Properties

Label 1476.1
Level 1476
Weight 1
Dimension 91
Nonzero newspaces 9
Newform subspaces 17
Sturm bound 120960
Trace bound 5

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Defining parameters

Level: \( N \) = \( 1476 = 2^{2} \cdot 3^{2} \cdot 41 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 9 \)
Newform subspaces: \( 17 \)
Sturm bound: \(120960\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1476))\).

Total New Old
Modular forms 1728 441 1287
Cusp forms 128 91 37
Eisenstein series 1600 350 1250

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 87 0 4 0

Trace form

\( 91 q + 3 q^{2} - 7 q^{4} + 2 q^{5} + 3 q^{8} + O(q^{10}) \) \( 91 q + 3 q^{2} - 7 q^{4} + 2 q^{5} + 3 q^{8} - 2 q^{10} - 2 q^{13} - 7 q^{16} + 2 q^{17} + 4 q^{19} + 2 q^{20} - 9 q^{25} + 2 q^{26} + 2 q^{29} - 4 q^{31} - 7 q^{32} - 12 q^{34} + 2 q^{37} - 2 q^{40} - 9 q^{41} + 16 q^{42} - 8 q^{45} - 7 q^{49} - q^{50} - 12 q^{52} + 2 q^{53} - 4 q^{55} - 8 q^{57} - 2 q^{58} - 6 q^{61} + 17 q^{64} - 6 q^{65} - 8 q^{66} - 4 q^{67} + 2 q^{68} - 2 q^{73} + 2 q^{74} + 4 q^{77} + 4 q^{79} + 2 q^{80} - 3 q^{82} - 10 q^{85} + 2 q^{89} - 8 q^{90} - 6 q^{97} + 3 q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1476))\)

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
1476.1.b \(\chi_{1476}(737, \cdot)\) None 0 1
1476.1.e \(\chi_{1476}(1313, \cdot)\) None 0 1
1476.1.g \(\chi_{1476}(739, \cdot)\) None 0 1
1476.1.h \(\chi_{1476}(163, \cdot)\) 1476.1.h.a 1 1
1476.1.h.b 2
1476.1.j \(\chi_{1476}(91, \cdot)\) 1476.1.j.a 2 2
1476.1.j.b 2
1476.1.l \(\chi_{1476}(665, \cdot)\) 1476.1.l.a 4 2
1476.1.o \(\chi_{1476}(655, \cdot)\) 1476.1.o.a 2 2
1476.1.o.b 2
1476.1.o.c 4
1476.1.o.d 8
1476.1.p \(\chi_{1476}(247, \cdot)\) None 0 2
1476.1.r \(\chi_{1476}(329, \cdot)\) None 0 2
1476.1.u \(\chi_{1476}(245, \cdot)\) None 0 2
1476.1.v \(\chi_{1476}(109, \cdot)\) None 0 4
1476.1.w \(\chi_{1476}(683, \cdot)\) 1476.1.w.a 4 4
1476.1.w.b 4
1476.1.z \(\chi_{1476}(127, \cdot)\) 1476.1.z.a 4 4
1476.1.ba \(\chi_{1476}(379, \cdot)\) 1476.1.ba.a 4 4
1476.1.bc \(\chi_{1476}(305, \cdot)\) None 0 4
1476.1.bf \(\chi_{1476}(269, \cdot)\) None 0 4
1476.1.bh \(\chi_{1476}(173, \cdot)\) None 0 4
1476.1.bj \(\chi_{1476}(319, \cdot)\) None 0 4
1476.1.bm \(\chi_{1476}(125, \cdot)\) None 0 8
1476.1.bo \(\chi_{1476}(307, \cdot)\) 1476.1.bo.a 8 8
1476.1.bo.b 8
1476.1.br \(\chi_{1476}(167, \cdot)\) None 0 8
1476.1.bs \(\chi_{1476}(85, \cdot)\) None 0 8
1476.1.bt \(\chi_{1476}(113, \cdot)\) None 0 8
1476.1.bw \(\chi_{1476}(221, \cdot)\) None 0 8
1476.1.by \(\chi_{1476}(139, \cdot)\) None 0 8
1476.1.bz \(\chi_{1476}(31, \cdot)\) None 0 8
1476.1.cc \(\chi_{1476}(35, \cdot)\) 1476.1.cc.a 16 16
1476.1.cc.b 16
1476.1.cd \(\chi_{1476}(145, \cdot)\) None 0 16
1476.1.ce \(\chi_{1476}(43, \cdot)\) None 0 16
1476.1.cg \(\chi_{1476}(5, \cdot)\) None 0 16
1476.1.ci \(\chi_{1476}(13, \cdot)\) None 0 32
1476.1.cj \(\chi_{1476}(11, \cdot)\) None 0 32

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1476))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1476)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(164))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(492))\)\(^{\oplus 2}\)