Properties

Label 536.1
Level 536
Weight 1
Dimension 38
Nonzero newspaces 4
Newform subspaces 5
Sturm bound 17952
Trace bound 1

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Defining parameters

Level: \( N \) = \( 536 = 2^{3} \cdot 67 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 5 \)
Sturm bound: \(17952\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(536))\).

Total New Old
Modular forms 436 168 268
Cusp forms 40 38 2
Eisenstein series 396 130 266

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 38 0 0 0

Trace form

\( 38q - q^{2} - 2q^{3} + 5q^{4} - 4q^{6} - q^{8} + q^{9} + O(q^{10}) \) \( 38q - q^{2} - 2q^{3} + 5q^{4} - 4q^{6} - q^{8} + q^{9} - 2q^{10} - 2q^{11} - 2q^{12} - 4q^{15} + 5q^{16} - 4q^{17} - 3q^{18} - 2q^{19} - 4q^{22} - 2q^{23} - 4q^{24} + 3q^{25} - 2q^{26} - 4q^{27} - q^{32} - 8q^{33} - 2q^{34} + q^{36} - 2q^{38} - 4q^{39} - 2q^{40} - 2q^{41} - 2q^{43} - 2q^{44} - 2q^{47} - 2q^{48} + 5q^{49} - q^{50} - 4q^{51} + 25q^{54} - 4q^{55} - 4q^{57} - 2q^{59} - 4q^{60} + 5q^{64} - 4q^{65} - 4q^{66} - q^{67} - 4q^{68} - 2q^{71} - 3q^{72} - 4q^{73} - 2q^{75} - 2q^{76} - 3q^{81} + 31q^{82} - 2q^{83} - 4q^{86} - 4q^{88} - 4q^{89} - 6q^{90} - 2q^{92} - 4q^{96} - 2q^{97} - q^{98} - 6q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(536))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
536.1.b \(\chi_{536}(401, \cdot)\) None 0 1
536.1.d \(\chi_{536}(135, \cdot)\) None 0 1
536.1.f \(\chi_{536}(403, \cdot)\) None 0 1
536.1.h \(\chi_{536}(133, \cdot)\) 536.1.h.a 3 1
536.1.h.b 3
536.1.k \(\chi_{536}(97, \cdot)\) None 0 2
536.1.m \(\chi_{536}(431, \cdot)\) None 0 2
536.1.o \(\chi_{536}(163, \cdot)\) 536.1.o.a 2 2
536.1.p \(\chi_{536}(365, \cdot)\) None 0 2
536.1.r \(\chi_{536}(5, \cdot)\) None 0 10
536.1.t \(\chi_{536}(59, \cdot)\) 536.1.t.a 10 10
536.1.v \(\chi_{536}(15, \cdot)\) None 0 10
536.1.x \(\chi_{536}(137, \cdot)\) None 0 10
536.1.z \(\chi_{536}(13, \cdot)\) None 0 20
536.1.ba \(\chi_{536}(19, \cdot)\) 536.1.ba.a 20 20
536.1.bc \(\chi_{536}(23, \cdot)\) None 0 20
536.1.be \(\chi_{536}(41, \cdot)\) None 0 20

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(536))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(536)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(268))\)\(^{\oplus 2}\)