Properties

Label 528.2
Level 528
Weight 2
Dimension 3104
Nonzero newspaces 16
Newform subspaces 57
Sturm bound 30720
Trace bound 11

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Newform subspaces: \( 57 \)
Sturm bound: \(30720\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(528))\).

Total New Old
Modular forms 8240 3268 4972
Cusp forms 7121 3104 4017
Eisenstein series 1119 164 955

Trace form

\( 3104q - 13q^{3} - 24q^{4} + 4q^{5} - 4q^{6} - 14q^{7} + 24q^{8} + 5q^{9} + O(q^{10}) \) \( 3104q - 13q^{3} - 24q^{4} + 4q^{5} - 4q^{6} - 14q^{7} + 24q^{8} + 5q^{9} - 24q^{10} + 12q^{11} - 40q^{12} - 30q^{13} - 24q^{14} + 5q^{15} - 72q^{16} - 4q^{17} - 36q^{18} + 2q^{19} - 32q^{20} - 28q^{21} - 56q^{22} - 16q^{23} - 76q^{24} - 28q^{25} - 40q^{26} - 37q^{27} - 40q^{28} + 20q^{29} - 60q^{30} - 62q^{31} - 17q^{33} - 64q^{34} + 12q^{35} - 52q^{36} + 58q^{37} + 16q^{38} + 9q^{39} + 8q^{40} + 92q^{41} + 68q^{42} + 20q^{43} + 40q^{44} + 38q^{45} + 56q^{46} + 60q^{47} + 108q^{48} + 80q^{49} + 72q^{50} - 23q^{51} + 24q^{52} + 12q^{53} + 76q^{54} - 2q^{55} + 31q^{57} - 72q^{58} - 56q^{59} - 36q^{60} - 158q^{61} + 24q^{62} - 31q^{63} - 168q^{64} + 24q^{65} - 72q^{66} - 92q^{67} - 64q^{68} - 66q^{69} - 464q^{70} - 4q^{71} - 132q^{72} - 230q^{73} - 304q^{74} - 17q^{75} - 488q^{76} - 176q^{77} - 376q^{78} - 98q^{79} - 456q^{80} - 59q^{81} - 488q^{82} - 28q^{83} - 244q^{84} - 394q^{85} - 288q^{86} + 8q^{87} - 648q^{88} - 148q^{89} - 52q^{90} - 22q^{91} - 288q^{92} - 153q^{93} - 440q^{94} + 12q^{95} - 108q^{96} - 262q^{97} - 360q^{98} + 29q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(528))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
528.2.a \(\chi_{528}(1, \cdot)\) 528.2.a.a 1 1
528.2.a.b 1
528.2.a.c 1
528.2.a.d 1
528.2.a.e 1
528.2.a.f 1
528.2.a.g 1
528.2.a.h 1
528.2.a.i 1
528.2.a.j 1
528.2.b \(\chi_{528}(65, \cdot)\) 528.2.b.a 2 1
528.2.b.b 2
528.2.b.c 2
528.2.b.d 4
528.2.b.e 6
528.2.b.f 6
528.2.d \(\chi_{528}(287, \cdot)\) 528.2.d.a 2 1
528.2.d.b 2
528.2.d.c 2
528.2.d.d 2
528.2.d.e 2
528.2.d.f 2
528.2.d.g 4
528.2.d.h 4
528.2.f \(\chi_{528}(265, \cdot)\) None 0 1
528.2.h \(\chi_{528}(439, \cdot)\) None 0 1
528.2.k \(\chi_{528}(23, \cdot)\) None 0 1
528.2.m \(\chi_{528}(329, \cdot)\) None 0 1
528.2.o \(\chi_{528}(175, \cdot)\) 528.2.o.a 4 1
528.2.o.b 8
528.2.q \(\chi_{528}(43, \cdot)\) 528.2.q.a 96 2
528.2.t \(\chi_{528}(133, \cdot)\) 528.2.t.a 40 2
528.2.t.b 40
528.2.u \(\chi_{528}(155, \cdot)\) 528.2.u.a 160 2
528.2.x \(\chi_{528}(197, \cdot)\) 528.2.x.a 184 2
528.2.y \(\chi_{528}(49, \cdot)\) 528.2.y.a 4 4
528.2.y.b 4
528.2.y.c 4
528.2.y.d 4
528.2.y.e 4
528.2.y.f 4
528.2.y.g 4
528.2.y.h 4
528.2.y.i 4
528.2.y.j 4
528.2.y.k 8
528.2.ba \(\chi_{528}(79, \cdot)\) 528.2.ba.a 8 4
528.2.ba.b 8
528.2.ba.c 32
528.2.bc \(\chi_{528}(41, \cdot)\) None 0 4
528.2.be \(\chi_{528}(71, \cdot)\) None 0 4
528.2.bh \(\chi_{528}(7, \cdot)\) None 0 4
528.2.bj \(\chi_{528}(25, \cdot)\) None 0 4
528.2.bl \(\chi_{528}(47, \cdot)\) 528.2.bl.a 32 4
528.2.bl.b 64
528.2.bn \(\chi_{528}(17, \cdot)\) 528.2.bn.a 8 4
528.2.bn.b 8
528.2.bn.c 8
528.2.bn.d 16
528.2.bn.e 24
528.2.bn.f 24
528.2.bo \(\chi_{528}(29, \cdot)\) 528.2.bo.a 736 8
528.2.br \(\chi_{528}(59, \cdot)\) 528.2.br.a 736 8
528.2.bs \(\chi_{528}(37, \cdot)\) 528.2.bs.a 384 8
528.2.bv \(\chi_{528}(19, \cdot)\) 528.2.bv.a 384 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(528))\) into lower level spaces

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