Properties

Label 403.1
Level 403
Weight 1
Dimension 4
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 13440
Trace bound 0

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Defining parameters

Level: \( N \) = \( 403 = 13 \cdot 31 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(13440\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(403))\).

Total New Old
Modular forms 366 322 44
Cusp forms 6 4 2
Eisenstein series 360 318 42

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

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

Trace form

\( 4q - 2q^{2} + 2q^{7} - 4q^{8} + O(q^{10}) \) \( 4q - 2q^{2} + 2q^{7} - 4q^{8} - 4q^{14} + 2q^{16} + 2q^{19} - 4q^{25} - 2q^{33} - 4q^{38} + 2q^{39} + 2q^{41} + 2q^{50} + 4q^{51} - 2q^{56} + 2q^{59} + 4q^{64} + 4q^{66} + 2q^{67} - 2q^{69} - 2q^{71} + 2q^{78} + 2q^{81} + 2q^{82} + 2q^{87} - 2q^{93} - 2q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(403))\)

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
403.1.b \(\chi_{403}(402, \cdot)\) None 0 1
403.1.d \(\chi_{403}(92, \cdot)\) None 0 1
403.1.j \(\chi_{403}(125, \cdot)\) None 0 2
403.1.m \(\chi_{403}(181, \cdot)\) None 0 2
403.1.n \(\chi_{403}(347, \cdot)\) None 0 2
403.1.o \(\chi_{403}(68, \cdot)\) None 0 2
403.1.p \(\chi_{403}(61, \cdot)\) 403.1.p.a 4 2
403.1.q \(\chi_{403}(88, \cdot)\) None 0 2
403.1.t \(\chi_{403}(30, \cdot)\) None 0 2
403.1.u \(\chi_{403}(192, \cdot)\) None 0 2
403.1.w \(\chi_{403}(274, \cdot)\) None 0 2
403.1.x \(\chi_{403}(27, \cdot)\) None 0 4
403.1.z \(\chi_{403}(77, \cdot)\) None 0 4
403.1.bb \(\chi_{403}(5, \cdot)\) None 0 4
403.1.bc \(\chi_{403}(98, \cdot)\) None 0 4
403.1.bd \(\chi_{403}(32, \cdot)\) None 0 4
403.1.bh \(\chi_{403}(67, \cdot)\) None 0 4
403.1.bm \(\chi_{403}(8, \cdot)\) None 0 8
403.1.bo \(\chi_{403}(53, \cdot)\) None 0 8
403.1.bq \(\chi_{403}(23, \cdot)\) None 0 8
403.1.br \(\chi_{403}(127, \cdot)\) None 0 8
403.1.bu \(\chi_{403}(17, \cdot)\) None 0 8
403.1.bv \(\chi_{403}(3, \cdot)\) None 0 8
403.1.bw \(\chi_{403}(29, \cdot)\) None 0 8
403.1.bx \(\chi_{403}(42, \cdot)\) None 0 8
403.1.by \(\chi_{403}(12, \cdot)\) None 0 8
403.1.ca \(\chi_{403}(7, \cdot)\) None 0 16
403.1.ce \(\chi_{403}(2, \cdot)\) None 0 16
403.1.cf \(\chi_{403}(20, \cdot)\) None 0 16
403.1.cg \(\chi_{403}(18, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(403))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(403)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( ( 1 + T )^{4}( 1 - T + T^{2} )^{2} \)
$3$ \( ( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \)
$5$ \( ( 1 + T^{2} )^{4} \)
$7$ \( ( 1 - T )^{4}( 1 + T + T^{2} )^{2} \)
$11$ \( ( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \)
$13$ \( ( 1 + T^{2} )^{2} \)
$17$ \( ( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \)
$19$ \( ( 1 - T )^{4}( 1 + T + T^{2} )^{2} \)
$23$ \( ( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \)
$29$ \( ( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \)
$31$ \( ( 1 + T^{2} )^{2} \)
$37$ \( ( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \)
$41$ \( ( 1 - T )^{4}( 1 + T + T^{2} )^{2} \)
$43$ \( ( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \)
$47$ \( ( 1 + T^{2} )^{4} \)
$53$ \( ( 1 + T^{2} )^{4} \)
$59$ \( ( 1 - T )^{4}( 1 + T + T^{2} )^{2} \)
$61$ \( ( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \)
$67$ \( ( 1 - T )^{4}( 1 + T + T^{2} )^{2} \)
$71$ \( ( 1 + T )^{4}( 1 - T + T^{2} )^{2} \)
$73$ \( ( 1 - T )^{4}( 1 + T )^{4} \)
$79$ \( ( 1 - T )^{4}( 1 + T )^{4} \)
$83$ \( ( 1 - T )^{4}( 1 + T )^{4} \)
$89$ \( ( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \)
$97$ \( ( 1 + T )^{4}( 1 - T + T^{2} )^{2} \)
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