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Properties

Label 496.1
Level 496
Weight 1
Dimension 7
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 15360
Trace bound 1

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Defining parameters

Level: \( N \) = \( 496 = 2^{4} \cdot 31 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(15360\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(496))\).

Total New Old
Modular forms 454 138 316
Cusp forms 34 7 27
Eisenstein series 420 131 289

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 7 0 0 0

Trace form

\( 7 q - q^{5} + q^{7} - 6 q^{8} + q^{9} + O(q^{10}) \) \( 7 q - q^{5} + q^{7} - 6 q^{8} + q^{9} - 6 q^{10} + q^{19} + 5 q^{31} + 5 q^{35} - q^{41} - q^{45} - 2 q^{47} - 6 q^{49} + 6 q^{50} + q^{59} + q^{63} + 6 q^{64} - 8 q^{67} - 6 q^{70} + q^{71} - 6 q^{76} + 6 q^{80} - 5 q^{81} - 13 q^{95} - q^{97} + 6 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(496))\)

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
496.1.d \(\chi_{496}(63, \cdot)\) None 0 1
496.1.e \(\chi_{496}(433, \cdot)\) 496.1.e.a 1 1
496.1.f \(\chi_{496}(311, \cdot)\) None 0 1
496.1.g \(\chi_{496}(185, \cdot)\) None 0 1
496.1.j \(\chi_{496}(61, \cdot)\) 496.1.j.a 2 2
496.1.j.b 4
496.1.l \(\chi_{496}(187, \cdot)\) None 0 2
496.1.p \(\chi_{496}(57, \cdot)\) None 0 2
496.1.q \(\chi_{496}(87, \cdot)\) None 0 2
496.1.r \(\chi_{496}(161, \cdot)\) None 0 2
496.1.s \(\chi_{496}(191, \cdot)\) None 0 2
496.1.v \(\chi_{496}(89, \cdot)\) None 0 4
496.1.w \(\chi_{496}(39, \cdot)\) None 0 4
496.1.ba \(\chi_{496}(209, \cdot)\) None 0 4
496.1.bb \(\chi_{496}(47, \cdot)\) None 0 4
496.1.bc \(\chi_{496}(67, \cdot)\) None 0 4
496.1.be \(\chi_{496}(37, \cdot)\) None 0 4
496.1.bi \(\chi_{496}(35, \cdot)\) None 0 8
496.1.bk \(\chi_{496}(29, \cdot)\) None 0 8
496.1.bl \(\chi_{496}(111, \cdot)\) None 0 8
496.1.bm \(\chi_{496}(17, \cdot)\) None 0 8
496.1.bq \(\chi_{496}(7, \cdot)\) None 0 8
496.1.br \(\chi_{496}(73, \cdot)\) None 0 8
496.1.bt \(\chi_{496}(13, \cdot)\) None 0 16
496.1.bv \(\chi_{496}(19, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(496))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(496)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(124))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(248))\)\(^{\oplus 2}\)