Properties

Label 476.1
Level 476
Weight 1
Dimension 8
Nonzero newspaces 1
Newform subspaces 3
Sturm bound 13824
Trace bound 0

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Defining parameters

Level: \( N \) = \( 476 = 2^{2} \cdot 7 \cdot 17 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 3 \)
Sturm bound: \(13824\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(476))\).

Total New Old
Modular forms 506 160 346
Cusp forms 26 8 18
Eisenstein series 480 152 328

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

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

Trace form

\( 8 q - 4 q^{4} - 4 q^{9} + O(q^{10}) \) \( 8 q - 4 q^{4} - 4 q^{9} - 4 q^{16} - 4 q^{17} + 4 q^{18} - 4 q^{21} - 4 q^{25} + 4 q^{26} + 4 q^{33} + 8 q^{36} - 4 q^{42} + 4 q^{53} + 8 q^{64} - 8 q^{66} - 4 q^{68} - 8 q^{69} + 4 q^{72} + 8 q^{77} + 8 q^{84} + 4 q^{93} - 4 q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(476))\)

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
476.1.c \(\chi_{476}(69, \cdot)\) None 0 1
476.1.d \(\chi_{476}(239, \cdot)\) None 0 1
476.1.g \(\chi_{476}(407, \cdot)\) None 0 1
476.1.h \(\chi_{476}(237, \cdot)\) None 0 1
476.1.j \(\chi_{476}(13, \cdot)\) None 0 2
476.1.m \(\chi_{476}(183, \cdot)\) None 0 2
476.1.n \(\chi_{476}(33, \cdot)\) None 0 2
476.1.o \(\chi_{476}(67, \cdot)\) 476.1.o.a 2 2
476.1.o.b 2
476.1.o.c 4
476.1.r \(\chi_{476}(375, \cdot)\) None 0 2
476.1.s \(\chi_{476}(341, \cdot)\) None 0 2
476.1.v \(\chi_{476}(15, \cdot)\) None 0 4
476.1.x \(\chi_{476}(321, \cdot)\) None 0 4
476.1.y \(\chi_{476}(89, \cdot)\) None 0 4
476.1.bb \(\chi_{476}(123, \cdot)\) None 0 4
476.1.bc \(\chi_{476}(29, \cdot)\) None 0 8
476.1.bf \(\chi_{476}(27, \cdot)\) None 0 8
476.1.bg \(\chi_{476}(151, \cdot)\) None 0 8
476.1.bi \(\chi_{476}(117, \cdot)\) None 0 8
476.1.bk \(\chi_{476}(3, \cdot)\) None 0 16
476.1.bn \(\chi_{476}(37, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(476))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(476)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(238))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(476))\)\(^{\oplus 1}\)