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Properties

Label 2132.1
Level 2132
Weight 1
Dimension 244
Nonzero newspaces 16
Newform subspaces 29
Sturm bound 282240
Trace bound 4

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Defining parameters

Level: \( N \) = \( 2132 = 2^{2} \cdot 13 \cdot 41 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 16 \)
Newform subspaces: \( 29 \)
Sturm bound: \(282240\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2132))\).

Total New Old
Modular forms 2670 1104 1566
Cusp forms 270 244 26
Eisenstein series 2400 860 1540

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 220 0 8 16

Trace form

\( 244 q + 2 q^{2} - 4 q^{4} + 12 q^{5} - 2 q^{6} - 4 q^{8} + 2 q^{9} + O(q^{10}) \) \( 244 q + 2 q^{2} - 4 q^{4} + 12 q^{5} - 2 q^{6} - 4 q^{8} + 2 q^{9} - 2 q^{10} + 4 q^{13} + 16 q^{14} + 16 q^{16} - 6 q^{17} - 4 q^{18} - 8 q^{20} - 4 q^{21} + 12 q^{22} + 2 q^{24} + 2 q^{26} - 6 q^{29} + 12 q^{30} - 18 q^{32} - 6 q^{33} - 16 q^{34} + 2 q^{36} - 2 q^{37} + 24 q^{38} + 4 q^{40} + q^{41} - 2 q^{45} + 6 q^{49} - 20 q^{50} - 10 q^{52} + 4 q^{53} - 2 q^{54} - 2 q^{56} - 4 q^{57} - 2 q^{58} - 12 q^{61} - 10 q^{62} - 4 q^{64} - 8 q^{65} + 2 q^{68} + 8 q^{70} + 2 q^{72} + 4 q^{73} - 2 q^{74} - 12 q^{77} + 8 q^{78} + 4 q^{80} - 6 q^{81} - q^{82} - 2 q^{84} - 6 q^{85} - 8 q^{86} - 12 q^{88} + 4 q^{90} + 4 q^{93} - 6 q^{94} - 16 q^{96} + 4 q^{97} + 2 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2132))\)

We only show spaces with odd 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
2132.1.c \(\chi_{2132}(1559, \cdot)\) None 0 1
2132.1.e \(\chi_{2132}(1067, \cdot)\) None 0 1
2132.1.f \(\chi_{2132}(2131, \cdot)\) 2132.1.f.a 1 1
2132.1.f.b 1
2132.1.f.c 1
2132.1.f.d 1
2132.1.h \(\chi_{2132}(1639, \cdot)\) None 0 1
2132.1.k \(\chi_{2132}(1721, \cdot)\) None 0 2
2132.1.l \(\chi_{2132}(911, \cdot)\) None 0 2
2132.1.n \(\chi_{2132}(73, \cdot)\) None 0 2
2132.1.p \(\chi_{2132}(1321, \cdot)\) None 0 2
2132.1.r \(\chi_{2132}(155, \cdot)\) 2132.1.r.a 2 2
2132.1.r.b 2
2132.1.r.c 4
2132.1.r.d 4
2132.1.t \(\chi_{2132}(1149, \cdot)\) None 0 2
2132.1.x \(\chi_{2132}(491, \cdot)\) None 0 2
2132.1.y \(\chi_{2132}(1147, \cdot)\) 2132.1.y.a 2 2
2132.1.y.b 2
2132.1.z \(\chi_{2132}(1395, \cdot)\) None 0 2
2132.1.bb \(\chi_{2132}(575, \cdot)\) None 0 2
2132.1.bd \(\chi_{2132}(1175, \cdot)\) 2132.1.bd.a 4 4
2132.1.bf \(\chi_{2132}(1093, \cdot)\) None 0 4
2132.1.bg \(\chi_{2132}(1585, \cdot)\) None 0 4
2132.1.bj \(\chi_{2132}(1227, \cdot)\) 2132.1.bj.a 4 4
2132.1.bl \(\chi_{2132}(1431, \cdot)\) None 0 4
2132.1.bn \(\chi_{2132}(51, \cdot)\) None 0 4
2132.1.bp \(\chi_{2132}(599, \cdot)\) None 0 4
2132.1.br \(\chi_{2132}(1091, \cdot)\) None 0 4
2132.1.bt \(\chi_{2132}(657, \cdot)\) None 0 4
2132.1.bv \(\chi_{2132}(419, \cdot)\) None 0 4
2132.1.bx \(\chi_{2132}(501, \cdot)\) None 0 4
2132.1.bz \(\chi_{2132}(401, \cdot)\) None 0 4
2132.1.cb \(\chi_{2132}(647, \cdot)\) 2132.1.cb.a 4 4
2132.1.cb.b 4
2132.1.cc \(\chi_{2132}(245, \cdot)\) None 0 4
2132.1.cf \(\chi_{2132}(681, \cdot)\) None 0 8
2132.1.ci \(\chi_{2132}(103, \cdot)\) 2132.1.ci.a 8 8
2132.1.ci.b 8
2132.1.ck \(\chi_{2132}(21, \cdot)\) None 0 8
2132.1.cm \(\chi_{2132}(5, \cdot)\) None 0 8
2132.1.co \(\chi_{2132}(131, \cdot)\) None 0 8
2132.1.cq \(\chi_{2132}(57, \cdot)\) None 0 8
2132.1.cs \(\chi_{2132}(167, \cdot)\) 2132.1.cs.a 8 8
2132.1.cv \(\chi_{2132}(601, \cdot)\) None 0 8
2132.1.cw \(\chi_{2132}(413, \cdot)\) None 0 8
2132.1.cy \(\chi_{2132}(219, \cdot)\) 2132.1.cy.a 8 8
2132.1.cz \(\chi_{2132}(107, \cdot)\) 2132.1.cz.a 8 8
2132.1.cz.b 8
2132.1.da \(\chi_{2132}(23, \cdot)\) None 0 8
2132.1.dd \(\chi_{2132}(139, \cdot)\) 2132.1.dd.a 8 8
2132.1.dd.b 8
2132.1.dd.c 16
2132.1.df \(\chi_{2132}(283, \cdot)\) None 0 8
2132.1.dh \(\chi_{2132}(47, \cdot)\) 2132.1.dh.a 16 16
2132.1.dk \(\chi_{2132}(129, \cdot)\) None 0 16
2132.1.dl \(\chi_{2132}(53, \cdot)\) None 0 16
2132.1.dn \(\chi_{2132}(151, \cdot)\) 2132.1.dn.a 16 16
2132.1.do \(\chi_{2132}(37, \cdot)\) None 0 16
2132.1.dq \(\chi_{2132}(43, \cdot)\) 2132.1.dq.a 16 16
2132.1.dq.b 16
2132.1.ds \(\chi_{2132}(33, \cdot)\) None 0 16
2132.1.du \(\chi_{2132}(197, \cdot)\) None 0 16
2132.1.dw \(\chi_{2132}(87, \cdot)\) None 0 16
2132.1.dz \(\chi_{2132}(45, \cdot)\) None 0 16
2132.1.ea \(\chi_{2132}(63, \cdot)\) 2132.1.ea.a 32 32
2132.1.ec \(\chi_{2132}(17, \cdot)\) None 0 32
2132.1.ed \(\chi_{2132}(29, \cdot)\) None 0 32
2132.1.eg \(\chi_{2132}(7, \cdot)\) 2132.1.eg.a 32 32

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2132))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2132)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(164))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(533))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1066))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2132))\)\(^{\oplus 1}\)