Properties

Label 1053.1
Level 1053
Weight 1
Dimension 30
Nonzero newspaces 8
Newform subspaces 11
Sturm bound 81648
Trace bound 16

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Defining parameters

Level: \( N \) = \( 1053 = 3^{4} \cdot 13 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 11 \)
Sturm bound: \(81648\)
Trace bound: \(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1053))\).

Total New Old
Modular forms 1360 646 714
Cusp forms 64 30 34
Eisenstein series 1296 616 680

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 30 0 0 0

Trace form

\( 30 q - 3 q^{4} + 2 q^{7} + O(q^{10}) \) \( 30 q - 3 q^{4} + 2 q^{7} - 8 q^{10} + q^{13} + q^{16} - 4 q^{19} + 4 q^{22} - 3 q^{25} - 4 q^{28} + 2 q^{31} - 4 q^{37} + 8 q^{40} + 6 q^{43} - q^{49} + 5 q^{52} - 8 q^{55} + 2 q^{61} - 2 q^{64} + 2 q^{67} - 4 q^{73} + 2 q^{76} + 2 q^{79} - 8 q^{82} - 4 q^{88} - 4 q^{91} - 8 q^{94} - 10 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1053))\)

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
1053.1.c \(\chi_{1053}(404, \cdot)\) None 0 1
1053.1.d \(\chi_{1053}(1052, \cdot)\) None 0 1
1053.1.j \(\chi_{1053}(811, \cdot)\) None 0 2
1053.1.k \(\chi_{1053}(107, \cdot)\) 1053.1.k.a 2 2
1053.1.m \(\chi_{1053}(296, \cdot)\) 1053.1.m.a 2 2
1053.1.n \(\chi_{1053}(350, \cdot)\) 1053.1.n.a 2 2
1053.1.n.b 2
1053.1.n.c 2
1053.1.n.d 4
1053.1.o \(\chi_{1053}(485, \cdot)\) None 0 2
1053.1.p \(\chi_{1053}(809, \cdot)\) None 0 2
1053.1.s \(\chi_{1053}(53, \cdot)\) None 0 2
1053.1.u \(\chi_{1053}(269, \cdot)\) 1053.1.u.a 2 2
1053.1.v \(\chi_{1053}(134, \cdot)\) 1053.1.v.a 2 2
1053.1.z \(\chi_{1053}(379, \cdot)\) 1053.1.z.a 4 4
1053.1.bb \(\chi_{1053}(109, \cdot)\) 1053.1.bb.a 4 4
1053.1.be \(\chi_{1053}(28, \cdot)\) 1053.1.be.a 4 4
1053.1.bg \(\chi_{1053}(163, \cdot)\) None 0 4
1053.1.bh \(\chi_{1053}(17, \cdot)\) None 0 6
1053.1.bi \(\chi_{1053}(116, \cdot)\) None 0 6
1053.1.bj \(\chi_{1053}(179, \cdot)\) None 0 6
1053.1.bk \(\chi_{1053}(152, \cdot)\) None 0 6
1053.1.bm \(\chi_{1053}(170, \cdot)\) None 0 6
1053.1.bp \(\chi_{1053}(35, \cdot)\) None 0 6
1053.1.bu \(\chi_{1053}(19, \cdot)\) None 0 12
1053.1.bv \(\chi_{1053}(154, \cdot)\) None 0 12
1053.1.bx \(\chi_{1053}(73, \cdot)\) None 0 12
1053.1.ca \(\chi_{1053}(23, \cdot)\) None 0 18
1053.1.cb \(\chi_{1053}(14, \cdot)\) None 0 18
1053.1.cc \(\chi_{1053}(29, \cdot)\) None 0 18
1053.1.cf \(\chi_{1053}(38, \cdot)\) None 0 18
1053.1.cg \(\chi_{1053}(95, \cdot)\) None 0 18
1053.1.ch \(\chi_{1053}(68, \cdot)\) None 0 18
1053.1.ci \(\chi_{1053}(31, \cdot)\) None 0 36
1053.1.cj \(\chi_{1053}(7, \cdot)\) None 0 36
1053.1.ck \(\chi_{1053}(58, \cdot)\) None 0 36

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1053))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1053)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(351))\)\(^{\oplus 2}\)