.y \(\chi_{528}(49, \cdot)\) n/a 240 4
528.6.ba \(\chi_{528}(79, \cdot)\) n/a 240 4
528.6.bc \(\chi_{528}(41, \cdot)\) None 0 4
528.6.be \(\chi_{528}(71, \cdot)\) None 0 4
528.6.bh \(\chi_{528}(7, \cdot)\) None 0 4
528.6.bj \(\chi_{528}(25, \cdot)\) None 0 4
528.6.bl \(\chi_{528}(47, \cdot)\) n/a 480 4
528.6.bn \(\chi_{528}(17, \cdot)\) n/a 472 4
528.6.bo \(\chi_{528}(29, \cdot)\) n/a 3808 8
528.6.br \(\chi_{528}(59, \cdot)\) n/a 3808 8
528.6.bs \(\chi_{528}(37, \cdot)\) n/a 1920 8
528.6.bv \(\chi_{528}(19, \cdot)\) n/a 1920 8

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(528))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(528)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 2}\)