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Properties

Label 832.1
Level 832
Weight 1
Dimension 15
Nonzero newspaces 5
Newform subspaces 6
Sturm bound 43008
Trace bound 5

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Defining parameters

Level: \( N \) = \( 832 = 2^{6} \cdot 13 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 5 \)
Newform subspaces: \( 6 \)
Sturm bound: \(43008\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(832))\).

Total New Old
Modular forms 930 257 673
Cusp forms 66 15 51
Eisenstein series 864 242 622

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 11 4 0 0

Trace form

\( 15 q + 2 q^{5} - q^{9} + O(q^{10}) \) \( 15 q + 2 q^{5} - q^{9} - 3 q^{13} - 4 q^{17} + 4 q^{21} - 7 q^{25} + 2 q^{33} + 4 q^{37} - 4 q^{41} + 2 q^{45} - q^{49} + 2 q^{53} - 4 q^{57} - 2 q^{65} + 2 q^{69} - 2 q^{73} + 4 q^{77} + q^{81} - 8 q^{85} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(832))\)

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
832.1.c \(\chi_{832}(831, \cdot)\) 832.1.c.a 1 1
832.1.d \(\chi_{832}(703, \cdot)\) None 0 1
832.1.g \(\chi_{832}(287, \cdot)\) None 0 1
832.1.h \(\chi_{832}(415, \cdot)\) None 0 1
832.1.j \(\chi_{832}(161, \cdot)\) None 0 2
832.1.m \(\chi_{832}(177, \cdot)\) None 0 2
832.1.o \(\chi_{832}(207, \cdot)\) None 0 2
832.1.q \(\chi_{832}(79, \cdot)\) None 0 2
832.1.r \(\chi_{832}(369, \cdot)\) None 0 2
832.1.t \(\chi_{832}(385, \cdot)\) 832.1.t.a 2 2
832.1.v \(\chi_{832}(159, \cdot)\) None 0 2
832.1.x \(\chi_{832}(95, \cdot)\) None 0 2
832.1.y \(\chi_{832}(127, \cdot)\) 832.1.y.a 2 2
832.1.bb \(\chi_{832}(191, \cdot)\) 832.1.bb.a 2 2
832.1.bb.b 4
832.1.bc \(\chi_{832}(57, \cdot)\) None 0 4
832.1.be \(\chi_{832}(103, \cdot)\) None 0 4
832.1.bh \(\chi_{832}(183, \cdot)\) None 0 4
832.1.bj \(\chi_{832}(265, \cdot)\) None 0 4
832.1.bl \(\chi_{832}(193, \cdot)\) 832.1.bl.a 4 4
832.1.bm \(\chi_{832}(145, \cdot)\) None 0 4
832.1.bo \(\chi_{832}(367, \cdot)\) None 0 4
832.1.bq \(\chi_{832}(303, \cdot)\) None 0 4
832.1.bt \(\chi_{832}(305, \cdot)\) None 0 4
832.1.bv \(\chi_{832}(33, \cdot)\) None 0 4
832.1.bx \(\chi_{832}(21, \cdot)\) None 0 8
832.1.bz \(\chi_{832}(51, \cdot)\) None 0 8
832.1.ca \(\chi_{832}(27, \cdot)\) None 0 8
832.1.cd \(\chi_{832}(5, \cdot)\) None 0 8
832.1.ce \(\chi_{832}(41, \cdot)\) None 0 8
832.1.cg \(\chi_{832}(55, \cdot)\) None 0 8
832.1.cj \(\chi_{832}(23, \cdot)\) None 0 8
832.1.cl \(\chi_{832}(137, \cdot)\) None 0 8
832.1.cm \(\chi_{832}(141, \cdot)\) None 0 16
832.1.co \(\chi_{832}(43, \cdot)\) None 0 16
832.1.cr \(\chi_{832}(3, \cdot)\) None 0 16
832.1.cs \(\chi_{832}(37, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(832))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(832)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(416))\)\(^{\oplus 2}\)