Properties

Label 2563.1
Level 2563
Weight 1
Dimension 14
Nonzero newspaces 2
Newform subspaces 6
Sturm bound 542880
Trace bound 1

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Defining parameters

Level: \( N \) = \( 2563 = 11 \cdot 233 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 6 \)
Sturm bound: \(542880\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2563))\).

Total New Old
Modular forms 2334 2092 242
Cusp forms 14 14 0
Eisenstein series 2320 2078 242

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 12 0

Trace form

\( 14q - 4q^{3} - 2q^{4} + 4q^{5} - 2q^{9} + O(q^{10}) \) \( 14q - 4q^{3} - 2q^{4} + 4q^{5} - 2q^{9} + 4q^{12} + 8q^{15} - 2q^{16} + 4q^{20} + 4q^{22} - 14q^{23} - 2q^{25} - 6q^{31} + 4q^{34} + 6q^{36} + 10q^{37} - 8q^{38} + 4q^{45} - 4q^{47} + 4q^{48} - 2q^{49} + 4q^{53} - 8q^{58} - 8q^{60} + 14q^{64} - 8q^{66} - 8q^{67} + 4q^{69} - 6q^{71} - 4q^{75} + 8q^{78} + 4q^{80} - 2q^{81} + 4q^{82} + 4q^{86} + 2q^{89} + 2q^{92} + 4q^{93} - 4q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2563))\)

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
2563.1.b \(\chi_{2563}(2562, \cdot)\) 2563.1.b.a 1 1
2563.1.b.b 1
2563.1.b.c 2
2563.1.b.d 2
2563.1.c \(\chi_{2563}(2331, \cdot)\) None 0 1
2563.1.e \(\chi_{2563}(2419, \cdot)\) 2563.1.e.a 4 2
2563.1.e.b 4
2563.1.i \(\chi_{2563}(12, \cdot)\) None 0 4
2563.1.k \(\chi_{2563}(700, \cdot)\) None 0 4
2563.1.l \(\chi_{2563}(931, \cdot)\) None 0 4
2563.1.n \(\chi_{2563}(788, \cdot)\) None 0 8
2563.1.p \(\chi_{2563}(97, \cdot)\) None 0 16
2563.1.s \(\chi_{2563}(32, \cdot)\) None 0 28
2563.1.t \(\chi_{2563}(98, \cdot)\) None 0 28
2563.1.v \(\chi_{2563}(109, \cdot)\) None 0 56
2563.1.x \(\chi_{2563}(34, \cdot)\) None 0 112
2563.1.z \(\chi_{2563}(29, \cdot)\) None 0 112
2563.1.ba \(\chi_{2563}(2, \cdot)\) None 0 112
2563.1.bc \(\chi_{2563}(7, \cdot)\) None 0 224
2563.1.bf \(\chi_{2563}(3, \cdot)\) None 0 448

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )( 1 + T ) \))(\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 - T )^{4}( 1 + T )^{4} \))
$3$ (\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )( 1 + T ) \))(\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( ( 1 + T )^{4}( 1 + T^{2} )^{2} \))(\( ( 1 + T^{4} )^{2} \))
$5$ (\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )( 1 + T ) \))(\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 - T )^{4}( 1 + T^{2} )^{2} \))
$7$ (\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 + T^{2} )^{4} \))
$11$ (\( 1 + T \))(\( 1 - T \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( 1 + T^{4} \))(\( 1 + T^{4} \))
$13$ (\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{2} \))
$17$ (\( 1 - T + T^{2} \))(\( 1 + T + T^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( 1 - T^{4} + T^{8} \))(\( 1 - T^{4} + T^{8} \))
$19$ (\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )( 1 + T ) \))(\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( ( 1 - T )^{4}( 1 + T )^{4} \))(\( ( 1 + T^{4} )^{2} \))
$23$ (\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{4} \))(\( ( 1 + T + T^{2} )^{4} \))
$29$ (\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )( 1 + T ) \))(\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( ( 1 - T )^{4}( 1 + T )^{4} \))(\( ( 1 + T^{4} )^{2} \))
$31$ (\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 - T^{2} + T^{4} )^{2} \))(\( ( 1 - T^{2} + T^{4} )^{2} \))
$37$ (\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{4} \))(\( ( 1 - T + T^{2} )^{4} \))
$41$ (\( 1 - T + T^{2} \))(\( 1 + T + T^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( 1 - T^{4} + T^{8} \))(\( 1 - T^{4} + T^{8} \))
$43$ (\( 1 - T + T^{2} \))(\( 1 + T + T^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( 1 - T^{4} + T^{8} \))(\( 1 - T^{4} + T^{8} \))
$47$ (\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )( 1 + T ) \))(\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T )^{4}( 1 + T^{2} )^{2} \))
$53$ (\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )( 1 + T ) \))(\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( ( 1 - T )^{4}( 1 + T^{2} )^{2} \))(\( ( 1 + T^{4} )^{2} \))
$59$ (\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{2} \))
$61$ (\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{2} \))
$67$ (\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 + T )^{4}( 1 + T^{2} )^{2} \))(\( ( 1 + T )^{4}( 1 + T^{2} )^{2} \))
$71$ (\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{4} \))(\( ( 1 + T + T^{2} )^{4} \))
$73$ (\( 1 - T + T^{2} \))(\( 1 + T + T^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( 1 - T^{4} + T^{8} \))(\( 1 - T^{4} + T^{8} \))
$79$ (\( 1 - T + T^{2} \))(\( 1 + T + T^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( 1 - T^{4} + T^{8} \))(\( 1 - T^{4} + T^{8} \))
$83$ (\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{2} \))
$89$ (\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 - T^{2} + T^{4} )^{2} \))(\( ( 1 - T^{2} + T^{4} )^{2} \))
$97$ (\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )( 1 + T ) \))(\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T )^{4}( 1 + T^{2} )^{2} \))
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