Properties

Label 103.1
Level 103
Weight 1
Dimension 2
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 884
Trace bound 0

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Defining parameters

Level: \( N \) = \( 103 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(884\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(103))\).

Total New Old
Modular forms 53 53 0
Cusp forms 2 2 0
Eisenstein series 51 51 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2q - q^{2} + q^{4} - q^{7} - 2q^{8} + 2q^{9} + O(q^{10}) \) \( 2q - q^{2} + q^{4} - q^{7} - 2q^{8} + 2q^{9} - q^{13} - 2q^{14} - q^{17} - q^{18} - q^{19} - q^{23} + 2q^{25} + 3q^{26} + 2q^{28} - q^{29} + 2q^{32} - 2q^{34} + q^{36} + 3q^{38} - q^{41} + 3q^{46} + q^{49} - q^{50} - 3q^{52} + q^{56} - 2q^{58} - q^{59} - q^{61} - q^{63} - q^{64} + 2q^{68} - 2q^{72} - 3q^{76} - q^{79} + 2q^{81} + 3q^{82} - q^{83} - 2q^{91} - 3q^{92} - q^{97} + 2q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(103))\)

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
103.1.b \(\chi_{103}(102, \cdot)\) 103.1.b.a 2 1
103.1.d \(\chi_{103}(47, \cdot)\) None 0 2
103.1.f \(\chi_{103}(3, \cdot)\) None 0 16
103.1.h \(\chi_{103}(5, \cdot)\) None 0 32

Hecke characteristic polynomials

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